Question : If a train 130 m long takes $6 \frac{1}{2}$ seconds to cross a man who is walking at 12 km/hr in the same direction in which the train going, then the speed of the train (in km/hr) is:
Option 1: 84
Option 2: 64
Option 3: 48
Option 4: 74
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Correct Answer: 84
Solution :
Man's speed in m/s = $12\text{ km/hr} \times \frac{5}{18} = 12 \times \frac{5}{18}\ \mathrm{ m/s} = \frac{10}{3}\text{ m/s}$
We know that the train crosses a 130-meter-long man in $\frac{13}{2}$ seconds.
$\therefore$ Relative speed = $\frac{130\ \mathrm{m}}{\frac{13}{2}\mathrm{s}} = 20\text{ m/s}$
Relative speed = (Train's speed in m/s) – (Man's speed in m/s)
$⇒20=$ (Train's speed in m/s) $-\frac{10}{3}$
$\therefore$ Train's speed in m/s = $20\text{ m/s} + \frac{10}{3}\text{ m/s} = \frac{70}{3} \text{ m/s}$
Now, Train's speed in km/hr = $\frac{70}{3} \times \frac{18}{5} = 84\text{ km/hr}$
Hence, the correct answer is 84.
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