Question

A man standing on a platform finds that a train takes $3$ seconds to pass him and another train of same length moving in the opposite direction takes $4$ seconds. The time taken by the trains to pass each other will be

• A. $2\frac{3}{7}$ seconds
• B. $3\frac{3}{7}$ seconds
• C. $4\frac{3}{7}$ seconds
• D. $5\frac{3}{7}$ seconds

Answer 1

Answer: (B)

$3\frac{3}{7}$ seconds

Let the length of 1st train $=$ length of the $2^{nd}$ train $=x$ metres
Then speed of the $1^{st}$ train $=$ $\frac{x}{3}$ m/s Speed of the $2^{nd}$ train $=$ $\frac{x}{4}$ m/s
Since both the trains are moving in opposite directions their relative speed $=$ $(\frac{x}{3}+\frac{x}{4})=\frac{7x}{12}$ m/s
$\therefore$ Time taken to pass each other $=$ $\frac{Distancetobecovered}{Relativespeed}$
$=\frac{x+x}{7x/12}=\frac{2x\times 12}{7x}=\frac{24}{7}$ seconds $=$ $3\frac{3}{7}$ sec.