In a 200-m linear race, if A gives B a start of 25 m, then A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. How long does A take to run 200m?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 77.5 seconds.
Let, A's speed = x m/sec and B's speed = y m/sec
200/x = 155/y
⇒ y = (155/200)x = (31/40)x
Also, 175/y = 200/x + 10
⇒ 175/(31/40)x = 200/x + 10
⇒ 7000/31x = 200/x + 10
⇒ 7000 = 6200 + 310x
⇒ 310x = 800
⇒ x = 800/310 = 80/31
Time taken by A = 200/(80/31) = 77.5 seconds
Therefore, A takes 77.5 seconds to run 200 meters.