Mixtures & Alligations (With Previous Year CAT Questions)

Distribution of Questions
Level 1 : 1 to 14
Level 2 : 15 to 36
Level 3 : 37 to 68
Level 4 : 69 to 86
Data Sufficiency : 87 to 95
CAT Previous Year Questions : 96 to 117

3

In what ratio should water be mixed with 80% wine so that a 60% wine solution is formed?

3

A vessel contains 25 litres of a mixture of milk and water containing 40% milk. Find the quantity (in litres) of pure milk to be added to the vessel so that the ratio of milk and water in the vessel becomes 1 : 1.

3

A milkman has 20 litres of pure milk. Find the quantity (in litres) of water to be added to it so that he gets 50% profit by selling it at its cost price.

3

Find the quantity of tea costing ₹12 per kg to be mixed with 18 kg of tea costing ₹9 per kg to form a mixture costing ₹10.2 per kg.

3

If two kinds of grapes costing ₹16 a kg and ₹21 a kg are mixed in the ratio of 2 : 3, then find the cost of mixture per kg (in ₹).

3

A trader claims to sell jeera at cost price but mixes freely available sand and thereby gains 25%. What is the percentage of sand in the mixture?

3

6 kg of sugar costing ₹10 per kg is added to 9 kg of sugar costing ₹15 per kg. At what price (in ₹) should this mixture be sold so that there is no loss or gain?

3

How many kilograms of an ore containing 95% iron and 5% nickel should be mixed with 120 kg of ore having
iron and nickel in the proportion 7 : 3 such that the resultant ore contains 4/5 of iron?

3

A solution of 80 litres contains 30% alcohol. How many litres of pure alcohol must be added to this mixture so
that the concentration of alcohol becomes 65%?

3

Two solutions of sulphuric acid are mixed in the ratio of 3 : 7. The first solution contains 20% sulphuric acid and
the second solution contains 30% sulphuric acid. Find the concentration (in %) of sulphuric acid in the final mixture.

3

A vessel contains 10 litres of pure milk. 1 litre of milk is taken out and replaced by an equal amount of water.
1 litre of mixture is then taken out and replaced by an equal amount of water. Find the ratio of milk and water
in the final mixture.

3

A vessel contains 20 litres of a mixture of milk and water containing 60% milk. 5 litres of pure milk is added to it.
Find the percentage of milk in the new mixture.

3

In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?

3

A vessel contains 70 litres of a mixture of milk and water containing 90% milk. Find the quantity (in litres) of
water to be added to the vessel so that the percentage of milk in the new solution is 87.5%

3

Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2 : 4 and 3 : 5 : 6. If the quantities in the two vessels are mixed in the ratio 1 : 1, what is the ratio of petrol, diesel and kerosene in the resultant mixture?

3

There are three varieties of rice A, B, and C costing ₹25/kg, ₹30/ kg, and ₹35/ kg, respectively. A total of 10 kg of
A and C and 8 kg of B is mixed to make a mixture costing ₹32/kg. Find the ratio in which A and C are mixed.

3

Two varieties of rice are mixed in the ratio 4 : 5. The mixture is sold at ₹60/kg at 20% profit. The prices of the
first and the second variety are in the ratio 5 : 6. Find the price of the cheaper variety. (in ₹ per kg)

3

Two mixtures of milk and water contain milk and water in the ratios 4 : 1 and 3 : 1, respectively. They are mixed
in such a way that the resultant mixture contains milk and water in the ratio 77 : 23. Find the ratio in which the
two mixtures are mixed.

3

A flask contains pure milk. Five litres of milk is removed and replaced with water. This process is repeated once
more. At this stage, the ratio of water and milk is 15 : 49. Find the amount of milk present in the flask at the beginning (in litres).

3

How many litres of water should a milkman add to 35 litres of milk costing ₹560, so that by selling the milk at ₹14 per litre, he just recovers his cost?

3

Fresh grapes contain 80% water by weight. Dry grapes contain 20% water by weight. How many kilograms of
fresh grapes will be required to prepare 20 kg of dry grapes?

3

A man bought 10 litres of pure milk and added 5 litres of water to it but spilt 2 litres of the mixture. Of the remaining mixture, he sold 3 litres, and again added 2 litres of water to the remaining quantity. Find the approximate percentage of milk in the final mixture.

3

A vessel is completely filled with milk. 20 litres is withdrawn from the vessel and is replaced with water. 20 litres
of the mixture is then replaced with water. The vessel now has 18 litres of milk. Find the capacity of the vessel (in litres).

3

A milkman bought 10 litres of pure milk at ₹10/litre and 10 litres of adulterated milk at ₹6/litre. He mixed both
and sold the mixture at ₹10/litre. Find his profit percentage.

3

A vessel had 20 ml of a mixture of milk and water.The mixture has 40% milk. X ml of milk was added to the
mixture. Y ml of water was then added to the mixture. Each of the two additions reverses the ratio of milk and
water in the vessel. Find the difference of X and Y.

3

A vessel contains 10 litres of pure milk. A person takes out 1 litre of milk from the vessel and replaces it with 1 litre of water. Again, 1 litre of the mixture is taken out and replaced with 1 litre of water. This process is repeated one more time. What is the quantity of milk left in the mixture? (in litres)

3

If 12 kg of rice which costs ₹24/kg is mixed with 6 kg of rice which costs ₹27/kg, then what is the cost of the
resulting mixture (in ₹/kg)?

3

Raju went to the market to buy 1.5 kg of dried peas having 20% water content. He went home and soaked them
for some time and the water content in the peas becomes 60%. Find the final weight of soaked peas.

3

There are two vessels P and Q, P containing 120 litres of milk and Q containing 120 litres of water. 30 litres is
drawn from P and poured into Q and then 30 litres from Q is poured back into P. This process is repeated once.
At the end of this repetition, what is the ratio of milk and water in P?

3

Two containers contain petrol and diesel in the ratios 4 : 3 and 3 : 1. How many litres from the first container
should be mixed with 16 litres from the second so that the ratio in the resultant mixture is 32 : 19?

3

Two varieties of rice are mixed in the ratio 2 : 5 and the mixture is sold at ₹12 per kg at a profit of 20%. If the first variety costs ₹7 per kg more than the second variety, find the cost per kg of the first variety.

3

A shop keeper mixes two varieties of wheat in the ratio 3 : 7, which cost ₹10 per kg and ₹15 per kg, respectively.
Find the ratio in which the two varieties of wheat should be mixed when the cost price of the second variety of
wheat drops by ₹0.50 per kg and the cost price of the mixture is maintained the same?

3

A certain quantity of rice costing ₹6/kg is mixed with another variety costing ₹8/kg so that the resulting mixture
costs ₹7.20/kg. In what ratio were they mixed?

