Question : A boy covers a certain distance between his house and school on a cycle. Riding at an average speed of 15 km/hr, he is late by 10 min. However, with an average speed of 20 km/hr, he reaches the school 5 min earlier. Find the distance between his house and school.
Option 1: 25 km
Option 2: 20 km
Option 3: 15 km
Option 4: 30 km
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Correct Answer: 15 km
Solution :
Let the distance between his house and school be $x$ km.
Given, the time taken to cover $x$ km at an average speed of 15 km/hr – Time taken to cover $x$ km at an average speed of 20 km/hr = 15 minutes
So, $\frac{x}{15}-\frac{x}{20}=\frac{15}{60}$
$⇒\frac{x}{60}=\frac{15}{60}$
$\therefore x=15$ km
Hence, the correct answer is 15 km.
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