Question

A train with a speed of $90$ km/hr crosses a bridge in $36$ seconds. Another train $100$ metres shorter crosses the same bridge at $45$ km/hr. What is the time taken by the second train to cross the bridge?

• A. $18$ seconds
• B. $52$ seconds
• C. $64$ seconds
• D. $72$ seconds

Answer 1

Answer: (C)

$64$ seconds

Let the length of the bridge be $x$ metres and length of the first train at $90$ km/hr be $y$ metres

Then $(x+y)=[(90\times \frac{5}{18})\times 36]$ m $=900$ m
The second train crosses the bridge by covering distance of $[x+(y-100\left)\right]m$ at the rate of $45$ km/hr
$12.5$ m/s i.e. $800$ m at $12.5$ m/s $(\because x+y=900\text{m})$
Time taken by the second train to cross the bridge $=\frac{800}{12.5}$ sec $=64$ seconds