3

A dishonest milkman professes to sell milk at cost price but he makes 100/3% profit by mixing it with water. What is the water content in the milk solution?

3

A shopkeeper mixed 3 varieties of wheat costing ₹12 per kg, ₹18 per kg and ₹21 per kg and sold the mixture at ₹15 per kg at 20% profit. Which of the following represents a possible ratio of the varieties mixed?

3

A mixture contains milk and water in the ratio 3 : 1. After adding 14 litres of water to it, the ratio of milk to water in the resultant solution became 2 : 3. What was the quantity of the original mixture?

3

Instead of adding the requisite quantity of water to dilute 50% wine to 40% wine, by mistake, the same quantity of pure wine is added. Now, how much water as a fraction of the original volume must be added to achieve the original objective?

3

Sixty litres of wine is drawn from 600 litres of wine and replaced with water. Sixty litres of the mixture is then drawn and replaced with water and this procedure is repeated once more. Find the present quantity of wine in the mixture.

3

Two cans contain mixtures of milk and water. The first can contains 73% water while the second can contains
41% water. The contents of the two cans are mixed in the ratio 3 : 5. What is the percentage of milk in the new
mixture?

3

A vessel has 300 ml of pure milk. Thirty millilitres of milk is removed and 30 ml of water is poured into the vessel
(bringing the volume of mixture in the vessel back to 300 ml). If this operation is repeated another 2 times, what is the percentage of milk in the vessel at the end?

3

From a vessel containing only milk, 10 litres are drawn and replaced with water. 10 litres of the mixture is now
taken out and replaced with water again. The ratio of milk to water now is 25 : 24. How many litres of milk was
there initially?

3

A water purifier filters and processes water and reduces the salt content in it by 50% in 5 minutes. If water with
salt content of 5% is poured into it, then in approximately how many minutes will the water be potable?
(The salt content in potable water is at the most 0.05%. Assume that the concentration of salt decreases exponentially with time. Take log2 = 0.3010)

3

Two varieties of tea powder costing ₹210/kg and ₹300/kg are mixed in certain ratios to form varieties X and
Y. X and Y are mixed in the ratio 3 : 2 to form variety Z which is sold at ₹315/kg at 25% profit. If X costs ₹240/kg,
the ratio in which the two varieties are mixed to form Y is

3

A vessel contains 80% alcohol solution. 20% of the solution was removed and replaced with water. If this process is repeated, find the percentage of alcohol which remains in the solution.

3

The volumes of two milk solutions are 18 litres and 12 litres. If these solutions are mixed, the concentration of
milk in the resultant solution is 40%. If one litre each of the two solutions are mixed, the concentration of milk
in the resultant solution is 350/9%. Find the respective volumes of milk in the two solutions, in litres.

3

Alloy I contains 30% zinc, 40% copper and the remaining is gold.
Alloy II contains 40% tin and some zinc and gold.
On mixing these two alloys in a certain ratio,
Alloy III, which has 30% zinc and 25% tin is obtained.

If equal weights of both Alloy I and Alloy III are mixed, then what percentage of the alloy formed will be copper?

3

Alloy I contains 30% zinc, 40% copper and the remaining is gold.
Alloy II contains 40% tin and some zinc and gold.
On mixing these two alloys in a certain ratio,
Alloy III, which has 30% zinc and 25% tin is obtained.

Find the percentage of gold in the new alloy, formed by mixing Alloy II and Alloy III in a certain ratio.

3

There is a 40 litres solution of milk and water in which milk forms 72%. How much water must be added to this
solution to make it a solution in which milk forms 60%? (in litres)

3

Two varieties of coffee - A and B are mixed in the ratio 3 : 2. The mixture is sold at ₹100 per kg at 100% profit.
If variety A costs ₹10 per kg more than variety B, what is the cost of variety B per kg?

3

Two varieties of rice A and B priced at ₹6.75 per kg and ₹9.75 per kg, respectively were mixed and sold at ₹10.80
per kg at a profit of 20%. Find the ratio in which A and B are mixed.

3

Each of the two vessels X and Y has 20 litres of a solution of milk and water. X has 10% water and certain quantity of water is added to it so as to raise the percentage of water to 25%. Y has milk and water in the ratio
3 : 2 and a certain quantity of water is added to this so as to reverse this ratio. What is the difference between the quantity of water added to X and that added to Y?

3

A 6-litre solution of sulphuric acid had 45% acid. It was mixed with a 5-litre solution of sulphuric acid which had
a% acid, where 40 ≤ a ≤ 50. The acid concentration in the resulting mixture is b%. Which of the following is not a
possible value of b?

3

Two containers A and B contain equal volumes of water and alcohol, respectively. 3 litres of water is taken from
A and poured into B. From the resulting solution in B, 3 litres is taken out and poured into A. If the quantity of water in both the containers is the same after the two transfers find the volume of alcohol in B initially (in litres).

3

The concentration of spirit in three vessels A, B and C are 45%, 30% and 25%, respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.

3

A milk solution has milk and water in the ratio 3 : 2. What part of the solution has to be substituted with water so as to reverse the ratio of milk and water in the solution?

3

A metal weighs 1500 kg per cubic metre and another metal weighs 2500 kg per cubic metre. Find the weight
(in kg) of 5 cubic metres of an alloy formed by mixing 40% of the first metal and 60% of the second metal.

3

Two cans A and B contain 80 litres each of milk and water, respectively. 10 litres of milk is taken from can A and
poured into can B. Then, 10 litres of solution from can B is removed and poured into can A. What are the respective quantities of milk in can B and that of water in can A (both in litres)?

3

Vessel A contains 5 litres of milk and vessel B contains 5 litres of water. One litre of milk is taken from A and
is poured into B. One litre of the mixture in B is then poured into A. If the present quantities of milk in B and
water in A are V and V*, respectively, then which of the following holds true?

3

Vessels A and B have 8 litres milk and 8 litres water, respectively. A jar C is filled with the milk from vessel A and
then emptied into B. Jar C is then filled with the mixture so formed, and then emptied into vessel A. If the ratio
of milk to water in vessel A at this stage is 2:1, find the volume of jar C (in litres).

3

There are two vessels A and B each containing wine and water in the ratio of 2 : 7 and 1 : 4, respectively. When 20 litres of water are added to the contents of vessel A the ratio of wine and water in both the vessels will become equal. If initially the quantities of wine in both the vessels is the same, how much wine should be added to vessel B, so that the concentration of wine in the vessel B will equal the initial concentration of wine in
vessel A?

3

In what ratio should Ram mix two varieties of barley costing ₹20 and ₹24 per kg so that by selling it at ₹27.60 per kg Ram makes a profit of 20%?

