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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 kmh-1 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
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two towns A and B are connected by a regular bus service with a bus le...
Let vkmh−1 be the constant speed with which the bus travel ply between the towns A and B .
Relative velocity of the bus from A to B with respect to the cyclist = (v − 20)kmh−1
Relative velocity of the bus from B to A with respect to the cyclist = (v + 20)kmh−1
Distance travelled by the bus in time T (minutes) = vT
As per question
Equating (i) and (ii) , we get
= 18v − 18 x 20 = 6v + 20 × 6
or 12v = 20 x 6 + 18 x 20 = 480 or v = 40 kmh−1
Putting this value of v in (i) , we get
40T = 18 x 40 − 18 x 20 = 18 x 20
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Community Answer
Two towns A and B are connected by a regular bus service with a bus le...
**Given information:**
- The speed of the man cycling is 20 km/h.
- The bus goes past the man every 18 minutes in the direction of his motion.
- The bus goes past the man every 6 minutes in the opposite direction.
**To find:**
- The period T of the bus service.
**Assumptions:**
- The distance between towns A and B is constant.
- The man is cycling at a constant speed.
**Approach:**
- Let the distance between towns A and B be D km.
- Let the time taken by the bus to travel from A to B be T1 minutes.
- Let the time taken by the bus to travel from B to A be T2 minutes.
**Understanding the problem:**
- When the man is cycling in the direction from A to B, the bus overtakes him every 18 minutes.
- When the man is cycling in the direction from B to A, the bus overtakes him every 6 minutes.
- This means that in the same amount of time, the bus covers a shorter distance in the direction from A to B compared to the direction from B to A.
**Calculating the bus speed:**
- Let the speed of the bus be V km/h.
- In the direction from A to B, the bus covers a distance of D in T1 minutes.
- Therefore, the speed of the bus in the direction from A to B is V = D/T1 km/h.
- In the direction from B to A, the bus covers a distance of D in T2 minutes.
- Therefore, the speed of the bus in the direction from B to A is V = D/T2 km/h.
**Calculating the man's speed:**
- The man's speed is given as 20 km/h.
**Calculating the number of bus trips:**
- In the direction from A to B, the bus overtakes the man every 18 minutes.
- Therefore, the time taken by the bus to complete one trip from A to B is T1 = 18 minutes.
- In the direction from B to A, the bus overtakes the man every 6 minutes.
- Therefore, the time taken by the bus to complete one trip from B to A is T2 = 6 minutes.
**Calculating the period of the bus service:**
- The period T of the bus service is the time taken for the bus to complete one round trip from A to B and back.
- The time taken for the bus to travel from A to B is T1 minutes.
- The time taken for the bus to travel from B to A is T2 minutes.
- Therefore, the period T is T = T1 + T2 = 18 + 6 = 24 minutes.
**Conclusion:**
- The period T of the bus service is 24 minutes.
- The speed of the man cycling is 20 km/h.
- The bus goes past the man every 18 minutes in the direction of his motion.
- The bus goes past the man every 6 minutes in the opposite direction.
**To find:**
- The period T of the bus service.
**Assumptions:**
- The distance between towns A and B is constant.
- The man is cycling at a constant speed.
**Approach:**
- Let the distance between towns A and B be D km.
- Let the time taken by the bus to travel from A to B be T1 minutes.
- Let the time taken by the bus to travel from B to A be T2 minutes.
**Understanding the problem:**
- When the man is cycling in the direction from A to B, the bus overtakes him every 18 minutes.
- When the man is cycling in the direction from B to A, the bus overtakes him every 6 minutes.
- This means that in the same amount of time, the bus covers a shorter distance in the direction from A to B compared to the direction from B to A.
**Calculating the bus speed:**
- Let the speed of the bus be V km/h.
- In the direction from A to B, the bus covers a distance of D in T1 minutes.
- Therefore, the speed of the bus in the direction from A to B is V = D/T1 km/h.
- In the direction from B to A, the bus covers a distance of D in T2 minutes.
- Therefore, the speed of the bus in the direction from B to A is V = D/T2 km/h.
**Calculating the man's speed:**
- The man's speed is given as 20 km/h.
**Calculating the number of bus trips:**
- In the direction from A to B, the bus overtakes the man every 18 minutes.
- Therefore, the time taken by the bus to complete one trip from A to B is T1 = 18 minutes.
- In the direction from B to A, the bus overtakes the man every 6 minutes.
- Therefore, the time taken by the bus to complete one trip from B to A is T2 = 6 minutes.
**Calculating the period of the bus service:**
- The period T of the bus service is the time taken for the bus to complete one round trip from A to B and back.
- The time taken for the bus to travel from A to B is T1 minutes.
- The time taken for the bus to travel from B to A is T2 minutes.
- Therefore, the period T is T = T1 + T2 = 18 + 6 = 24 minutes.
**Conclusion:**
- The period T of the bus service is 24 minutes.
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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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer? for NEET 2026 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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer?.
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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer? for NEET 2026 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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 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 kmh-1in 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 isa)4.5 minb)9 minc)12 mind)24 minCorrect answer is option 'B'. Can you explain this answer?.
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