A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled…
2024
A cycled from P to Q at 10 kmph and returned at the rate of 9 kmph. B cycled both ways at 12 kmph. In the whole journey B took 10 minutes less than A. Find the distance between P and Q.
- A.
3 km
- B.
3.25 km
- C.
3.75 km
- D.
4 km
Attempted by 27 students.
Show answer & explanation
Correct answer: C
Let the distance between P and Q be d km.
Time taken by the first cyclist = d/10 + d/9 = 19d/90 hours
Time taken by the second cyclist = d/12 + d/12 = d/6 hours
Given that the second cyclist took 10 minutes (1/6 hour) less than the first, set up the equation:
19d/90 - d/6 = 1/6
Solve: (19d - 15d)/90 = 1/6 ⇒ 4d/90 = 1/6 ⇒ d = (1/6) * (90/4) = 15/4 = 3.75 km.
Answer: 3.75 km