3

Dinku Beora was a chronic alcoholic and because of persistent health problems, he decided to quit drinking. He
devised an ingenuous way of doing so. He bought a 750 ml ‘goodbye’ bottle of Old Monk. On the first day, he
drank 5% of the contents in it and replaced that quantity with water. Next day he drank 10% of the contents in the bottle and replaced it with water. Like this, he continued. On the 19th day, he drank 95% of the contents in the bottle and replaced it with water and on the 20th (last day) he drank the entire contents of the bottle. Find the ratio of the total quantities of alcohol and water that he drank in the entire process.

3

A grocer has two varieties of rice, Rice A and Rice B costing ₹10 per kg and ₹12 per kg, respectively. He sells the
total mixture of Rice A and Rice B having 420 kg of Rice A for ₹25,200 with a profit margin of 20%. How much
quantity of rice B is present in the mixture sold?

3

There are two containers with mixtures of Pepsi and Coke. In container 1, Pepsi and Coke are in the ratio 3 : 2 and in container 2 Pepsi and Coke are in the ratio 2 : 3. How many litres of the mixture should be taken from
container 1 and mixed with an appropriate quantity of the mixture from container 2 in order to make 20 litres
of a mixture containing Pepsi and Coke in the ratio 9 : 11?

3

Two vessels A and B of equal volume contain milk and water in the ratio 3 : 2 and 2 : 1 to their brim respectively.
Two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion of the volume of vessel C should be the volume of water that shall be added so that the ratio of milk and water in vessel C becomes 1 : 1?

3

Alloy X has 75% aluminium and 25% zinc. A certain process decreases the quantity of aluminium by one-fourth
and the quantity of zinc by one-eighth. Further applications of the process have the same effect as the first one.
The least number of times that the process must be applied to X in order to obtain an alloy in which the proportion of aluminum is 60% or less is

3

There are three vessels (with equal volumes) filled with mixtures of water and milk in the ratios 1 : 2, 2 : 3 and
3 : 4, respectively. These are all poured into a big vessel. What proportion of the mixture in the big vessel should
be substituted by water so that the milk forms 50% of the resulting mixture?

3

A vessel contains a solution of milk and water containing 90% milk. 10 litres of solution is withdrawn from the
vessel and replaced by water. The procedure is repeated one more time. If the fi nal quantity of milk in the vessel is 72.9 litres, then find the initial quantity of the solution in the vessel (in litres).

3

Jar A has 3 litres of a solution that is 30% acid. Jar B has 6 litres of a solution that is 40% acid. Jar C has 4 litres of
a solution that is x% acid. A certain quantity was drawn from C and mixed with the entire contents of A. The remaining solution in C was mixed with the entire contents of B. If each of these mixtures has 50% acid, find x.

3

A vessel contains an 80% alcohol solution. 20% of the solution was removed and replaced with water. If this
process is repeated, find the percentage of alcohol which remains in the solution.

3

A local grocer mixed three qualities of coffee T1, T2 and T3 priced at ₹79 per kg, ₹64 per kg and ₹62 per kg, respectively in the ratio 1 : 2 : 4. To 4 kg of this mixture he adds quantities of T1 and T3 which are in the ratio
1 : 5. He now sells this new mixture for ₹77.88 per kg thereby making a profit of 20%. How much of T1 did he mix with the mixture?

3

Vessels A and B contain mixtures of milk and water. A has a% milk and B has b% milk. Mixture P is formed by
mixing a% of vessel A’s contents with (100 – b)% of vessel B’s contents. Mixture Q is formed by mixing (100 – a)%
of vessel A’s contents with b% of vessel B’s contents. Mixtures P and Q have k% milk each. If a ≠ b, find a + b.

3

Three vessels contain three different mixtures of milk and water. Volume of each mixture is 12 litres and their
respective concentrations of milk are 60%, 40% and 20%. 4 litres of the first, 8 litres of the second and 12 litres of the third are mixed and the mixture is named A. The left overs of the three vessels are mixed and this mixture is named B. Six litres of A and 9 litres of B are mixed to form mixture C.

Which of the following statements is true regarding the milk concentrations of A, B and C?
I : A has the highest concentration.
II : B has the lowest concentration.
III : C has the highest concentration.
IV : A has neither the highest nor the lowest concentration.

3

A vessel is filled to its capacity with pure milk. Nine litres are withdrawn from the vessel and replaced with an
equal amount of water. Nine litres of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes, the vessel contains 17.1 litres of milk less than it did initially.

Find the capacity of the vessel (in litres).

3

A vessel is filled to its capacity with pure milk. Nine litres are withdrawn from the vessel and replaced with an
equal amount of water. Nine litres of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes, the vessel contains 17.1 litres of milk less than it did initially.

What is the least number of such additional replacements required, so that the vessel contains less than 75% milk?

3

There are five solutions A, B, C, D, and E with concentrations 10%, 20%, 40%, 50%, 80%, respectively. (X, Y) denotes a mixture of X and Y in which X and Y are mixed in some proportion, such that both are included. Similarly (X, Y, Z) denotes a mixture in which X, Y and Z are mixed in some proportion, such that each is included.

Which of the following cannot have a concentration of 75 %?

3

There are five solutions A, B, C, D, and E with concentrations 10%, 20%, 40%, 50%, 80%, respectively. (X, Y) denotes a mixture of X and Y in which X and Y are mixed in some proportion, such that both are included. Similarly (X, Y, Z) denotes a mixture in which X, Y and Z are mixed in some proportion, such that each is included.

There are three containers P, Q, and R. Each is filled with one of the above 5 solutions. By taking some solution from each of the containers P, Q and R and mixing them, a new solution N is prepared. The concentration of this new solution N is 50%. In how many ways can the solutions be taken in the 3 containers so that it is possible to prepare N?

3

Two large drums A and W, have 1000 litres of alcohol and 1000 litres of water, respectively. Two litres of the contents in drum A are removed and mixed with the contents of drum W. This is the first operation. Two litres of the contents of drum W are then mixed with the contents of drum A. This is the second operation. The first
and the second operations together constitute process P. Process P is carried out 3 times. After that, only the first operation is done. After this, ‘a’ is the alcohol in the first drum and ‘w’ is the water in the second drum. What is the relation between a and w?

3

The volumes of two milk solutions are 18 litres and 12 litres. If these solutions are mixed, the concentration of
milk in the resultant solution is 40%. If one litre each of the two solutions are mixed, the concentration of milk
in the resultant solution is 350/9%. Find the respective volumes of milk in the two solutions, in litres.

3

There are 10 litres of milk in container A and 10 litres of water in container B. One litre of milk is transferred from A to B. After that, one litre of the contents of B are transferred back to A. This entire process is carried out
once again. What is the final concentration of milk in A?

