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14 litres are drawn from a cask full of petrol and is then filled with kerosene. This operation is performed three more times. The ratio of the kerosene to that of the quantity of petrol now left in cask is 625 : 1296 . How much petrol did the cask originally hold?

14 litres are drawn from a cask full of petrol and is then filled with kerosene. This operation is performed three more times. The ratio of the kerosene to that of the quantity of petrol now left in cask is 625 : 1296 . How much petrol did the cask originally hold? Correct Answer 84 litres

Let initial quantity of petrol = x litres

After a total of 4 operations,

Quantity of kerosene = x(1 – (y/x))n

⇒ x(1 – 14/x)4

Given that after a total of 4 operations,

The ratio of the kerosene to that of the quantity of petrol now left in cask = 625 : 1296 .

x (1 – 14/x)4/x = 625 : 1296 

⇒ (1 – 14/x)4 = (5/6)4

⇒ 1 – 14/x = 5/6

⇒ 6x – 84 = 5x

⇒ x = 84

∴ The initial quantity of petrol = 84 litres

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