Question

A train takes 30 s to cross a pole while traveling at a speed of 120 km/h. How much time will it take to cross the pole if its speed is increased by 30 km/h?

• A. $20s$
• B. $24s$
• C. $18s$
• D. $22s$

Answer 1

The correct option is B $24s$

Given, traveling at a speed of 120km/h, a train crosses a pole in 30 s.

We know that, if the speed of the train increases, then the time taken to cross the pole will be less.

$\text{So, Speed}\left(x\right)\propto \frac{1}{\text{Time}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=120km/h$
$y_1=30s$
$x_2=120+30=150km/h$
$\text{and,}{y}_2=\text{time taken at 150 km/h}$

$\Rightarrow \frac{120}{150}=\frac{y_2}{30}$
$\Rightarrow y_2=\frac{120\times 30}{150}=24s$

So, the time taken to cross the pole if the speed of the train is increased by 30 km/h is 24 s.