A beats B by 15 sec in a 200 m race B beats C by 25 sec in a 500 m race C beats D by 32 sec in ...........

Quant (SSC) Time & distance

A beats B by 15 sec in a 200 m race, B beats C by 25 sec in a 500 m race, C beats D by 32 sec in 800 m race and D beats E by 35 sec in a 1 km race. What must be the speed of A in order to beat E by 800 m in a 2 km race?

2.5 m/s

3.33 m/s

5 m/s

6.66 m/s

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Explanation:

A beats B by 15 sec means A reaches the destination 15 sec ahead of B or B reaches 15 sec later than B.
Let all of them compete in a 2 km or 2000 m race, now we can compare them as follows:
A beats B by 150 sec, B beats C by 100 sec, C beats D by 80 sec, D beats E by 70 sec,
⇒ E would finish the race 400 sec after A.
Now, if A has to beat E by 800 m then we can say that E will cover the remaining 800m in 400sec, and cover 2000m in 1000 sec.
A has to reach 400s earlier i.e in 600 sec,
so A’s speed = 2000/600 = 3.33 m/s