3

There are two vessels, A and B, of equal capacity. A is filled completely with pure benzene and B is left empty.
Each operation involves transferring some quantity of liquid from A to B and then refilling A with the same
quantity of water. At the end of n such operations (n > 1), it is ensured that B is full. If n = 2, then what is the
maximum possible concentration of water in B?

3

Alloy A has 80% copper and 20% tin. A certain process when applied repeatedly to the alloy decreases the copper quantity in the alloy by one - fifth and the tin quantity in it by one - tenth, each time it is applied. The minimum number of times the process must be applied so that the concentration of copper in the alloy is less than 70% is

3

A mixture has 25% salt. Using a filtration process, the mixture can be purified. Each iteration will decrease the
salt content in the mixture by 20%. The least number of iterations required for the salt content in the mixture to
decrease to 2% or less of the initial salt content is (Assume log 2 = 0.3010)

3

Two cans P and Q contain x liters of pure milk and x liters of water respectively. An empty can R has a volume of
5 liters. R is filled using a part of the contents of P. The contents of R are now emptied into Q. Now, 5 liters of Q
are transferred to P. If the ratio of the volumes of milk and water in P is 5 : 1, what is the value of x?

3

There are N liters of milk in container A and N liters of water in container B. X liters of milk is transferred from
A to B. After thorough mixing, X liters of the contents of B are transferred back to A. The difference of the final
concentrations of milk in A and water in A is 75 percentage points. Find the final concentration of milk in B.

3

There are N liters of milk in container A and N liters of water in container B. X liters of milk is transferred from
A to B. After the contents are thoroughly mixed, X liters of the contents of B are transferred back to A. The final concentration of milk in A is 3/4. What is the value of X/N?

3

In what ratio must two varieties of wheat be mixed so that the mixture is worth ₹1.54 per kg?

Statement 1 : First variety of wheat costs ₹1.6 per kg.

Statement 2 : Second variety of wheat costs ₹0.15 per kg less than the first.

3

In a mixture, the ratio of milk and water is 2 : 1. In order to change the ratio of milk and water by addition of water to 1 : 2, the volume of water to be added is w litres. Find w.

Statement 1 : The volume of the initial mixture is 60 litres.

Statement 2 : The volume of water in the initial mixture is 20 litres.

3

A certain alloy contains lead, copper and tin. How many kilograms of tin is contained in 60 kilograms of the alloy?

Statement 1 : By weight, the alloy has 2/5th lead and 3/16th copper.

Statement 2 : By volume, the alloy has 1/3rd lead and 1/3rd copper.

3

Between two mixtures x and y - each containing milk and water, the concentration of which mixture is more?

Statement 1 : x has three parts of water to seven parts of milk.

Statement 2 : y has seven parts of water to thirteen parts of milk.

3

Variety A of rice costs ₹32 per kg. Variety B of rice costs ₹22 per kg. The two varieties of rice are mixed in a certain ratio. What is the ratio in which they are mixed?

Statement 1 : The mixture is sold at ₹36 per kg at 20% profit.

Statement 2 : Weight of the mixture is 12 kg.

3

Can A contains milk and water solution and can B contains orange juice and water solution. These solutions
are mixed. What is the ratio of water, milk and orange juice in the resultant solution?

Statement 1 : Can A contains 40% water and can B contains 35% orange juice.

Statement 2 : Half of the resultant solution is water.

3

There are three vessels A, B and C whose capacities are in the ratio 3 : 6 : 8. In vessel A there is 12 litres of milk
solution in which milk and water are in the ratio 3 : 1. If there are 20 litres and 30 litres of milk solutions in vessels B and C respectively, how many litres of milk solution can vessel C hold?

Statement 1 : The total quantity of pure milk in these vessels is 45 litres.

Statement 2 : The total quantity of water in these vessels is 20% of the total capacity of all the three vessels.

3

Of the two containers A and B, A contains pure milk and B contains water. 50% of A is shifted to B. After thoroughly mixing it, 50% of the contents in B are shifted to A. Is the ratio of pure milk to water in A, greater than 1?

Statement 1 : Initial volume of milk in A ≥ Initial volume of water in B.

Statement 2 : Initial volume of milk in A ≤ Initial volume of water in B.

3

A trader mixed two varieties of raisins, one costing ₹96 per kg and the other ₹112 per kg. How much of the dearer variety raisins did he mix in each pack?

Statement 1 : The trader packed the raisins in a 700-gm pack.

Statement 2 : He sold the 700-gm packet at a price of ₹105 and got 50% profit.

CAT PREVIOUS YEAR QUESTIONS

3

An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is
CAT 2020

3

A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one - fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?
CAT 2020

3

Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72 % alcohol. If solution A has 60 % alcohol, then the percentage of alcohol in solution B is
CAT 2020

3

A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is
CAT 2019

3

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is
CAT 2019

3

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio
CAT 2018

3

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now
CAT 2018

3

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions
A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is
CAT 2018

3

A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is
CAT 2018

3

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is
CAT 2018

3

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
CAT 2018

3

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the
CAT 2017

3

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in
9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?
CAT 2017

3

A 100 ml flask contains 30% acid solution. What quantity of the solution should be replaced with 12% acid solution so that the resultant solution contains 21% acid?
CAT 2016

3

From a vessel completely filled up with pure wine, 140 litres of content is removed and replaced with equal quantity of water. The process is repeated one more time. In a 98 litres sample of the resulting solution 80 litres is water. Find the capacity (in litres) of the vessel.
CAT 2015

3

The percentage volumes of milk in three solutions A, B and C form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 2 : 3 : 4, by volume, we obtain a solution containing 32% milk. If we mix them in the ratio 3 : 2 : 1, by volume, we obtain a solution containing 22% milk. What is the percentage of milk in A?
CAT 2014

3

An empty metal container (without its handle) weighs 15% of what it weighs when completely filled with a particular liquid. After adding the handle, the weight of the fully filled container increases by 5%. If the weight of a partly filled container is 1/3 of the completely filled container with the handle attached, then what fraction of container is utilized?
CAT 2014

3

From a vessel containing 160 litres of milk, ‘x’ litres is drained out and replaced with water. Then ‘x’ litres of
milk-water solution is drained out and replaced with water. If the quantity of milk left in the vessel is 90 litres, then what is the value of ‘x’?
CAT 2011

3

One hundred ml of alcohol is mixed with y ml of water. Forty ml of this alcohol-water mixture is added to 2y ml of another alcohol-water mixture whose alcohol concentration is 26%. If the percentage of water in the resultant mixture is 2y%, then what is the value of y?
CAT 2010

3

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?
CAT 2004

3

There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water.
Three cups of alcohol from the first container is taken out and is mixed well in the second container. Then
three cups of this mixture is taken out and is mixed in the first container. Let A denote the proportion of water in the first container and B denote the proportion of alcohol in the second container. Then
CAT 1998

3

What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume)

Statement 1 : The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.

