Question

A train overtakes two persons who are waling the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes the completely in 9 and 10 seconds respectively. The length of the train is

• A. 72 m
• B. 54 m
• C. 50 m
• D. 45 m

Answer 1

The correct option is C 50 m

$2kmph=(2\times \frac{5}{18})m/sec=\frac{5}{9}m/sec\text{and 4 kmph}=\frac{10}{9}m/sec.\text{Let the length of the train be}x\text{meters and let be}y\text{~m/sec.}Then,\frac{x}{(y-\frac{5}{9})}=9and\frac{x}{y-\frac{10}{9}}=10.\therefore 9y-5=xand10(9y-10)=9x.\therefore 9y-x=5and90y-9x=100\text{On solving we get}x=50.\therefore \text{Length of the train is 50 m.}$