From a taxi stand, two cabs start at a speed of 54 km/hr at an interval of 29 minutes, both cabs travelling in the same direction. A man coming in the opposite direction towards the taxi stand meets the cabs at an interval of 12 minutes. Find the speed (in km/hr) of the man.

74.8

82.1

76.5

80.4

APEDIA

NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

From a taxi stand, two cabs start at a speed of 54 km/hr at an interval of 29 minutes, both cabs travelling in the same direction. A man coming in the opposite direction towards the taxi stand meets the cabs at an interval of 12 minutes. Find the speed (in km/hr) of the man.

Correct Answer

76.5

[Distance Blueprint]: The initial physical distance established between the two cabs is generated by the first cab traveling alone for 29 minutes at 54 km/hr. D......

💡 Analysis & Explanation

[Distance Blueprint] ▼

The initial physical distance established between the two cabs is generated by the first cab traveling alone for 29 minutes at 54 km/hr. Distance = 54 × (29 / 60) km.

[Relative Motion Logic] ▼

When the man (traveling at 'v' km/hr) encounters the first cab, the second cab is exactly that distance away. Since they move in opposite directions, their relative approach speed is (54 + v) km/hr.

[Equation Formulation] ▼

This distance is covered at the relative speed in exactly 12 minutes. So, (54 + v) × (12 / 60) = 54 × (29 / 60).

[Mathematical Resolution] ▼

Cancelling the 60s from the denominators gives 12 × (54 + v) = 1566. Dividing by 12 yields 54 + v = 130.5. Consequently, v = 130.5 - 54 = 76.5 km/hr.

Conclusion ▼

The pedestrian's speed is 76.5 km/hr.

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From a taxi stand, two cabs start at a speed of 54 km/hr at an interval of 29 minutes, both cabs travelling in the same direction. A man coming in the opposite direction towards the taxi stand meets the cabs at an interval of 12 minutes. Find the speed (in km/hr) of the man.