Statement 2 : The ratio of liquid A to liquid B in vessel 3 is 4 : 3.
CAT 1996

Mixtures & Alligations (With Previous Year CAT Questions)

In what ratio should water be mixed with 80% wine so that a 60% wine solution is formed?

A vessel contains 25 litres of a mixture of milk and water containing 40% milk. Find the quantity (in litres) of pure milk to be added to the vessel so that the ratio of milk and water in the vessel becomes 1 : 1.

A milkman has 20 litres of pure milk. Find the quantity (in litres) of water to be added to it so that he gets 50% profit by selling it at its cost price.

Find the quantity of tea costing ₹12 per kg to be mixed with 18 kg of tea costing ₹9 per kg to form a mixture costing ₹10.2 per kg.

If two kinds of grapes costing ₹16 a kg and ₹21 a kg are mixed in the ratio of 2 : 3, then find the cost of mixture per kg (in ₹).

A trader claims to sell jeera at cost price but mixes freely available sand and thereby gains 25%. What is the percentage of sand in the mixture?

6 kg of sugar costing ₹10 per kg is added to 9 kg of sugar costing ₹15 per kg. At what price (in ₹) should this mixture be sold so that there is no loss or gain?

How many kilograms of an ore containing 95% iron and 5% nickel should be mixed with 120 kg of ore havingiron and nickel in the proportion 7 : 3 such that the resultant ore contains 4/5 of iron?

A solution of 80 litres contains 30% alcohol. How many litres of pure alcohol must be added to this mixture sothat the concentration of alcohol becomes 65%?

Two solutions of sulphuric acid are mixed in the ratio of 3 : 7. The first solution contains 20% sulphuric acid andthe second solution contains 30% sulphuric acid. Find the concentration (in %) of sulphuric acid in the final mixture.

A vessel contains 10 litres of pure milk. 1 litre of milk is taken out and replaced by an equal amount of water.1 litre of mixture is then taken out and replaced by an equal amount of water. Find the ratio of milk and waterin the final mixture.

A vessel contains 20 litres of a mixture of milk and water containing 60% milk. 5 litres of pure milk is added to it.Find the percentage of milk in the new mixture.

In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?

A vessel contains 70 litres of a mixture of milk and water containing 90% milk. Find the quantity (in litres) ofwater to be added to the vessel so that the percentage of milk in the new solution is 87.5%

Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2 : 4 and 3 : 5 : 6. If the quantities in the two vessels are mixed in the ratio 1 : 1, what is the ratio of petrol, diesel and kerosene in the resultant mixture?

There are three varieties of rice A, B, and C costing ₹25/kg, ₹30/ kg, and ₹35/ kg, respectively. A total of 10 kg ofA and C and 8 kg of B is mixed to make a mixture costing ₹32/kg. Find the ratio in which A and C are mixed.

Two varieties of rice are mixed in the ratio 4 : 5. The mixture is sold at ₹60/kg at 20% profit. The prices of thefirst and the second variety are in the ratio 5 : 6. Find the price of the cheaper variety. (in ₹ per kg)

Two mixtures of milk and water contain milk and water in the ratios 4 : 1 and 3 : 1, respectively. They are mixedin such a way that the resultant mixture contains milk and water in the ratio 77 : 23. Find the ratio in which thetwo mixtures are mixed.

A flask contains pure milk. Five litres of milk is removed and replaced with water. This process is repeated oncemore. At this stage, the ratio of water and milk is 15 : 49. Find the amount of milk present in the flask at the beginning (in litres).

How many litres of water should a milkman add to 35 litres of milk costing ₹560, so that by selling the milk at ₹14 per litre, he just recovers his cost?

Fresh grapes contain 80% water by weight. Dry grapes contain 20% water by weight. How many kilograms offresh grapes will be required to prepare 20 kg of dry grapes?

A man bought 10 litres of pure milk and added 5 litres of water to it but spilt 2 litres of the mixture. Of the remaining mixture, he sold 3 litres, and again added 2 litres of water to the remaining quantity. Find the approximate percentage of milk in the final mixture.

A vessel is completely filled with milk. 20 litres is withdrawn from the vessel and is replaced with water. 20 litresof the mixture is then replaced with water. The vessel now has 18 litres of milk. Find the capacity of the vessel (in litres).

A milkman bought 10 litres of pure milk at ₹10/litre and 10 litres of adulterated milk at ₹6/litre. He mixed bothand sold the mixture at ₹10/litre. Find his profit percentage.

A vessel had 20 ml of a mixture of milk and water.The mixture has 40% milk. X ml of milk was added to themixture. Y ml of water was then added to the mixture. Each of the two additions reverses the ratio of milk andwater in the vessel. Find the difference of X and Y.

If 12 kg of rice which costs ₹24/kg is mixed with 6 kg of rice which costs ₹27/kg, then what is the cost of theresulting mixture (in ₹/kg)?

Raju went to the market to buy 1.5 kg of dried peas having 20% water content. He went home and soaked themfor some time and the water content in the peas becomes 60%. Find the final weight of soaked peas.

There are two vessels P and Q, P containing 120 litres of milk and Q containing 120 litres of water. 30 litres isdrawn from P and poured into Q and then 30 litres from Q is poured back into P. This process is repeated once.At the end of this repetition, what is the ratio of milk and water in P?

Two containers contain petrol and diesel in the ratios 4 : 3 and 3 : 1. How many litres from the first containershould be mixed with 16 litres from the second so that the ratio in the resultant mixture is 32 : 19?

Two varieties of rice are mixed in the ratio 2 : 5 and the mixture is sold at ₹12 per kg at a profit of 20%. If the first variety costs ₹7 per kg more than the second variety, find the cost per kg of the first variety.

A certain quantity of rice costing ₹6/kg is mixed with another variety costing ₹8/kg so that the resulting mixturecosts ₹7.20/kg. In what ratio were they mixed?

A dishonest milkman professes to sell milk at cost price but he makes 100/3% profit by mixing it with water. What is the water content in the milk solution?

A shopkeeper mixed 3 varieties of wheat costing ₹12 per kg, ₹18 per kg and ₹21 per kg and sold the mixture at ₹15 per kg at 20% profit. Which of the following represents a possible ratio of the varieties mixed?

A mixture contains milk and water in the ratio 3 : 1. After adding 14 litres of water to it, the ratio of milk to water in the resultant solution became 2 : 3. What was the quantity of the original mixture?

Instead of adding the requisite quantity of water to dilute 50% wine to 40% wine, by mistake, the same quantity of pure wine is added. Now, how much water as a fraction of the original volume must be added to achieve the original objective?

