Question

A vessel contains liquids A and B in ratio 5 : 3. If 16 litres of the mixture are removed and the same quantity of liquid B is added the ratio becomes 3 : 5 What quantity does the vessel hold?
1. 40 litres
2. 50 litres
3. 60 litres
4. none of the above

Answer 1

Correct Answer - Option 1 : 40 litres

 Suppose the vessel contains 5x litres and 3x litres of liquids A and B respectively.

The removed quantity contains = 16/(5 + 3) × 5 = 10litres of A and 16 - 10 = 6 litres of B

Now, (5x - 10) : (3x - 6 + 16) = 3 : 5

⇒ (5x - 10) / (3x + 10) = 3/5

⇒ 25x - 50 = 9x + 30

⇒ 16x = 80

⇒ x = 5

∴ Capacity of vessel = 8x = 8 × 5 = 40