A train passes two bridges of lengths 600 m and 200 m in 80 s and 40 s respectively. The length of the train is :

Correct option is D

Given:

Time to cross 600 m bridge = 80 s

Time to cross 200 m bridge = 40 s

We are to find the length of the train

Formula Used:

Speed = $$\frac{\text{Total distance}}{\text{Time taken}}$$​​

Solution:

Let length of the train be l

Since the speed is the same in both cases:

​$$\frac{l + 600}{80} = \frac{l + 200}{40}$$​​

40(l + 600) = 80(l + 200)

40l + 24000 = 80l + 16000

24000 - 16000 = 80l - 40l

8000 = 40l

l = $$\frac{8000}{40}$$​= 200 m

Alternate Solution:

Difference in bridge lengths = 600 - 200 = 400 m

Difference in time taken = 80 - 40 = 40 s

Speed of train = $$\frac{400}{40}$$​= 10 m/s

Total distance = $$10 \times 80$$​ = 800 m

l = 800 - 600 = 200 m