Sixty litres of wine is drawn from 600 litres of wine and replaced with water. Sixty litres of the mixture is then drawn and replaced with water and this procedure is repeated once more. Find the present quantity of wine in the mixture.

Two cans contain mixtures of milk and water. The first can contains 73% water while the second can contains41% water. The contents of the two cans are mixed in the ratio 3 : 5. What is the percentage of milk in the newmixture?

A vessel has 300 ml of pure milk. Thirty millilitres of milk is removed and 30 ml of water is poured into the vessel(bringing the volume of mixture in the vessel back to 300 ml). If this operation is repeated another 2 times, what is the percentage of milk in the vessel at the end?

From a vessel containing only milk, 10 litres are drawn and replaced with water. 10 litres of the mixture is nowtaken out and replaced with water again. The ratio of milk to water now is 25 : 24. How many litres of milk wasthere initially?

Two varieties of tea powder costing ₹210/kg and ₹300/kg are mixed in certain ratios to form varieties X andY. X and Y are mixed in the ratio 3 : 2 to form variety Z which is sold at ₹315/kg at 25% profit. If X costs ₹240/kg,the ratio in which the two varieties are mixed to form Y is

A vessel contains 80% alcohol solution. 20% of the solution was removed and replaced with water. If this process is repeated, find the percentage of alcohol which remains in the solution.

There is a 40 litres solution of milk and water in which milk forms 72%. How much water must be added to thissolution to make it a solution in which milk forms 60%? (in litres)

Two varieties of coffee - A and B are mixed in the ratio 3 : 2. The mixture is sold at ₹100 per kg at 100% profit.If variety A costs ₹10 per kg more than variety B, what is the cost of variety B per kg?

Two varieties of rice A and B priced at ₹6.75 per kg and ₹9.75 per kg, respectively were mixed and sold at ₹10.80per kg at a profit of 20%. Find the ratio in which A and B are mixed.

A 6-litre solution of sulphuric acid had 45% acid. It was mixed with a 5-litre solution of sulphuric acid which hada% acid, where 40 ≤ a ≤ 50. The acid concentration in the resulting mixture is b%. Which of the following is not apossible value of b?

The concentration of spirit in three vessels A, B and C are 45%, 30% and 25%, respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.

A milk solution has milk and water in the ratio 3 : 2. What part of the solution has to be substituted with water so as to reverse the ratio of milk and water in the solution?

A metal weighs 1500 kg per cubic metre and another metal weighs 2500 kg per cubic metre. Find the weight (in kg) of 5 cubic metres of an alloy formed by mixing 40% of the first metal and 60% of the second metal.

In what ratio should Ram mix two varieties of barley costing ₹20 and ₹24 per kg so that by selling it at ₹27.60 per kg Ram makes a profit of 20%?

A grocer has two varieties of rice, Rice A and Rice B costing ₹10 per kg and ₹12 per kg, respectively. He sells thetotal mixture of Rice A and Rice B having 420 kg of Rice A for ₹25,200 with a profit margin of 20%. How muchquantity of rice B is present in the mixture sold?

A vessel contains an 80% alcohol solution. 20% of the solution was removed and replaced with water. If thisprocess is repeated, find the percentage of alcohol which remains in the solution.

There are 10 litres of milk in container A and 10 litres of water in container B. One litre of milk is transferred from A to B. After that, one litre of the contents of B are transferred back to A. This entire process is carried outonce again. What is the final concentration of milk in A?

There are N liters of milk in container A and N liters of water in container B. X liters of milk is transferred fromA to B. After the contents are thoroughly mixed, X liters of the contents of B are transferred back to A. The final concentration of milk in A is 3/4. What is the value of X/N?

In what ratio must two varieties of wheat be mixed so that the mixture is worth ₹1.54 per kg?Statement 1 : First variety of wheat costs ₹1.6 per kg.Statement 2 : Second variety of wheat costs ₹0.15 per kg less than the first.

A certain alloy contains lead, copper and tin. How many kilograms of tin is contained in 60 kilograms of the alloy?Statement 1 : By weight, the alloy has 2/5th lead and 3/16th copper.Statement 2 : By volume, the alloy has 1/3rd lead and 1/3rd copper.

Between two mixtures x and y - each containing milk and water, the concentration of which mixture is more?Statement 1 : x has three parts of water to seven parts of milk.Statement 2 : y has seven parts of water to thirteen parts of milk.

Variety A of rice costs ₹32 per kg. Variety B of rice costs ₹22 per kg. The two varieties of rice are mixed in a certain ratio. What is the ratio in which they are mixed?Statement 1 : The mixture is sold at ₹36 per kg at 20% profit.Statement 2 : Weight of the mixture is 12 kg.

A trader mixed two varieties of raisins, one costing ₹96 per kg and the other ₹112 per kg. How much of the dearer variety raisins did he mix in each pack?Statement 1 : The trader packed the raisins in a 700-gm pack.Statement 2 : He sold the 700-gm packet at a price of ₹105 and got 50% profit.

An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is CAT 2020

Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72 % alcohol. If solution A has 60 % alcohol, then the percentage of alcohol in solution B is CAT 2020

A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is CAT 2019

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio CAT 2018

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now CAT 2018

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio CAT 2018

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the CAT 2017

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio? CAT 2017

A 100 ml flask contains 30% acid solution. What quantity of the solution should be replaced with 12% acid solution so that the resultant solution contains 21% acid? CAT 2016

From a vessel completely filled up with pure wine, 140 litres of content is removed and replaced with equal quantity of water. The process is repeated one more time. In a 98 litres sample of the resulting solution 80 litres is water. Find the capacity (in litres) of the vessel. CAT 2015

From a vessel containing 160 litres of milk, ‘x’ litres is drained out and replaced with water. Then ‘x’ litres of milk-water solution is drained out and replaced with water. If the quantity of milk left in the vessel is 90 litres, then what is the value of ‘x’? CAT 2011

One hundred ml of alcohol is mixed with y ml of water. Forty ml of this alcohol-water mixture is added to 2y ml of another alcohol-water mixture whose alcohol concentration is 26%. If the percentage of water in the resultant mixture is 2y%, then what is the value of y? CAT 2010

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk? CAT 2004

In what ratio should water be mixed with 80% wine so that a 60% wine solution is formed?

A vessel contains 25 litres of a mixture of milk and water containing 40% milk. Find the quantity (in litres) of pure milk to be added to the vessel so that the ratio of milk and water in the vessel becomes 1 : 1.

A milkman has 20 litres of pure milk. Find the quantity (in litres) of water to be added to it so that he gets 50% profit by selling it at its cost price.

Find the quantity of tea costing ₹12 per kg to be mixed with 18 kg of tea costing ₹9 per kg to form a mixture costing ₹10.2 per kg.

