In a race of 1000 m A beats B by 100 m or 10 s If they start a race of 1000 m simultaneously from th...........

Quantitative Aptitude (CDS) Time & distance

In a race of 1000 m, A beats B by 100 m or 10 s. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets 65halved, then by how much time will A beat B?

65 s

60 s

50 s

45 s

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Explanation:

Since, either A beats B by 100 m or 10 s. It means that B runs 100 m in 10 s.
therefore Speed of B = 100/10 =10m/s
Because B gets injured at a distance of 450 m and his speed gets halved.
So, time taken by B to cover 1000 m= 450/10+550/5 = 155
Because Ratio of speed of A and B is equal to ratio of distance covered by A and B.
A : B=1000 : 900 = 10 : 9
Now, speed of A = 10/9x10 = 100/9 m/s
Time taken by A to cover 1000m = 1000/100x9 = 90 s
Hence, A beat B by length of time = (155 − 90) = 65 s