Question

A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6 km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train (in metres) is:

• A. 120 m
• B. 150 m
• C. 125 m
• D. None of these

Answer 1

The correct option is B 150 m

Let the length of the train be x metre, and let the speed of train be y km/h, then
$x=(y+3)\frac{5}{18}\times 36$ ...(i)
and $x=(y+6)\times \frac{5}{18}\times 30$ ...(ii)
From Eq, (i) and (ii), we get
$(y+3)\times 36=(y+6)\times 30$
y = 12 km/h
$\therefore x=(y+3)\times \frac{5}{18}\times 36$
or $x=15\times \frac{5}{18}\times 36$
$x=150m$