Arun and Bhaskar run a race of 3 km. First, Arun gives Bhaskar a head start of 400 m and beats him by 30 seconds. While coming back, Arun gives Bhaskar a lead of 2.5 minutes and gets beaten by 500 m. What is the difference between the times in minutes in which Arun and Bhaskar can run the race for one side separately?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1.5 min.
Time = Distance × Speed
Let's assume the total time taken to cover the distance by Arun and Bhasker is x and y respectively.
1st Case:
2600 × y - 3000 × x = 30 seconds
⇒ 260y - 300x = 3 .......................(1)
2nd Case:
3000 × y - 2500 × x = 2.5 min = 150 seconds ......................(2)
⇒ 60y - 50x = 3 ........................(3)
multiply by 6 in equation 3 and subtract from equation 1
⇒ 260y - 360y - 300x + 300x = 3 - 18
⇒ -100y = -15
⇒ 3000y = 450 seconds (Total time taken by Bhasker to complete 3 km)
Put the value of 3000y in Equation 2
450 - 2500x = 150
⇒2500x = 300
⇒ x = 300/2500
⇒ 3000x = (300/2500) × 3000 = 360 seconds (Total time taken by Arun to complete 3 km)
Difference in time = 450 - 360 = 90 seconds = 90/60 = 1.5 min