Question

In a vessel, there are 10 litres of alcohol. An operation is defined as taking out five litres of what is present in the vessel and adding 10 litres of pure water to it. What is the ratio of alcohol to water after two operations?

Answer 1

answer : 1 : 5

case 1 : initially, vessel contains only alcohol of volume 10Litres

now, 5 litres is taken out and adding 10 litres of water is added into it.

so, amount of water in mixture = 10litre

and amount of alcohol in mixture = 5litre

case 2 : volume of mixture = 15 litres

and ratio of alcohol to water = 5 : 10 = 1 : 2.

now 5 litre of liquid is taken out,

volume of alcohol contains in vessel = 5 - 5 × 1/(1 + 2) = 5 - 5/3 = 10/3

and volume of water contains in vessel = 10 - 5 × 2/(1 + 2) = (30 - 10)/3

= 20/3 litres

now, 10 litres of water is added.

so, volume of water contains in vessel = 20/3 + 10 = 50/3 litres

so, the final ratio of water : alcohol = 10/3 : 50/3 = 1 : 5