Question

A train running at 72 kmph takes 20 seconds to pass a platform. It takes 12 seconds to pass a man walking at 6 kmph in the same direction. What is the length of the platform?

• A. 240 m
• B. 360 m
• C. 200 m
• D. 300 m

Hint:

Always convert km/h to m/s using \( \frac{5}{18} \) factor, and use relative speed when people/objects move in the same direction.

Answer 1

The Correct Option is B

Step 1: Convert train speed to m/s
\[ \text{Speed of train} = 72 \text{ kmph} = \frac{72 \times 1000}{3600} = 20 \text{ m/s} \] Step 2: Let length of train be \( L \)
Time to cross a man = 12 seconds \[ \text{Speed of man} = 6 \text{ kmph} = \frac{6 \times 1000}{3600} = \frac{5}{3} \text{ m/s} \] \[ \text{Relative speed (train w.r.t man)} = 20 - \frac{5}{3} = \frac{55}{3} \text{ m/s} \] \[ \text{Length of train (L)} = \text{Relative speed} \times \text{Time} = \frac{55}{3} \times 12 = 220 \text{ m} \] Step 3: Train passes platform in 20 seconds
\[ \text{Distance covered} = \text{Speed} \times \text{Time} = 20 \times 20 = 400 \text{ m} \] \[ \text{Length of platform} = 400 - 220 = \boxed{180 \text{ m}} \] Wait — no such option. Let’s verify again. ALTERNATIVE APPROACH – find directly using time difference \[ \text{Length of train (L)} = \text{Speed of train} \times \text{Time to cross man} = 20 \times 12 = 240 \text{ m} \] \[ \text{Length of platform (P)} = \text{Total distance} - \text{Train length} = 20 \times 20 - 240 = 400 - 240 = \boxed{160 \text{ m}} \] Still not matching any option. Let’s correct: Use same direction relative speed again. \[ \text{Relative speed} = \frac{55}{3} \Rightarrow \text{Train length} = \frac{55}{3} \times 12 = 220 \text{ m} \] \[ \text{Distance crossing platform} = 20 \times 20 = 400 \text{ m} \Rightarrow \text{Platform length} = 400 - 220 = \boxed{180 \text{ m}} \] No match still. Perhaps options mismatch. Let’s try with static observer: If train takes 20 seconds to cross platform, and its length is \(L\), total distance covered = \(L + P\) \[ L + P = 20 \times 20 = 400 \Rightarrow P = 400 - L \] We earlier found \(L = 240\), so: \[ P = 400 - 240 = \boxed{160 \text{ m}} \] Correct value = 160 m, but not in given options — typo possible.