Circular track - P and Q crossings
Question
P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m. ?
Options
12
13
14
15
Explanation
P and Q move in opposite directions, so their relative speed is the sum of their individual speeds: 5 + 3 = 8 rounds per hour. This means they cross each other exactly 8 times every hour. From 5:00 a.m. to 7:00 a.m. (2 hours), total crossings = 8 × 2 = 16. We must exclude the crossings that occurred between 5:00 a.m. and 5:20 a.m. (1/3 of an hour). Crossings in this early window = 8 × (1/3) = 2.66, meaning exactly 2 full crossings occurred before 5:20 a.m. Crossings strictly between 5:20 and 7:00 = Total - earlier crossings = 16 - 2 = 14.
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q17
Section
Numerical Ability
Sub-topic
Time, Speed & Distance
Type
Time-speed-distance
Difficulty
Hard
Source hint
Speed-distance application
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