Question

A moving train $66$ m long overtakes another train $88$ m long moving in the same direction in $0.168$ min. If the second train is moving at $30$ km/hr, at what speed is the first train moving ?

• A. $85$ km/hr
• B. $50$ km/hr
• C. $55$ km/hr
• D. $25$ km/hr

Answer 1

Answer: (A)

$85$ km/hr

Let the speed of the first train be $x$ km/hr

Then Relative speed of first train w.r.t. second train $=(x-30)$ km/hr

$=(x-30)$ $\times \frac{5}{18}$ m/sec

Total distance travelled $=(66+88)$ m $=154$ m
Time taken $=0.168$ min $=(0.168\times 60)$ sec $=10.08$
$\therefore$ $(x-30)$ $\times \frac{5}{18}$ $\times 10.08=154$

$\Rightarrow x-30=\frac{154\times 18}{5\times 10.08}=55$

$\Rightarrow x=85$ km/hr