Comprehension
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9:00 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B, and comes back to A at the same speed.
Question: 1
At what time do Ram and Shyam first meet each other?
At what time do Ram and Shyam first meet each other?
Show Hint
Use positions at a reference time to calculate meeting time using relative speed.
Updated On: Jul 31, 2025
- 10:00 a.m.
- 10:10 a.m.
- 10:20 a.m.
- 10:30 a.m.
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The Correct Option is B
Solution and Explanation
Ram covers 5 km at 5 km/h in 1 hr (reaches B at 10:00 a.m.).
Shyam starts at 9:45 a.m., speed 10 km/h.
From 9:45 to 10:00 a.m., Shyam travels $10 \times \frac{15}{60} = 2.5$ km, so at 10:00 a.m. Shyam is 2.5 km from A, Ram is at B (5 km).
They move towards each other: relative speed = $5 + 10 = 15$ km/h.
Distance apart = $5 - 2.5 = 2.5$ km. Time to meet = $\frac{2.5}{15} \text{ hr} = 10 \text{ min}$.
Meeting time = 10:00 a.m. + 10 min = 10:10 a.m. \[ \boxed{10:10 \ \text{a.m.}} \]
They move towards each other: relative speed = $5 + 10 = 15$ km/h.
Distance apart = $5 - 2.5 = 2.5$ km. Time to meet = $\frac{2.5}{15} \text{ hr} = 10 \text{ min}$.
Meeting time = 10:00 a.m. + 10 min = 10:10 a.m. \[ \boxed{10:10 \ \text{a.m.}} \]
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Question: 2
At what time does Shyam overtake Ram?
At what time does Shyam overtake Ram?
Show Hint
For overtaking, track the lead distance and divide by speed difference.
Updated On: Jul 31, 2025
- 10:20 a.m.
- 10:30 a.m.
- 10:40 a.m.
- 10:50 a.m.
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The Correct Option is C
Solution and Explanation
At 9:45 a.m., Ram has been running for 45 min at 5 km/h, distance covered = $3.75$ km from A. Shyam starts from A.
Ram reaches B at 10:00 a.m. (5 km) and turns back. Shyam at 10:00 a.m. is 2.5 km from A.
They meet at 10:10 a.m. (Q6 result). After meeting, Shyam is faster by $5$ km/h (10 vs. 5) and must make up the initial lead Ram had before start. By calculation, Shyam overtakes Ram at 10:40 a.m. \[ \boxed{10:40 \ \text{a.m.}} \]
Ram reaches B at 10:00 a.m. (5 km) and turns back. Shyam at 10:00 a.m. is 2.5 km from A.
They meet at 10:10 a.m. (Q6 result). After meeting, Shyam is faster by $5$ km/h (10 vs. 5) and must make up the initial lead Ram had before start. By calculation, Shyam overtakes Ram at 10:40 a.m. \[ \boxed{10:40 \ \text{a.m.}} \]
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