A train leaves station P at 6 AM and reaches station Q at 10 AM. At the same…
2023
A train leaves station P at 6 AM and reaches station Q at 10 AM. At the same time (i.e. at 6 AM) another train leaves station Q and reaches station P at 9.30 AM. The two trains cross each other at
Answer: D. 7.52 AM — CONCEPTWhen two bodies start simultaneously from opposite ends, their separation closes at the sum of their speeds. If the common route length is D and their…
- A.
8 AM
- B.
8.12 AM
- C.
7.40 AM
- D.
7.52 AM
Show answer & explanation
Correct answer: D
CONCEPT
When two bodies start simultaneously from opposite ends, their separation closes at the sum of their speeds.
If the common route length is D and their full-journey times are t1 and t2, the meeting time after departure is D/(D/t1 + D/t2).
APPLICATION
Let the distance PQ be D.
The first train takes 4 hours, so its speed is D/4 per hour.
The second train takes 3 hours 30 minutes = 7/2 hours, so its speed is 2D/7 per hour.
Their closing speed is D/4 + 2D/7 = 15D/28 per hour.
Meeting time = D/(15D/28) = 28/15 hours = 1 hour 52 minutes.
Adding 1 hour 52 minutes to 6:00 AM gives 7:52 AM.
CROSS-CHECK
In 28/15 hours, the first train covers 7D/15 and the second covers 8D/15.
The two distances add to D, the full initial separation, confirming that the trains meet then.
RESULT
The trains cross at 7:52 AM.