Rajiv, Sanjiv and Vijay join in a running race. The distance is 1500 meters.…
2020
Rajiv, Sanjiv and Vijay join in a running race. The distance is 1500 meters. Rajiv beats Sanjiv by 30 meters and Vijay by 100 meters. By how much could Sanjiv beat Vijay over the full distance if they both ran as before?
- A.
72.3 m
- B.
71.5 m
- C.
71.4 m
- D.
70.2 m
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
In races, each runner moves at a constant speed, so the distances any two runners cover in the SAME time are always in a fixed ratio equal to the ratio of their speeds. “A beats B by d metres over a course of length L” means that in the time A finishes L, B has covered only (L − d). To compare B and C directly, express both of their covered distances over one shared time window, then scale that ratio up to a full course for the runner you want as the winner.
Application
In the time Rajiv runs 1500 m, Sanjiv runs 1500 − 30 = 1470 m (Rajiv beats Sanjiv by 30 m).
In that same time, Vijay runs 1500 − 100 = 1400 m (Rajiv beats Vijay by 100 m).
So over one shared time interval, Sanjiv : Vijay distances = 1470 : 1400 = 21 : 20 (this equals the ratio of their speeds).
Now let Sanjiv run the full 1500 m. In that time Vijay covers 1500 × (1400 / 1470) = 1500 × (20 / 21) = 30000 / 21 = 1428.57 m.
Margin = 1500 − 1428.57 = 500/7 = 71.43 m ≈ 71.4 m.
Cross-check
Verify by the speed ratio: Vijay covers 20/21 of whatever Sanjiv covers. Over 1500 m, Vijay falls short by 1500 × (1/21) = 1500/21 = 500/7 = 71.43 m — the same value, confirming Sanjiv beats Vijay by about 71.4 m.