A 310 metres long train, travelling at a uniform speed, crosses a platform in 46.5 seconds and a man standing on the platform in 31 seconds. What is the length of the platform?

A 124 metres

B 93 metres

C 310 metres

D Cannot be determined

E None of these

Correct Answer: Option E

Let the length of the platform = x metres

When a train crosses a platform,

Total distance covered = Length of the train + Length of the platform

Thus, total distance = 310 + x ---(1)

Total time taken = 46.5 seconds (given) ---(2)

When a train crosses a man,

Total distance travelled = Length of the train

Thus, total distance = 310m ---(3)

Total time taken = 31 seconds (given) ---(4)

Now, Average speed = (Total Distance Travelled)/(Total Time taken)

∴ From 1 and 2,

Average speed = (310 + x)/46.5 ---(5)

From 3 and 4,

Average speed = 310/31 = 10m/s ---(6)

Equating 5 and 6,

\(\frac{{310\; + \;x}}{{46.5}} = \;10\)

⇒ 310 + x = 465

⇒ x = 155m

Thus, length of the platform is 155m.