Question

A train overtakes two persons walking along a railway track. The first person walks at 9 km/hr and the other walks at 10.8 km/hr. The train needs 16.8 and 17 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

• A. 108 km/hr
• B. 126 km/hr
• C. 144 km/hr
• D. 162 km/hr
• E. 180 km/hr

Answer 1

The correct option is D

162 km/hr

Let x is the length of the train in meter and y is its speed in kmph.

$\frac{x}{16.8}=(y-9)\times \frac{5}{18}$ --- (1)

$\frac{x}{17}=(y-10.8)\times \frac{5}{18}$ --- (2)

Dividing 1 by 2

$\frac{17}{16.8}=\frac{y-9}{y-10.8}$

=> 16.8y - 16.8 $\times$ 9 = 17y -- 17 $\times$ 10.8

$\Rightarrow$ 0.2y = 17 $\times$ 10.8 - 16.8 $\times$ 9

=> 0.2y = 183.6 - 151.2 = 32.4

=> y = 162 kmph