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A train leaves station A at 5 AM and reaches station B at 9 AM on the same day. Another train leaves station B at 7 AM and reaches station A at 10:30 AM on the same day. The time at which the two trains cross each other is :
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- 8 : 26 AM
- 7: 36 AM
- 7: 56 AM
- 8 AM
Correct Option: C
Here distance is constant.
| ∴ Speed ∝ | |
| Time |
∴ Ratio of the speeds of A and B
| = | = 7 : 8 | |
| 2/4 |
∴ A’s speed = 7x kmph (let)
B’s speed = 8x kmph
B = 7x × 4 = 28x km.
Let both trains cross each other after t hours from 7 a.m.
According to the question,
7x (t + 2) + 8x × t = 28x
⇒ 7t + 14 + 8t = 28
⇒ 15t = 28 – 14 = 14
| ⇒ t = | hours | |
| 15 |
| = |  | × 60 |  | minutes | |
| 15 |
= 56 minutes
∴ Required time = 7 : 56 A.M.
