Question

Amit starts to go to Delhi from Patna at a speed of 50 km/hr. Distance between Delhi and Patna is 1000 km. He takes a rest of 20 minutes every 3 hours. How much time will he take to arrive in Delhi?
(a) 20 hours
(b) 21 hours
(c) 22 hours
(d) 23 hours

Answer 1

Hint: To begin with, we will find the time required for Amit to go from Patna to Delhi at 50 km/hr without any stop. Then we will add the total time he took rest, which was 20 mins after every 3 hours. To account for this rest time, we will find how many batches of 3 hours occurred during the journey. Thus, we can find the total time it took Amit to reach Delhi from Patna.

Complete step-by-step answer:
To find the time required by Amit to reach Delhi from Patna at 50 km/hr can be found out by using the speed formula from physics. The distance between Delhi and Patna is given as 1000 km.
The speed formula is v = $ \dfrac{\text{s}}{\text{t}} $ , where v is the speed, s is the distance and t is the time required to cover distance s at speed v.
Thus, 50 = $ \dfrac{1000}{\text{t}} $
 $ \Rightarrow $ t = $ \dfrac{1000}{50} $
 $ \Rightarrow $ t = 20 hours.
Therefore, if the Amit doesn’t take any break, he will need 20 hours to reach Delhi from Patna.
But it is given that he takes a break every 3 hours.
So, the first break will be at the third hour, the second break will be at the sixth hour and so on.
Thus, the number of breaks will be the integer part of the quotient of time required when going non-stop and 3.
Thus, number of breaks = $ \dfrac{20}{3}=6.66 $ .
So, Amit took 6 breaks.
In every break, he spent 20 mins.
So, total time in breaks is 20 $ \times $ 6 = 120 mins.
Now, we need to convert this into hours. To convert minutes into hours, we need to divide time in minutes by 60.
Thus 120 mins = $ \dfrac{120}{60} $ mins = 2 hours
Therefore, time taken by Amit to reach Delhi to Patna is 20 + 2 hours = 22 hours
Hence, option (c) is the correct option.

Note: If the number of hours required for non-stop journey would have been a multiple of 3, then the number of breaks would be one less than the quotient of numbers of hours for non-stop journey and 3. This is because he cannot take a break after reaching the destination.