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A train running at 25 km per hour take 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at the rate of 5 km per hr. in the same direction. Find the length of the platform.
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- 25 metres
- 20 metres
- 24 metres
- 28 metres
Correct Option: A
Let the length of train be x metres and the length of platform be y metres.
| Speed of the train = |  | 25 × |  | m/sec | |
| 18 |
| = | m per sec. | |
| 18 |
Time taken by train to pass the platform
| = |  | (x + y) × |  | sec. | ||
| 125 |
| ∴ (x + y) × | = 18 | |
| 125 |
or, x + y = 125 ...(i)
Speed of train relative to man = (25 + 5) km per hr.
| = | | 30 × | | m per sec. | |
| 18 |
| = | m per sec. | |
| 3 |
Time taken by the train to pass the man
| = | | x × | | sec. | |
| 25 |
| = | sec. | |
| 25 |
| ∴ | = 12 | |
| 25 |
| ⇒ x = | | | = 100 metres | |
| 3 |
Putting x = 100 in equation (i),
we get, y = 25 metres.
∴ Length of train = 100 metres
and length of the platform = 25 metres.
