Question

A mixture of 240 litres of juice and water contains 15% water. How much more water (in litres) should be added to this so that the strength of water will become 25% in the new mixture

Answer 1

Answer:

This is a simple case of Alligation

Traditional method :

40 litres => milk = 30 water = 10

Let us add x litres water

New volume = 40 + x

New volume of water in new mixture

= 10 + x

We know, 10 + x = 30% of (40 + x)

=> 10 + x = 3/10(40 + x)

=> 100 + 10x = 120 + 3x

=> 7x = 20

=> x = 20/7 litres

Elegant method of Alligations :

When we mix 25% water with 100% water to get 30% water, we have :-

Mixture - - - - - - - pure water

25% - - - - - - - - - - - - 100%

- - - - - - - - 30% - - - - - -

70% - - - - - - - - - - - - - 5%

The ratio of existing mixture and pure water in the new liquid should be 70:5 = 14:1

So 40 litres ==> 14 parts

=> 20/7 litres ==> 1 part

Refer to this post for more details on Mixture and Alligations :