Having started from the same point and at the same time, two runners – P and Q – are running around a circular track of length 500 m in opposite directions with the speeds of 6 m/s and 10 m/s, respectively. If they exchange their speeds after meeting for the first time, who will reach the starting point first?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. Both P and Q will reach at the same time.
When two persons run in opposite direction, their relative speed is equal to the sum of their individual speeds.
Relative speed of P and Q = 10 + 6 = 16 m/s
Time = Distance/Relative speed
⇒ 500/16 = 31.25 sec
Now, distance covered by P = 6 × 31.25 = 187.5 m
Distance covered by Q = 10 × 31.25 = 312.5 m
When the speeds of P and Q are reversed,
Time taken by P to reach the starting point = 312.5/10 = 31.25 sec
Time taken by Q to reach the starting point = 187.5/6 = 31.25 sec
Hence the required answetr is both P and Q will reach at the same time.