Question

A boy walking at a speed of $10$ km/hr reaches his school $15$ minutes late. Next time he increases his speed by $2$ km/hr, but still, he is late by $5$ minutes. Find the distance of his school from his house.

• A. $10$ km
• B. $15$ km
• C. $20$ km
• D. $25$ km

Answer 1

The correct option is A $10$ km

Let the distance of his school from the house be $x$

$\Rightarrow$ The difference in time $=(15-5)min$

$=10min$

$=\frac{10}{60}hr$

$=\frac{1}{6}hr$

$\Rightarrow$ Speed during next journey $=10+2=12km/hr$

According to the question,

$\Rightarrow$ $\frac{x}{10}-\frac{x}{12}=\frac{1}{6}$

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

$\Rightarrow$ $\frac{6x-5x}{30}=\frac{1}{3}$

$\Rightarrow$ $\frac{x}{30}=\frac{1}{3}$

$\Rightarrow$ $x=\frac{30}{3}$

$\therefore$ $x=10km$

$\therefore$ The distance of boy school from house is $10km$