In a race of 1000 m, A beats B by 100 m or 10 seconds. 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 halved, then by how much time will A beat B?

In a race of 1000 m, A beats B by 100 m or 10 seconds. 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 halved, then by how much time will A beat B? Correct Answer 65 seconds

Let the speed of A and B be ‘a’ and ‘b’ (m/s) respectively

Time taken by B – Time taken by A to cover 1000 m = 10 seconds

⇒ 1000/b – 1000/a = 10

⇒ In the same time A covers 1000 m, B covers (1000 – 100) = 900 meters

Speed of A/Speed of B = Distance covered by A/Distance covered by B

⇒ a/b = 1000/900

⇒ a = 10b/9

⇒ 1000/b – 1000/ (10b/9) = 10

⇒ 1000/b – 900/b = 10

⇒ 100/b = 10

⇒ b = 10 m/s

⇒ a = 10b/9 = 100/9 m/s

Now B’s speed gets halved after covering 450 m

⇒ Time taken by B = 450/b + 550/ (b/2) = 450/10 + 550/5 = 155 seconds

⇒ Time taken by B (if no injury occurred) = 1000/10 = 100 seconds

⇒ Time taken by A = Time taken by B (without injury) - 10 = 90 seconds