After travelling 100 km, a train met with an accident. Its speed then became \(\frac{3}{4}\) of its usual speed, and it reached the station 40 minutes late. Had the accident happened 30 km further on, the train would have reached 30 minutes late. What is the reduced speed of the train (in km/hr)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 45
The delay arises only on the stretch run at the reduced speed. Moving the accident 30 km further on puts those 30 km at the usual speed, and that is what cuts the delay from 40 to 30 minutes.
Let the usual speed be \(v\) km/hr, so the reduced speed is \(\frac{3}{4}v\)
Time for 30 km at the reduced speed \(\displaystyle =\frac{30}{\frac{3}{4}v}=\frac{40}{v}\) hr
Time for 30 km at the usual speed \(\displaystyle =\frac{30}{v}\) hr
Extra time on these 30 km \(\displaystyle =\frac{40}{v}-\frac{30}{v}=\frac{10}{v}\) hr
This equals the drop in delay: \(40-30=10\) min \(\displaystyle =\frac{1}{6}\) hr
\(\displaystyle \frac{10}{v}=\frac{1}{6}\), so \(v=60\) km/hr
Reduced speed \(\displaystyle =\frac{3}{4}\times60=45\) km/hr