Question : A train P travelling at a speed of 15 m/s can cross a platform of 200 metres in length completely in 30 seconds. Approximately how long will it take train P to cross a man who is coming towards the train on his bike at a speed of 27 km/hr?
[Note: Ignore the length of the bike.]
Option 1: 15 s
Option 2: 11.1 s
Option 3: 16.7 s
Option 4: 18.3 s
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Correct Answer: 11.1 s
Solution :
Let $l$ be the length of the train.
Speed of train = $\frac{\text{distance covered}}{\text{time}}$
$⇒15 = \frac{200+l}{30}$
$⇒450 = 200 + l$
$\therefore l = 450 - 200 = 250$ m
Speed of man = 27 km/hr
= 27 × $\frac{5}{18}$
= $\frac{15}{2}$
= 7.5 m/s
Relative speed = 15 + 7.5 = 22.5 m/s
Time taken = $\frac{250}{22.5}= \frac{100}{9}= 11.11$ s
Hence, the correct answer is 11.11 s.
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