Question

A train starts from Agra to Mathura at a speed of 60 km/hr and reaches there in 45 min. If in return its speed is reduced by 10%, how long will it take to reach Agra from Mathura?
(a) 1 hr
(b) 50 mins
(c) 1 hr 20 mins
(d) 49 mins

Answer 1

Hint: To begin with, we will assume some variable for the distance between Agra and Mathura. Then, we will find the distance between the two stops by using the formula of speed from physics, $v=\dfrac{s}{t}$, where v is the speed of the train, s is the distance and t is the time required to cover that distance. Then, we will find the new value of speed, which is 10% less than the original speed. The distance will remain the same. We will again apply the speed formula and find the new required time.

Complete step by step answer:
Let the distance between Agra and Mathura be s.
The speed of the train is 60 km/hr and time required by the train to cover the distance s with constant speed of 60 km/hr is 45 mins.
Now, we will convert the time in hours as the speed with us is in km per hour.
To convert time into hours, we need to divide the given time in minutes by 60.
$\Rightarrow \dfrac{45}{60}=\dfrac{3}{4}=0.75$
Thus, the time is 0.75 hours.
Now, we will use the speed formula to find the distance between Agra and Mathura.
$\begin{align}
  & \Rightarrow 60=\dfrac{s}{0.75} \\
 & \Rightarrow s=60\left( 0.75 \right) \\
 & \Rightarrow s=45 \\
\end{align}$
Therefore, the distance between Agra and Mathura is 45 km.
Now, it is given that on return journey, the speed is reduced by 10%.
Thus, the modified speed will be (original speed – 10% of original speed).
10% of original speed is $\dfrac{10}{100}\times 60=6$
Therefore, the modified speed will be (60 – 6) = 54 km/hr.
Now, we will use the speed formula to get the time t required to cover 45 km of distance at a speed of 54 km/hr
$\begin{align}
  & \Rightarrow 54=\dfrac{45}{t} \\
 & \Rightarrow t=\dfrac{45}{54} \\
 & \Rightarrow t=0.83 \\
\end{align}$
Therefore, the time required to cover this distance is 0.83 hours. Now, we need to convert this time into mins. To convert from hours to mins, we have to multiply the time by 60.
Time in mins = $0.83\times 60=50$mins.
Hence, option (b) is the correct option.

Note: It is important to be well acquainted with the basic concepts of physics to solve such practical problems. Also, in this question, the concept of percentage is also used.