In a circular race of 1600 m in length, Bhaskar and Vinay start with speeds of 27 km/h and 45 km/h starting at the same time from the same point. When will they meet for the first time on the track when running in the opposite directions and the same direction, respectively?
- (a)1 minute 40 seconds and 5 minutes 20 seconds
- (b)1 minute 20 seconds and 5 minutes 20 seconds
- (c)2 minutes 40 seconds and 5 minutes 40 seconds
- (d)2 minutes 20 seconds and 4 minutes 20 seconds
Answer
Why
Correct — B. The track is in metres, so convert both speeds to m/s (multiply by 5 ⁄ 18).
27 km/h = 27 × 5 ⁄ 18 = 7.5 m/s
45 km/h = 45 × 5 ⁄ 18 = 12.5 m/s
Opposite directions — the speeds add:
relative speed = 7.5 + 12.5 = 20 m/s
time = 1600 ⁄ 20 = 80 s = 1 minute 20 seconds
Same direction — the speeds subtract:
relative speed = 12.5 − 7.5 = 5 m/s
time = 1600 ⁄ 5 = 320 s = 5 minutes 20 seconds
The pair 1 min 20 s and 5 min 20 s is option (b).
Why the others are wrong
- (a)1 minute 40 seconds and 5 minutes 20 seconds — The same-direction half is right, but 1 minute 40 seconds is 100 s, which would need a relative speed of 16 m/s. Adding 7.5 and 12.5 gives 20 m/s, so the first meeting comes at 80 s.
- (c)2 minutes 40 seconds and 5 minutes 40 seconds — 2 minutes 40 seconds is 160 s, the time to cover 1600 m at 10 m/s — the average of the two speeds. A meeting time is set by relative speed, not by average speed.
- (d)2 minutes 20 seconds and 4 minutes 20 seconds — Neither half fits: 140 s and 260 s need relative speeds of about 11.4 m/s and 6.2 m/s. The pair of speeds given can only produce 20 m/s and 5 m/s, so 80 s and 320 s.
Concept
Two runners who start together on a circular track meet again when the gap between them has grown by one full lap, wherever on the track that happens.
Running in opposite directions the gap opens at the sum of the speeds, so the relative speed is 7.5 + 12.5 = 20 m/s.
Running in the same direction the faster gains on the slower at the difference, 12.5 − 7.5 = 5 m/s.
Each time is then the track length divided by that relative speed — 1600 m once, because the question asks for the first meeting.
Meeting on the track is not the same event as meeting at the starting point. Meeting anywhere needs one lap of relative gain, while meeting back at the start needs the LCM of the two individual lap times.
The stem puts opposite directions first and the same direction second, and the option pairs follow that order — read both halves of a pair before choosing.
Key facts
- To convert km/h to m/s multiply by 5 ⁄ 18, so 27 km/h is 7.5 m/s and 45 km/h is 12.5 m/s.
- The first meeting anywhere on a circular track takes track length divided by relative speed.
- Relative speed is the sum of the speeds in opposite directions and their difference in the same direction.
Study next
Common traps
- Leaving the speeds in km/h and dividing 1.6 km by 20, which yields hours rather than seconds.
- Matching only the first time in a pair, when two options share 5 minutes 20 seconds.
- Using the average of the speeds in place of their sum or difference.
SSC repeats this template with fresh numbers — a track length in metres, two speeds, and the direction stated.
A same-direction version is set at 9 Sep 2024, 09:00, Quant Q.3, and opposite-direction versions at 13 Sep 2024, 12:30, Quant Q.5 and 18 Sep 2024, 12:30, Quant Q.12.
Related PYQs
No directly related past PYQ was found.