Question

A train normally covers a certain distance at a speed of 60 km/hr. However, if it were to halt for a fixed time interval in each hour its average speed reduced to 50 km/hr. What is the time interval for which the train halt in each hour?

• A. 10 minutes
• B. 20 minutes
• C. 6 minutes
• D. 12 minutes

Answer 1

The correct option is A 10 minutes

This question can be solved by alligation.
Speed when moving = 60 km/h
Speed when at rest = 0 km/h
Average speed = 50 km/h (Given)

Hence, time ratio = 5 : 1.
$\therefore$ In one hour, train moved for 50 min and rested for 10 min.

Alternate Approach:
For this type question, take the LCM of speeds and assume the LCM as the distance.
then the time taken @ speed of 60km/hr $=\frac{300}{60}$= 5 hrs
again the time taken @ speed of 50 km/hr $=\frac{300}{50}$ = 6hrs
Thus we see that in place of 5 hrs train takes 6 hours. It means the train takes 1 hour extra and this one hour is stopping period in the total time of 6 hours. Thus in 6 hours, train halts for 1 hour. So in 1 hour, the train will stop for $\frac{1}{6}$ hours or 10 minutes.

Alternatively: (short cut)
Halting (or stopping) time $=(1-\frac{slowerspeed}{fasterspeed})hours$
$=1-\frac{50}{60}=\frac{10}{60}=\frac{1}{6}hours$
= 10 minutes
($\because$ 1 hour = 60 minutes)