A’s speed is 20/17 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?Approaching this question logically would be the best start rather than thinking about formulas.
A’s speed is 20/17 times that of B.
From the above statement, we can assume that if B's speed is 17 km/hr then, A's speed would be 20 km/hr. In other words, if B covers 17 km , at the same time A will cover 20 km. Since the length of the race is not given, we have freedom to decide the race length.
What would be the best pick ?
100 km ? No way. This will end up in lots of unnecessary calculations.
20 km would be the right assumption to get the answer immediately or any multiple of 20 should also work.
Now, Why is 20 km the best pick?
As we already know that when A covers 20 km , B will cover only 17 km i.e 3 km behind A.
So, if we assume that the race length is 20 km, and to end the race in dead heat i.e both A and B should finish the race at the same time, B should have a head start of 3 km i.e 3/20 of the race length.
Option D is the answer.Thanks,
Clifin J Francis,
GMAT QUANT SME
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Crackverbal Prep Team
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