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Q104 (IAS/2004) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m x 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other if they continue to walk till 12 : 30 p.m?

Result
Your answer: —  Â·  Correct: B
Explanation

Perimeter of the rectangular field = 2(0.4 km + 0.3 km) = 1.4 km. Speeds are 3 km/h (A) and 2.5 km/h (B), and walking time is 5.5 hours (7:00–12:30) as given in the problem statement. With the same direction, relative speed = 3 − 2.5 = 0.5 km/h. Using distance = speed × time, the relative distance A gains on B in 5.5 hours = 0.5 × 5.5 = 2.75 km [1]. Each overtaking requires the faster walker to gain one full perimeter (1.4 km). Number of overtakes = floor(2.75 / 1.4) = floor(1.964…) = 1. Therefore they cross each other once.

Sources

  1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > Speed = Total distance covered Total time taken > p. 114
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