Question : If a boy walks from his house to school at the rate of 4 km/h, he reaches the school 10 minutes earlier than the scheduled time. However, if he walks at the rate of 3 km/h, he reaches 10 minutes late. Find the distance of his school from his house.
Option 1: 5 km
Option 2: 4 km
Option 3: 6 km
Option 4: 4.5 km
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Correct Answer: 4 km
Solution :
Given: If a boy walks from his house to school at the rate of 4 km/h, he reaches the school 10 minutes earlier than the scheduled time. However, if he walks at the rate of 3 km/h, he reaches 10 minutes late.
We know the formula, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Let $x$ km be the distance.
The time taken at 4 km/h is $\frac{x}{4}$ hours.
The amount of time at 3 km/h is $\frac{x}{3}$ hours.
The timings difference is (10 + 10) = 20 minutes
According to the question,
$\frac{x}{3}-\frac{x}{4}=\frac{20}{60}$
⇒ $\frac{4x-3x}{12}=\frac{20}{60}$
⇒ $\frac{x}{12}=\frac{1}{3}$
⇒ $x$ = 4
Hence, the correct answer is 4 km.
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