P and Q start running in opposite directions on a circular track from the same point. If their speeds are 10 m/s and 8 m/s, respectively, then after what time will they meet if the length of the track is 1620 m?
- (a)110 seconds
- (b)70 seconds
- (c)120 seconds
- (d)90 seconds
Answer
Why
Correct — D. They run in opposite directions on a closed track, so the gap between them closes at the sum of the speeds.
Relative speed = 10 + 8 = 18 m/s
They first meet when the two of them together have covered one whole lap, 1,620 m.
Time = 1,620 ⁄ 18 = 90 seconds → option (d)
Check: in 90 s P covers 900 m and Q covers 720 m, and 900 + 720 = 1,620 m.
Why the others are wrong
- (a)110 seconds — In 110 s the pair covers 18 × 110 = 1,980 m, which is 360 m past the meeting point. They met earlier and are already running apart again.
- (b)70 seconds — In 70 s they cover 18 × 70 = 1,260 m between them, 360 m short of the 1,620 m lap. The gap has not closed yet.
- (c)120 seconds — In 120 s they cover 18 × 120 = 2,160 m, a lap plus 540 m. The lap is completed at 90 s, so 120 s overshoots the first meeting.
Concept
On a circular track the two runners are always separated by some arc, and the question is how fast that arc shrinks.
Running towards each other around the loop, the arc closes at 10 + 8 = 18 m/s. Running the same way, it would close at 10 − 8 = 2 m/s.
The first meeting comes when the shrinking arc reaches zero — which, starting from the same point, means the pair has jointly covered one full circumference.
Note this is the first meeting anywhere on the track, not the first return to the start.
Both runners begin at the same point, so the arc to be closed is the entire 1,620 m lap rather than some smaller head start.
Key facts
- Opposite directions on a closed track make the relative speed the sum of the speeds.
- The first meeting happens when the two together have covered one full lap.
- Same direction instead makes the relative speed the difference of the speeds.
Study next
Common traps
- Subtracting the speeds, which is the same-direction rule.
- Dividing the lap by one runner's speed alone.
- Solving for the return to the starting point instead of the first meeting anywhere on the track.
The opposite-direction form also runs at Quant Q.6 of the 12 Sep 2024, 09:00 sitting, where two walkers at 5 and 2 rounds per hour are counted for crossings. The same-direction form, with the speeds subtracted, is at Quant Q.15 of the 26 Sep 2024, 09:00 sitting.
Related PYQs
No directly related past PYQ was found.