Examples of Alligation and Mixture 2

In this class, We discuss Examples of Alligation and Mixture 2.

The reader should have prior knowledge of alligation and mixture formulae. Click Here.

Example 1:

Tea costs Rs 126 per KG, and Rs 135 per KG are mixed with a third variety in the ratio 1: 1: 2

the mixture costs Rs 153 per KG, then the price of the third variety.

Solution:

Ratio = 1: 1: 2

The first two are mixed in the ratio 1: 1.

The mixture of first two varieties cost = (126 + 135)/2 = 130.50

Ratio of the mixture and third variety = 2: 2 = 1: 1

The below diagram shows the alligation rule.

(x – 153)/22.50 = 1/1

x = 175/50

Example 2:

A jar full of whisky contains 40% of alcohol.

Another containing 19% alcohol replaces part of the whisky, and now the percentage of alcohol is 26%.

The quantity of whisky replaced?

Solution:

The below diagram shows the alligation rule.

The ratio is 1: 2

The quantity replaced = 2/3

Example 3:

The milk and water in the two vessels are in the ratio of 4: 3 and 2: 3.

In what ratio the liquid in two vessels is mixed to obtain a new mixture containing half milk and half water?

Solution:

The below diagram shows the alligation rule.

Ratio = 1/10: 1/14

Ratio = 7: 5