Mixtures & Alligations Practice Questions

A collection of questions that typically appear from mixtures and alligation in Indian Business Schools entrance tests such as TANCET and CAT and international tests such as GMAT and GRE. Once you have grasped the basics well, it is quite easy to ace this topic. Concept tested include weighted average, simple mixtures, rules of alligation, compound mixtures, replacement, and multiple replacements.

1. A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?

   1. 17 : 3
   2. 9 : 1
   3. 3 : 17
   4. 5 : 3

   Concept: Repeated replacement

   Choice (2)The ratio of milk and water in the mixture is 9 : 1 Correct answer Explanatory Answer Medium

2. In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?

   1. 1 : 2 : 4
   2. 3 : 7 : 6
   3. 1 : 4 : 2
   4. None of these

   Concept: Mixture of 3 products

   Choice (3)The 3 variants should be mixed in the ratio 1 : 4 :2 Correct answer Explanatory Answer Medium

3. A merchant mixes three variants of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30/kg. How many kg of the second variant will be in the mixture if 2 kg of the third variant is present in the mixture?

   1. 1 kg
   2. 5 kg
   3. 3 kg
   4. 6 kg

   Concept: Mixture of 3 products

   Choice (2)The mixture will contain 5 kg of the second variety Correct answer Explanatory Answer Hard

4. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

   1. 7 litres
   2. 10 litres
   3. 5 litres
   4. None of these

   Concept: Simple Mixture

   Choice (3)5 litres of water was added Correct answer Explanatory Answer Easy

5. How many kg of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kg of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?

   1. 20 kg
   2. 12.5 kg
   3. 16 kg
   4. 200 kg

   Concept: Mixtures & Profits

   Choice (1)20 kg of Basmati rice should be mixed Correct answer Explanatory Answer Medium

6. How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?

   1. 4 litres
   2. 2 litres
   3. 1 litre
   4. 1.5 litres

   Concept: Mixtures : Replacement

   Choice (2)2 litres of the mixture should be replaced with milk Correct answer Explanatory Answer Easy

7. A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

   1. 6 litres
   2. 10 litres
   3. 30 litres
   4. None of these

   Concept: Mixtures : Replacement

   Choice (2)10 litres of the mixture should be replaced Correct answer Explanatory Answer Easy

8. A farmer counted the heads of the animals / birds in the farm and found it to be 80. When he counted the legs he found it to be 260. If the farm had either pigeons or horses and nothing else, how many horses were there in the farm? In the farm, each horse had four legs and each pigeon had two legs.

   1. 40
   2. 30
   3. 50
   4. 60

   Concept: Simple Alligation

   Choice (3)The farm had 50 horses Correct answer Explanatory Answer Easy

9. From a cask of milk containing 30 litres, 6 litres are drawn out and is replaced with water. If the same process is repeated two more times, how many litres of milk will be left in the cask?

   1. 0.512 litres
   2. 12 litres
   3. 14.38 litres
   4. 15.36 litres

   Concept: Mixtures : Repeated replacement

   Choice (4)The cask will be left with 15.36 litres of milk Correct answer Explanatory Answer Hard

10. A 20 litres mixture of milk and water comprising 60% pure milk is mixed with "x" litres of pure milk. The new mixture comprises 80% milk. What is the value of "x"?

    1. 40 litres
    2. 20 litres
    3. 8 litres
    4. 16 litres

    Concept: Simple Alligation

    Choice (2)The value of x is 20 litres Correct answer Explanatory Answer Easy

11. Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product M?

    1. 328 units
    2. 368 units
    3. 392 units
    4. 616 units
    5. None of the above

    Concept: Compound Mixtures

    Choice (B)368 units of water has been added to product M to get the final mixture Correct answer Explanatory Answer Video Explanation XAT 2015