Question

There are two vessels which are filled only with the pure components. vessel 1 contains 20 litres of brandy and vessel 2 contains 20 litres of water. five litres of brandy is taken from the vessel 1 and placed in the vessel 2. then 4 litres of mixture is transferred from vessel 2 to vessel 1. find the ratio of amount of water in vessel 1 to the amount of brandy in vessel 2.

Answer 1

Answer: -

16:21

Explanation: -

Vessel 1 had 20 litres of Brandy

Vessel 2 had 20 litres of water

5 litres of brandy is taken from 1 and added to vessel 2

Now vessel 1 has 15 litres of brandy

Vessel 2 has 20 litres of water + 5 litres of brandy.

4 litres of mixture is now taken from vessel 2.

This mixture contained water and brandy in the ratio 20 : 5

So 4 litres contained 3.2 litres of water and 0.8 litres of brandy.

So vessel 2 was left with (20-3.2) water and (5-0.8) brandy

                                    = 16.8 litres water and 4.2 litres brandy.

Vessel 1 got 3.2 litres of water and 15+0.8=15.8 litres of brandy from vessel 2.

Amount of water in vessel 1 = 3.2 litres

Amount of brandy in vessel 2 = 4.2 litres

Required ratio = $\frac{3.2}{4.2}$

                       = 16 : 21