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The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12?
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The Rajdhani express and the Shatabdi express enter a tunnel from oppo...
Length of Rajdhani express:
- Let the length of Rajdhani express be x meters.
- Since Shatabdi express is 5/3 times as fast as Rajdhani express, the length of Shatabdi express will be (5/3)x meters.
Time taken for Rajdhani and Shatabdi to enter the tunnel:
- Let the speed of Rajdhani express be r m/s and the speed of Shatabdi express be s m/s.
- Time taken by Rajdhani express to enter the tunnel = x/r = 12 seconds
- Time taken by Shatabdi express to enter the tunnel = (5/3)x/s = 4 seconds
Distance between the two trains:
- Distance traveled by Rajdhani express = r * 12 = 12r meters
- Distance traveled by Shatabdi express = s * 4 = 4s meters
- Total distance traveled by both trains = 12r + 4s = 34^(3/8) meters
- Since Shatabdi express is 5/3 times as fast as Rajdhani express, we have s = (5/3)r
Solving the equations:
- Substituting s = (5/3)r in 12r + 4s = 34^(3/8), we get r = 5 m/s and s = 8.33 m/s
- Substituting r = 5 m/s in x/r = 12, we get x = 60 meters
Calculating the total time taken:
- Time taken for the two trains to cross each other completely = Total length of both trains / Relative speed
- Total length of both trains = x + (5/3)x = 8x meters
- Relative speed = 8.33 - 5 = 3.33 m/s
- Time taken = 8x / 3.33 = 24 seconds
Therefore,
- Length of Rajdhani express = 60 meters (Option D)
- Time taken for the two trains to cross each other completely = 24 seconds (Option D)
- Let the length of Rajdhani express be x meters.
- Since Shatabdi express is 5/3 times as fast as Rajdhani express, the length of Shatabdi express will be (5/3)x meters.
Time taken for Rajdhani and Shatabdi to enter the tunnel:
- Let the speed of Rajdhani express be r m/s and the speed of Shatabdi express be s m/s.
- Time taken by Rajdhani express to enter the tunnel = x/r = 12 seconds
- Time taken by Shatabdi express to enter the tunnel = (5/3)x/s = 4 seconds
Distance between the two trains:
- Distance traveled by Rajdhani express = r * 12 = 12r meters
- Distance traveled by Shatabdi express = s * 4 = 4s meters
- Total distance traveled by both trains = 12r + 4s = 34^(3/8) meters
- Since Shatabdi express is 5/3 times as fast as Rajdhani express, we have s = (5/3)r
Solving the equations:
- Substituting s = (5/3)r in 12r + 4s = 34^(3/8), we get r = 5 m/s and s = 8.33 m/s
- Substituting r = 5 m/s in x/r = 12, we get x = 60 meters
Calculating the total time taken:
- Time taken for the two trains to cross each other completely = Total length of both trains / Relative speed
- Total length of both trains = x + (5/3)x = 8x meters
- Relative speed = 8.33 - 5 = 3.33 m/s
- Time taken = 8x / 3.33 = 24 seconds
Therefore,
- Length of Rajdhani express = 60 meters (Option D)
- Time taken for the two trains to cross each other completely = 24 seconds (Option D)
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The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12?
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The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12?.
The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12?.
Solutions for The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? in English & in Hindi are available as part of our courses for UPSC.
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The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12?, a detailed solution for The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? has been provided alongside types of The Rajdhani express and the Shatabdi express enter a tunnel from opposite directions on parallel tracks. Rajdhani express takes 12 seconds to completely enter the tunnel while Shatabdi express takes 4 seconds. The distance between the points where the engines cross each other to the point where the last compartments cross each other is 34^(3/8)m .Shatabdi express is 5/3 times as fast as Rajdhani express. 26.What is the length of Rajdhani express in metres? (A) 82.5 (B) 165 (C) 110 (D) 120 27.How many seconds do the two trains take to cross each other completely? (A) 5 (B) 7 (C) 10 (D) 12? theory, EduRev gives you an
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