Question : A moving train passes a 50-metre-long platform in 14 seconds and a lamp post in 10 seconds. The speed of the train (in km/hr) is:
Option 1: 24 km/hr
Option 2: 36 km/hr
Option 3: 40 km/hr
Option 4: 45 km/hr
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Correct Answer: 45 km/hr
Solution : Length of platform = 50 m Time taken to pass the platform = 14 s Time taken to pass the lamp post = 10 s Let the length of the train be $l$ and the train's speed be $s$. $s$ = $\frac{l+50}{14}$ ----------(1) $s$ = $\frac{l}{10}$ -------------(2) ⇒ $\frac{l+50}{14}$ = $\frac{l}{10}$ ⇒ $10l+500$ = $14l$ ⇒ $500$ = $4l$ ⇒ $l$ = $\frac{500}{4}$ = 125 m Speed of the train = $\frac{125}{10}×\frac{18}{5}$ = 45 km/hr Hence, the correct answer is 45 km/hr.
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