Atul gives Vishu a head-start of 20 seconds in a 900 m race and beats him by 135 m. While running the same race again Atul gives a start of 189 m and beats him by 8 seconds. In how much time can Vishu complete the full race of 900 m?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 3 minutes 20 seconds.
Let x be the speed of Atul and y be the speed of Vishu.
The time taken by Atul to run 900 m
Time = 900/x
The time taken by Vishu to run 765 m (after the head start)
Time = 765/y
⇒ 765/y = Time taken by Atul + 20
⇒ 765/y = 900/x + 20
⇒ 765/y - 900/x = 20....(1)
In second race
The time taken by Atul to run 900 m
Time = 900/x
The time taken by Vishu to run 711 m
⇒ Time = 711/y
⇒ 711/y = Time taken by Atul + 8
⇒ 711/y = 900/x + 8
⇒ 711/y - 900/x = 8...(2)
Subtracting eq 2 from eq 1
⇒ 765/y - 900/x - 711/y + 900/x = 20 - 8
⇒ 765/y - 711/y = 12
⇒ 54/y = 12
⇒ y = 54/12
⇒ y = 4.5 m/s
Thus, the time taken by Vishu = 900/4.5 = 200 sec or 3 minutes 20 seconds