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A train running at the speed of 72 km/hr passes a tunnel completely in 3 minutes. While inside the tunnel, it meets another
direction at the speed of 90km/hr and passes it completely intrain of 3 of its length coming from opposite 4 3 1 seconds. Find the length of the tunnel. 2
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- 3510 metre
- 3500 metre
- 3400 metre
- 3600 metre
Correct Option: A
Trains are running in opposite directions.
∴ Relative speed = 72 + 90
= 162 kmph
= 162 × | = 45 m/sec | |
18 |
Let the length of the first train be = x metre.
∴ Length of the second train
= | x meter. | |
4 |
Now,
distance travelled in 3 | seconds at 45 m/sec. | |
2 |
= 45 × | = | metre | ||
2 | 2 |
This distance is equal to sum of the lengths of trains.
∴ x + | = | ||
4 | 2 |
⇒ | = | ||
4 | 2 |
⇒ | = | ||
4 | 2 |
⇒ x = | × | = 90 | ||
2 | 7 |
Hence, the length of the first train = 90 metre.
Speed of first train = 72 kmph
= 72 × | = 20 m/sec | |
18 |
Time taken by the first train to cross the tunnel
= 3 minutes = 180 seconds
∴ Distance covered by it in 180 seconds
= 180 × 20 = 3600 metre
∴ Length of (first train + tunnel) = 3600 metre
∴ Length of tunnel
= 3600 – 90 = 3510 metre