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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.

Answer Options:
(1) 4, 5
(2) 6, 8
(3) 5, 7
(4) 8, 10
(5) 7, 9

### Answer and Explanation

Answer key: 1 Solution: 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

[i]
[i]