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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is (a) 4.5 min (b) 9 min (c) 12 min (d) 24 min?
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Two towns A and B are connected by a regular bus service with a bus le...

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Two towns A and B are connected by a regular bus service with a bus le...
Understanding the Problem
The problem describes a man cycling from town A to town B at a speed of 20 km/h. Buses leave every T minutes in both directions.

Bus Passing Time Analysis
- The man observes a bus passing him every 18 minutes in the direction of his motion (from A to B).
- He notices a bus passing him every 6 minutes in the opposite direction (from B to A).

Calculating the Speed of the Buses
- Let's denote the speed of the buses as V_b km/h.
- The relative speed of the bus going from A to B when overtaking the cyclist is (V_b - 20) km/h.
- The time interval for buses in the same direction is given by:
\[
\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{T \cdot \frac{V_b}{60}}{(V_b - 20) \cdot \frac{1}{60}} = 18 \text{ minutes}
\]
Simplifying gives:
\[
T \cdot V_b = 18(V_b - 20)
\]
- The relative speed of the bus going from B to A is (V_b + 20) km/h.
- The time interval for buses in the opposite direction is given by:
\[
T \cdot \frac{V_b}{60} = 6 \cdot (V_b + 20) \cdot \frac{1}{60}
\]
Simplifying gives:
\[
T \cdot V_b = 6(V_b + 20)
\]

Setting Up the Equations
- From the first equation:
\[
T \cdot V_b = 18V_b - 360
\]
- From the second equation:
\[
T \cdot V_b = 6V_b + 120
\]

Equating and Solving for T
- Set the two equations equal:
\[
18V_b - 360 = 6V_b + 120
\]
- Rearranging gives:
\[
12V_b = 480 \quad \Rightarrow \quad V_b = 40 \text{ km/h}
\]
- Substitute back to find T:
\[
T \cdot 40 = 6(40 + 20) \quad \Rightarrow \quad T = 9 \text{ minutes}
\]

Conclusion
The period T of the bus service is **9 minutes**. The correct answer is (b) 9 min.
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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is (a) 4.5 min (b) 9 min (c) 12 min (d) 24 min?
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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is (a) 4.5 min (b) 9 min (c) 12 min (d) 24 min? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is (a) 4.5 min (b) 9 min (c) 12 min (d) 24 min? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is (a) 4.5 min (b) 9 min (c) 12 min (d) 24 min?.
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