Question

A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40 minutes will be:
A. 60 km/h
B. 55 km/h
C. 40 km/h
D. 70 km/h

Answer 1

Hint: First convert all the time from minutes to hours. Then use formula, distance=speed $\times $ time to find distance after that find speed by using formula speed$=\dfrac{\text{distance}}{time}$ to get the desired result.

Complete step-by-step answer:
In the question it is said that a train covers a particular distance in 50 minutes. If its average speed for the whole journey is 48 km/hr.
So, as we know that, if we are given the speed of the train and time for which it was running then we can find the distance it travelled.
The distance travelled will be the product of speed and time.
The time given is 50 minutes which can be converted into hours by dividing it by 60, so we get
$\Rightarrow $ Time$\Rightarrow Time=\dfrac{50}{60}=\dfrac{5}{6}hrs$
Now the speed given is 48 km/hr.
So, the distance can be obtained using the formula,
distance $=$ speed$\times $ time
So, by substituting speed as 48km/hr and time as $\dfrac{5}{6}$ hour we get,
Distance $=48\times \dfrac{5}{6}=40$ km
Therefore, the total distance train travelled is 40 km.
Now it is said that by how much speed would the train move to reduce the time to 40 minutes.
The distance is 40 km and the time is 40 minutes which can be converted to hours by dividing it by 60. So, time will be $\dfrac{40}{60}$ hours.
Then, speed will be equal to distance per unit time so,
$\text{Speed}=\dfrac{\text{distance}}{\text{time}}$
Substituting the above values, we get
$\text{Speed}=\dfrac{\text{40}}{\dfrac{40}{60}}=60 km/hr $
Therefore, the speed at which the train must run to reduce the time of journey to 40 minutes will be 60kmph.
Hence the correct option is “A”.

Note: Students make mistakes while comparing quantities without using about units which make their answer wrong. They should also be careful about the calculations and units. While solving this types of problems, we should keep in mind that the distance travelled is always same whatever the speed may be.