Question

200 litres of a mixture contains 15% water and the rest is milk. The amount of milk that must be added so that the resulting mixture contains 87.5% milk is:
1. 45 litres
2. 40 litres
3. 35 litres
4. 30 litres

Answer 1

Correct Answer - Option 2 : 40 litres

Given:

A mixture contains = 200 litres 

Water = 15% 

The amount of milk that must be added so that the resulting mixture contains  87.5% milk is ;

Calculation :

The initial amount of milk = 85/100 ×  200 = 170 litres 

Let the amount of milk to be added be = a

The new amount of milk = a + 170 litres  

The total amount of mixture becomes = 200 + a

We express the new quantity of milk as a percentage of the total  mixture as follows.

⇒ (a + 170) / (a + 200) × 100 = 87.5

⇒ 100a + 17000 = 87.5a + 17500

⇒ 100a - 87.5a = 17500 - 17000 

⇒ 12.5a = 500 

⇒ a = 40

∴ The milk is 40 litres.