A and B take part in 100 meters race where A beats B by 10 meters To favour B A starts 10 mete...........

Quantitative Aptitude( Paper-I ) Time & distance

A and B take part in 100 meters race, where A beats B by 10 meters. To favour B, A starts 10 meters behind the starting line in a second 100 meters race, running at their earlier speeds. Which one among the following is true in view of the second race?

A and B reach the finishing line simultaneously

B beats A by 1 meter

B beats A by 2 meters

A beats B by 1 meter

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Explanation:

First race
If A finishes the race (100m) in T time, then during T time, B has covered only 90 meters.
Speed x Time=Distance.
Therefore,
Speed of A=100/T
Speed of B=90/T

Second Race
A has to cover 110 meters @speed 100/T
Time taken by A=(110/100)x T=1.1T
B has to cover only 100 meters @speed 90/T
Time taken by B=(100/90) x T=1.1111…T
So even in second race A is taking less time than B, because 1.1 T is smaller than 1.1111…T
Therefore A finishes the race, quicker than B even in second race. In the light of this information, consider the answer options.