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Question:

A petrol tank at a filling station has a capacity of 400 litres. The attendant sells 40 litres of petrol from the tank to one customer and then replenishes it with kerosene oil. This process is repeated with six customers. What quantity of pure petrol will the seventh customer get when he purchases 40 litres of petrol?

Explanation:

$\frac{Quantity of petrol remaining after n^{th} replacement}{Total Quantity}$ = ${(\frac{x - y}{x})}^{n}$

where x is the original quantity,

y is the quantity that is replaced, and

n is the number of times the replacement process is repeated.

∴ At the end of 6 replacements, each litre contains

${(\frac{400 - 40}{400})}^{6}$ = ${(\frac{360}{400})}^{6}$ = (0.9)⁶ ≈ 0.53 litres of petrol

∴ The customer who purchases 40 litres of petrol gets 40 × 0.53 ≈ 21.2 litres of pure petrol.

Hence, option (b).

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