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Question:

The duration of the journey from your home to the College in the local train varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the diesel used per km., and inversely as the number of carriages in the train. If, in a journey of 70 km. in 45 minutes with 15 carriages, 10 litres of diesel is required, then the diesel that will be consumed in a journey of 50 km. in half an hour with 18 carriages is

Explanation:

T = $\frac{K \times D \times C}{\sqrt{A}}$

Where T is the time taken, D is the distance, C is the number of carriages, A is the diesel used per km and K is the proportionality constant.

Based on the data given:

45 = $\frac{K \times 70 \times 15}{\sqrt{\frac{1}{7}}}$

K = $\frac{3}{70 \sqrt{7}}$

T' = $\frac{3 \times D' \times C'}{70 \sqrt{7} \times \sqrt{A'}}$

30 = $\frac{3 \times 50 \times 18}{70 \sqrt{7} \times \sqrt{A'}}$

Solving, A’ = 11.8 liters

Hence, option (b).

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