Question : A student goes to school at the rate of $\frac{5}{2}$ km/hr and reaches 6 minutes late. If he travels at the speed of 3 km/hr, he reaches 10 minutes earlier. The distance from the school is:
Option 1: 45 km
Option 2: 20 km
Option 3: 10 km
Option 4: 4 km
Correct Answer: 4 km
Solution :
Let the distance from the school be $x$ km.
According to the question,
$\frac{x}{\frac{5}{2}}-\frac{x}{3}=\frac{6+10}{60}$
⇒ $\frac{2x}{5}-\frac{x}{3}=\frac{16}{60}$
⇒ $6x-5x=\frac{16}{60}×15$
$\therefore x=4$ km
Hence, the correct answer is 4 km.
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