If two kinds of grapes costing ₹16 a kg and ₹21 a kg are mixed in the ratio of 2 : 3, then find the cost of mixture per kg (in ₹).

A trader claims to sell jeera at cost price but mixes freely available sand and thereby gains 25%. What is the percentage of sand in the mixture?

6 kg of sugar costing ₹10 per kg is added to 9 kg of sugar costing ₹15 per kg. At what price (in ₹) should this mixture be sold so that there is no loss or gain?

How many kilograms of an ore containing 95% iron and 5% nickel should be mixed with 120 kg of ore having
iron and nickel in the proportion 7 : 3 such that the resultant ore contains 4/5 of iron?

A solution of 80 litres contains 30% alcohol. How many litres of pure alcohol must be added to this mixture so
that the concentration of alcohol becomes 65%?

Two solutions of sulphuric acid are mixed in the ratio of 3 : 7. The first solution contains 20% sulphuric acid and
the second solution contains 30% sulphuric acid. Find the concentration (in %) of sulphuric acid in the final mixture.

A vessel contains 10 litres of pure milk. 1 litre of milk is taken out and replaced by an equal amount of water.
1 litre of mixture is then taken out and replaced by an equal amount of water. Find the ratio of milk and water
in the final mixture.

A vessel contains 20 litres of a mixture of milk and water containing 60% milk. 5 litres of pure milk is added to it.
Find the percentage of milk in the new mixture.

A vessel contains 70 litres of a mixture of milk and water containing 90% milk. Find the quantity (in litres) of
water to be added to the vessel so that the percentage of milk in the new solution is 87.5%

There are three varieties of rice A, B, and C costing ₹25/kg, ₹30/ kg, and ₹35/ kg, respectively. A total of 10 kg of
A and C and 8 kg of B is mixed to make a mixture costing ₹32/kg. Find the ratio in which A and C are mixed.

Two varieties of rice are mixed in the ratio 4 : 5. The mixture is sold at ₹60/kg at 20% profit. The prices of the
first and the second variety are in the ratio 5 : 6. Find the price of the cheaper variety. (in ₹ per kg)

Two mixtures of milk and water contain milk and water in the ratios 4 : 1 and 3 : 1, respectively. They are mixed
in such a way that the resultant mixture contains milk and water in the ratio 77 : 23. Find the ratio in which the
two mixtures are mixed.

A flask contains pure milk. Five litres of milk is removed and replaced with water. This process is repeated once
more. At this stage, the ratio of water and milk is 15 : 49. Find the amount of milk present in the flask at the beginning (in litres).

Fresh grapes contain 80% water by weight. Dry grapes contain 20% water by weight. How many kilograms of
fresh grapes will be required to prepare 20 kg of dry grapes?

A vessel is completely filled with milk. 20 litres is withdrawn from the vessel and is replaced with water. 20 litres
of the mixture is then replaced with water. The vessel now has 18 litres of milk. Find the capacity of the vessel (in litres).

A milkman bought 10 litres of pure milk at ₹10/litre and 10 litres of adulterated milk at ₹6/litre. He mixed both
and sold the mixture at ₹10/litre. Find his profit percentage.

A vessel had 20 ml of a mixture of milk and water.The mixture has 40% milk. X ml of milk was added to the
mixture. Y ml of water was then added to the mixture. Each of the two additions reverses the ratio of milk and
water in the vessel. Find the difference of X and Y.

If 12 kg of rice which costs ₹24/kg is mixed with 6 kg of rice which costs ₹27/kg, then what is the cost of the
resulting mixture (in ₹/kg)?

Raju went to the market to buy 1.5 kg of dried peas having 20% water content. He went home and soaked them
for some time and the water content in the peas becomes 60%. Find the final weight of soaked peas.

There are two vessels P and Q, P containing 120 litres of milk and Q containing 120 litres of water. 30 litres is
drawn from P and poured into Q and then 30 litres from Q is poured back into P. This process is repeated once.
At the end of this repetition, what is the ratio of milk and water in P?

Two containers contain petrol and diesel in the ratios 4 : 3 and 3 : 1. How many litres from the first container
should be mixed with 16 litres from the second so that the ratio in the resultant mixture is 32 : 19?

A certain quantity of rice costing ₹6/kg is mixed with another variety costing ₹8/kg so that the resulting mixture
costs ₹7.20/kg. In what ratio were they mixed?

Two cans contain mixtures of milk and water. The first can contains 73% water while the second can contains
41% water. The contents of the two cans are mixed in the ratio 3 : 5. What is the percentage of milk in the new
mixture?

A vessel has 300 ml of pure milk. Thirty millilitres of milk is removed and 30 ml of water is poured into the vessel
(bringing the volume of mixture in the vessel back to 300 ml). If this operation is repeated another 2 times, what is the percentage of milk in the vessel at the end?

From a vessel containing only milk, 10 litres are drawn and replaced with water. 10 litres of the mixture is now
taken out and replaced with water again. The ratio of milk to water now is 25 : 24. How many litres of milk was
there initially?

Two varieties of tea powder costing ₹210/kg and ₹300/kg are mixed in certain ratios to form varieties X and
Y. X and Y are mixed in the ratio 3 : 2 to form variety Z which is sold at ₹315/kg at 25% profit. If X costs ₹240/kg,
the ratio in which the two varieties are mixed to form Y is

There is a 40 litres solution of milk and water in which milk forms 72%. How much water must be added to this
solution to make it a solution in which milk forms 60%? (in litres)

Two varieties of coffee - A and B are mixed in the ratio 3 : 2. The mixture is sold at ₹100 per kg at 100% profit.
If variety A costs ₹10 per kg more than variety B, what is the cost of variety B per kg?

Two varieties of rice A and B priced at ₹6.75 per kg and ₹9.75 per kg, respectively were mixed and sold at ₹10.80
per kg at a profit of 20%. Find the ratio in which A and B are mixed.

A 6-litre solution of sulphuric acid had 45% acid. It was mixed with a 5-litre solution of sulphuric acid which had
a% acid, where 40 ≤ a ≤ 50. The acid concentration in the resulting mixture is b%. Which of the following is not a
possible value of b?

A metal weighs 1500 kg per cubic metre and another metal weighs 2500 kg per cubic metre. Find the weight
(in kg) of 5 cubic metres of an alloy formed by mixing 40% of the first metal and 60% of the second metal.

A grocer has two varieties of rice, Rice A and Rice B costing ₹10 per kg and ₹12 per kg, respectively. He sells the
total mixture of Rice A and Rice B having 420 kg of Rice A for ₹25,200 with a profit margin of 20%. How much
quantity of rice B is present in the mixture sold?

A vessel contains an 80% alcohol solution. 20% of the solution was removed and replaced with water. If this
process is repeated, find the percentage of alcohol which remains in the solution.

