November 24, 2016

Quantitative Aptitude - Alligation or Mixture

Hi friends,

In the previous post, we did the Fill in the Blanks in General English for Bank exams.

Today, we will do some problems on Alligation or Mixture in Quantitative Aptitude.

Quantitative Aptitude for IBPS, SBI, RBI

Solving problems like →

Q: The ratios of milk to water are 5 : 1 and 8 : 6 respectively in two pots. In which ratio should they be mixed so that new ratio of milk to water is 9 : 5?

A: The ratio required to get the ratio 9 : 5 is 3 : 8


  • To solve this problem we use the Alligation formula.
    • Quantity of Cheaper ÷ Quantity of Dearer = 
    •  = (Cost price of Dearer - Mean price) ÷ (Mean price - Cost price of Cheaper)

This is the actual formula.

we can solve the above problem this way;

→ Pot A ratio is 5 : 1, in this total 6 parts (5 + 1), part of milk is 5. so we can take it as 5/6

→ Pot B ratio is 8 : 6, in this total 14 parts (8 + 6), part of milk is 8, so we can take it as 8/14

→ The required ratio is 9 : 5, in the total 14 parts, milk is 9, so we have 9/14

Now, finding the required ratio

So, the required ration is 1/14 : 8/42 = 1/14 x 42/8 = 3/8 = 3 : 8


Alligation is the rule to find the ratio of the ingredients of a mixture at a certain price to get a particular price.

This alligation rule is applied when finding the ratio of the ingredients in the mixture, price of the items, quantity of the item.

It has three terms → Cost price of the Cheaper item c, Cost price of the Dearer item d and the Mean Price m.

Mean Price m:  The cost of the unit quantity of the mixture.

→ Another formula to fin out of the quantity of the pure liquid
     If a container contains x litres of liquid from which y litres are taken out and replaced by water. After n times, the quantity of pure liquid is

Quantitative Aptitude for SBI, IBPS PO, Clerk, RBI exams

The formula and rule is given above.

Let's do some similar problems

Alligation or Mixture Practice problems

  1. Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69 3/13 % milk is;
  2. A merchant has 1000 kg of sugar, part of which he sell at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is;
  3. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture of Rs. 9.24 per kg?
  4. The milk and water in the vessel A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture containing half milk and half water?
  5. How many kgs of wheat costing Rs. 8 per kg must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?


  1. 2 : 7
  2. 600 kg
  3. 63 kg (first find the mean price and then use alligation rule)
  4. 7 : 5
  5. 10.8 kg (first find the mean price and then use alligation rule)

Alligation -Practice Sets

Set 1 Set 2 Set 3 Set 4 Set 5 Set 6 Set 7

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