Question

If a student cycles at 10 km/h he reaches the school late by 4 minutes. If he cycles at 12 km/h he reaches the school early by 2 minutes. What is the distance of the school from his home?

• A. 4 km
• B. 6 km
• C. 7 km
• D. 8 km

Hint:

Formula: $D = \frac{S_1 \times S_2}{S_2 - S_1} \times \text{Difference in time}$. Here: $\frac{10 \times 12}{2} \times \frac{6}{60} = 6$.

Answer 1

The Correct Option is B

Step 1: Concept
Distance ($D$) = Speed $\times$ Time.

Step 2: Analysis
Let distance be $D$. Time difference = 4 min (late) + 2 min (early) = 6 minutes = $6/60$ hours = 0.1 hours.

Step 3: Reasoning
Time at 10 km/h - Time at 12 km/h = $6/60$.
$D/10 - D/12 = 1/10$
$(6D - 5D)/60 = 1/10$
$D/60 = 1/10 \Rightarrow D = 6$ km.

Step 4: Conclusion
The distance is 6 km. Note: While the text mentioned 4, the official key (2250) and math confirm 6. Final Answer: (B)