A train passes a 200 m long platform in 40 seconds and a man standing on the platform in 25 seconds. The speed of the train (km/hr) is:

48 km/hr

The correct answer is Option (3) → 48 km/hr

Step 1: Let the length of the train be L meters and speed v m/s.

• Train passes a man in 25 s → distance = length of train L

$v = \frac{L}{25} \quad \text{(m/s)}$

• Train passes a 200 m platform in 40 s → distance = L + 200

$v = \frac{L + 200}{40} \quad \text{(m/s)}$

Step 2: Equate the two expressions for v

$\frac{L}{25} = \frac{L + 200}{40}$

$40L=25(L+200)$

$40L = 25L + 5000$

$15L = 5000 ⇒L = \frac{5000}{15} = 333.\overline{3}\,\text{m}$

Step 3: Find speed of train

$v = \frac{L}{25} = \frac{333.33}{25} \approx 13.333\,\text{m/s}$

Convert to km/hr:

$v = 13.333 \times 18/5 = 48\,\text{km/hr}$