Examples of Alligation or Mixture 1

In this class, We discuss Examples of Alligation or Mixture 1.

The reader should know the basics of alligation or mixture formulae. Click Here.

Example 1:

In what ratio must water be mixed with milk to gain 20% by selling the milk at cost?

Solution:

Let CP of milk Rs 1 per liter.

SP of the mixture is Rs 1 per liter.

Gain percentage = 20

CP = (100 / (100 + 20)) * 1 From profit and loss formulae.

CP = 5/6

By the rule of alligation, the ratios are shown in the below diagram.

Ratio of water to milk = 1: 5

Example 2:

How many KG of wheat costing Rs 8 per KG must be mixed with 36 KG of rice costing Rs 5.40 per KG, so a 20% gain is obtained by selling the mixture at Rs 7.20 per KG.

Solution:

The selling price of 1 KG of mixture = Rs 7.20.

Gain = 20%

CP = (100/120) * 7.20

CP = 6.

The below diagram shows the ratios from the alligation rule.

The amount is converted to paise to avoid decimals.

Ratio of wheat: rice = 3: 10

3: 10 = x: 36

Product of extremes = Product of mean terms

10x = 36 * 3

x = 10.8