Arithmetic

Time, Speed & Distance

Medium

A train with 90 kmph crosses a bridge in 36 s. Another train 100 m shorter crosses the same bridge at 45 kmph. The time taken by the second train to cross the bridge will be

60 s

64 s

68 s

72 s

✅ Correct Option: 2

Understanding what we need to find: When a train crosses a bridge, it travels a distance equal to (length of train + length of bridge).

Convert speeds from kmph to m/s since time is given in seconds:

$90 \text{ kmph} = 90 \times \dfrac{5}{18} = 25 \text{ m/s}$

$45 \text{ kmph} = 45 \times \dfrac{5}{18} = 12.5 \text{ m/s}$

For the first train, using Distance = Speed × Time:

$\text{Length of train} + \text{Length of bridge} = 25 \times 36 = 900 \text{ m}$

Let $L =$ length of first train

Then:

Length of second train $= L - 100$ (given: 100 m shorter)
Length of bridge $= 900 - L$ (from previous step)

For second train to cross the bridge:

$\text{Distance to cover} = (L - 100) + (900 - L) = 800 \text{ m}$

Notice: The $L$ terms cancel out, so we don't need to find individual lengths.

Calculate time for second train:

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{800}{12.5} = 64 \text{ seconds}$

Therefore, the second train takes 64 seconds to cross the bridge.

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