Question

A student reached his school late by 20 minutes by travelling at a speed of 9 km/hr Had he travelled at the speed of 12 km/hr he would have reached his school 20 minutes early Find the distance between his house and the school?

• A. 12 km
• B. 6 km
• C. 3 km
• D. 24 km

Answer 1

The correct option is D 24 km

Let the distance of the house from the school be x km Then $\frac{x}{9}-\frac{1}{3}=\frac{x}{12}+\frac{1}{3}\Rightarrow \frac{x}{9}-\frac{x}{12}=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$
$\Rightarrow \frac{4x-3x}{36}=\frac{2}{3}\Rightarrow \frac{x}{36}=\frac{2}{3}\Rightarrow x=(\frac{2}{3}\times 36)km=24km$