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Two trains 230 m and 270 m long are running in opposite directions at speeds of 42 km/h and 48 km/h, respectively. They cross each other in:
Question

Two trains 230 m and 270 m long are running in opposite directions at speeds of 42 km/h and 48 km/h, respectively. They cross each other in:

A.

22 seconds

B.

20 seconds

C.

25 seconds

D.

30 seconds

Correct option is B

Given:

Length of the first train = 230 meters

Length of the second train = 270 meters

Speed of the first train = 42 km/h

Speed of the second train = 48 km/h

The trains are running in opposite directions.

Formula Used:

Relative speed = Speed of first train + Speed of second train

Time = Total DistanceRelative Speed\frac{\text{Total Distance}}{\text{Relative Speed}}​​

Solution:

Since the trains are running in opposite directions, their relative speed is:

Relative Speed = 42 km/h + 48 km/h = 90 km/h

The total distance is the sum of the lengths of both trains:

Total Distance = 230 m + 270 m = 500 m

Time = 500 m90×518 m/s=500×18 m90×5 m/s=20 seconds \frac{500 \, \text{m}}{90\times \frac {5}{18} \, \text{m/s}}= \frac{500 \times 18\, \text{m}}{90\times 5 \, \text{m/s}}= 20 \, \text{seconds}

Thus, the two trains will take 20 seconds to cross each other.

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