There are 10 litres of milk in container A and 10 litres of water in container B. One litre of milk is transferred from A to B. After that, one litre of the contents of B are transferred back to A. This entire process is carried out
once again. What is the final concentration of milk in A?

There are N liters of milk in container A and N liters of water in container B. X liters of milk is transferred from
A to B. After the contents are thoroughly mixed, X liters of the contents of B are transferred back to A. The final concentration of milk in A is 3/4. What is the value of X/N?

In what ratio must two varieties of wheat be mixed so that the mixture is worth ₹1.54 per kg?

Statement 1 : First variety of wheat costs ₹1.6 per kg.

Statement 2 : Second variety of wheat costs ₹0.15 per kg less than the first.

A certain alloy contains lead, copper and tin. How many kilograms of tin is contained in 60 kilograms of the alloy?

Statement 1 : By weight, the alloy has 2/5th lead and 3/16th copper.

Statement 2 : By volume, the alloy has 1/3rd lead and 1/3rd copper.

Between two mixtures x and y - each containing milk and water, the concentration of which mixture is more?

Statement 1 : x has three parts of water to seven parts of milk.

Statement 2 : y has seven parts of water to thirteen parts of milk.

Variety A of rice costs ₹32 per kg. Variety B of rice costs ₹22 per kg. The two varieties of rice are mixed in a certain ratio. What is the ratio in which they are mixed?

Statement 1 : The mixture is sold at ₹36 per kg at 20% profit.

Statement 2 : Weight of the mixture is 12 kg.

An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is
CAT 2020

Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72 % alcohol. If solution A has 60 % alcohol, then the percentage of alcohol in solution B is
CAT 2020

A chemist mixes two liquids 1 and 2. One litre of liquid 1 weighs 1 kg and one litre of liquid 2 weighs 800 gm. If half litre of the mixture weighs 480 gm, then the percentage of liquid 1 in the mixture, in terms of volume, is
CAT 2019

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio
CAT 2018

A jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now
CAT 2018

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
CAT 2018

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the
CAT 2017

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in
9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?
CAT 2017

A 100 ml flask contains 30% acid solution. What quantity of the solution should be replaced with 12% acid solution so that the resultant solution contains 21% acid?
CAT 2016

From a vessel completely filled up with pure wine, 140 litres of content is removed and replaced with equal quantity of water. The process is repeated one more time. In a 98 litres sample of the resulting solution 80 litres is water. Find the capacity (in litres) of the vessel.
CAT 2015

From a vessel containing 160 litres of milk, ‘x’ litres is drained out and replaced with water. Then ‘x’ litres of
milk-water solution is drained out and replaced with water. If the quantity of milk left in the vessel is 90 litres, then what is the value of ‘x’?
CAT 2011

One hundred ml of alcohol is mixed with y ml of water. Forty ml of this alcohol-water mixture is added to 2y ml of another alcohol-water mixture whose alcohol concentration is 26%. If the percentage of water in the resultant mixture is 2y%, then what is the value of y?
CAT 2010

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?
CAT 2004

How many kilograms of an ore containing 95% iron and 5% nickel should be mixed with 120 kg of ore having
iron and nickel in the proportion 7 : 3 such that the resultant ore contains 4/5 of iron?

A solution of 80 litres contains 30% alcohol. How many litres of pure alcohol must be added to this mixture so
that the concentration of alcohol becomes 65%?

Two solutions of sulphuric acid are mixed in the ratio of 3 : 7. The first solution contains 20% sulphuric acid and
the second solution contains 30% sulphuric acid. Find the concentration (in %) of sulphuric acid in the final mixture.

A vessel contains 10 litres of pure milk. 1 litre of milk is taken out and replaced by an equal amount of water.
1 litre of mixture is then taken out and replaced by an equal amount of water. Find the ratio of milk and water
in the final mixture.

A vessel contains 20 litres of a mixture of milk and water containing 60% milk. 5 litres of pure milk is added to it.
Find the percentage of milk in the new mixture.

A vessel contains 70 litres of a mixture of milk and water containing 90% milk. Find the quantity (in litres) of
water to be added to the vessel so that the percentage of milk in the new solution is 87.5%

There are three varieties of rice A, B, and C costing ₹25/kg, ₹30/ kg, and ₹35/ kg, respectively. A total of 10 kg of
A and C and 8 kg of B is mixed to make a mixture costing ₹32/kg. Find the ratio in which A and C are mixed.

Two varieties of rice are mixed in the ratio 4 : 5. The mixture is sold at ₹60/kg at 20% profit. The prices of the
first and the second variety are in the ratio 5 : 6. Find the price of the cheaper variety. (in ₹ per kg)

Two mixtures of milk and water contain milk and water in the ratios 4 : 1 and 3 : 1, respectively. They are mixed
in such a way that the resultant mixture contains milk and water in the ratio 77 : 23. Find the ratio in which the
two mixtures are mixed.

A flask contains pure milk. Five litres of milk is removed and replaced with water. This process is repeated once
more. At this stage, the ratio of water and milk is 15 : 49. Find the amount of milk present in the flask at the beginning (in litres).

Fresh grapes contain 80% water by weight. Dry grapes contain 20% water by weight. How many kilograms of
fresh grapes will be required to prepare 20 kg of dry grapes?

A vessel is completely filled with milk. 20 litres is withdrawn from the vessel and is replaced with water. 20 litres
of the mixture is then replaced with water. The vessel now has 18 litres of milk. Find the capacity of the vessel (in litres).

A milkman bought 10 litres of pure milk at ₹10/litre and 10 litres of adulterated milk at ₹6/litre. He mixed both
and sold the mixture at ₹10/litre. Find his profit percentage.

A vessel had 20 ml of a mixture of milk and water.The mixture has 40% milk. X ml of milk was added to the
mixture. Y ml of water was then added to the mixture. Each of the two additions reverses the ratio of milk and
water in the vessel. Find the difference of X and Y.

If 12 kg of rice which costs ₹24/kg is mixed with 6 kg of rice which costs ₹27/kg, then what is the cost of the
resulting mixture (in ₹/kg)?

Raju went to the market to buy 1.5 kg of dried peas having 20% water content. He went home and soaked them
for some time and the water content in the peas becomes 60%. Find the final weight of soaked peas.

There are two vessels P and Q, P containing 120 litres of milk and Q containing 120 litres of water. 30 litres is
drawn from P and poured into Q and then 30 litres from Q is poured back into P. This process is repeated once.
At the end of this repetition, what is the ratio of milk and water in P?

Two containers contain petrol and diesel in the ratios 4 : 3 and 3 : 1. How many litres from the first container
should be mixed with 16 litres from the second so that the ratio in the resultant mixture is 32 : 19?