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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