Prakash runs 2 km in 4 min and Shikha in 4 min 10 sec. How many meters start must Prakash give Shikha so that the race may end in a dead heat?

A 80 m

B 72 m

C 85 m

D 77 m

E 89 m

Correct Answer: Option A

Speed = distance/time

Time taken by Prakash to run 2000m = 4 min = 4 × 60 = 240 sec

∴ Speed of Prakash, x = 2000/240 m/s

Time taken by Shikha to run 2000m = 4min 10sec = 4 × 60 + 10 = 250 sec

∴Speed of Shikha, y = 2000/250 m/s

To meet dead heat, both of them must complete the race in equal time, i.e. 240 sec

Difference in speeds = x – y = \(\frac{{2000}}{{240}} - \frac{{2000}}{{250}} = \frac{1}{3}m/sec\)

Total distance by which Shikha should be ahead of Prakash at the beginning of the race

\(= \frac{1}{3} \times 240 = 80m\)