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Oliveboard Question of the day
Question: Rohan and Sohan run a race of 2000m. First, Rohan gives Sohan a start of 200m and beats him by 30 seconds. Again Rohan gives Sohan a start of 3 min and is beaten by 1000 m.
Find the time in minutes in which Rohan and Sohan can finish the race separately.
(1) 4, 5
(2) 6, 8
(3) 5, 7
(4) 8, 10
(5) 7, 9
Solution posted below. Click on the plus sign to view the solution.
Answer and Explanation
Answer key: 1
Let the speeds of Rohan and Sohan be r and s m/sec.
According to first condition, suppose Rohan runs 2000 m in t sec then Sohan runs 1800 m in (t +30) sec.
So, 1800/s – 2000/r = 30 …(i)
Now let’s consider the 2nd condition.
Total distance travelled by Sohan in 3 min = 180s m
So the remaining distance that Sohan has to run = (2000 – 180s) m
Now time taken by Sohan to travel this distance = (2000 – 180s)/s
Now in the same time Rohan will travel 1000 m hence time = 1000/r
(2000 – 180s)/s = 1000/r …(ii)
Solving equations (i) and (ii), we get r = 25/3 m/s and s = 20/3 m/s
Time taken by Rohan to finish the race = 2000/(25/3) = 240 s = 4 min
Time taken By Sohan to finish the race = 2000/(20/3) = 300 s = 5 min