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A train overtakes two person walking at 2 km per hr. and 4 km per hr. respectively and
passes completely them in 9 sec. and 10 sec. respectively. What is the length of the train?
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- 65 metres
- 60 metres
- 55 metres
- 50 metres
Correct Option: D
Let the length of the train be x km and its speed y km per hr.
Case I : When it passes the man walking at 2 km per hr. in the same direction
Relative speed of train = (y – 2) km per hr.
| ∴ | = 9 seconds | |
| y − 2 |
| = | = | hour ...(i) | ||
| 3600 | 400 |
Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
Relative speed of train= (y – 4) km per hr.
| ∴ | = 10 sec. | |
| y − 4 |
| ⇒ | = | hrs. | ||
| y − 4 | 3600 |
| ⇒ | = | hrs. ...(ii) | ||
| y − 4 | 360 |
On dividing equation (i) by (ii),
we have
| = | = | = | ||||
| y − 2 | 1/360 | 400 | 10 |
⇒ 10y – 40 = 9y – 18
⇒ 10y – 9y = 40 – 18
⇒ y = 22 km per hr.
∴ From equaton (i), we have
| = | ||
| 22 − 2 | 400 |
| ⇒ x = | km | |
| 20 |
| = | = 50 metres. | |
| 20 |
