A boy walking at a speed of 10 kmph reaches his school 15 min. late. After receiving a warning from his teacher, next day he increases his speed by 2 kmph, but still late by 5 min. Find the distance of his school from his house.

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5 km

7.5 km

8 km

10 km

answer is D.

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Detailed Solution

Distance = x km,

Time = t hrs

$\frac{x}{10} = t + \frac{15}{60}$

$\frac{x}{10} = t + \frac{1}{4} \to 1$

$\frac{x}{12} = t + \frac{5}{60}$

$\frac{x}{12} = t + \frac{1}{12} \to 2$

$\frac{x}{10} - \frac{x}{12} = \frac{1}{4} - \frac{1}{12}$

$\frac{6 x - 5 x}{60} = \frac{3 - 1}{12}$

$\frac{x}{5} = 2$

$x = 10 k m$

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