Question

A train crosses a pole in 20 seconds, and it crosses a cyclist coming in opposite direction at 5 km/h in 18
seconds. What is the speed of the train?
A)40 km/h
B)45 km/h
C)62 km/h
D)65 km/h​

Answer 1

Answer:

45 km/h

Step-by-step explanation:

let speed be x

$x \div 180 = ( x + 5) \div 200 \\ \\ 200x = 180x + 900 \\ \\ 20x = 900 \\ \\ x = 45$

the speed of the train is 45 km/h

Answer 2

answer : option (B) 45 km/h

Let speed of train is x km/h and length of train is l km.

a/c to question,

The train crosses the pole in 20 seconds.

so, time taken by train to cross the pole = length of train/speed of train

or, 20/3600 hr = l/x [ as 20sec = 20/3600 hr ]

or, 1/180 = l/x ......(1)

again, the train crosses a cyclist coming in opposite direction at 5km/h in 18sec

so, time taken by train to cross the cyclist = length of train/(speed of train + speed of cyclist)

or, 18/3600 = l/(x + 5)

or, 1/200 = l/(x + 5) ....(2)

from equations (1) and (2),

(1/180)/(1/200) = (l/x)/{l/(x+5)}

or, 200/180 = (x + 5)/x

or, 10/9 = (x + 5)/x

or, 10x = 9x + 45

or, x = 45

hence, speed of train is 45km/h.