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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
- a)6
- b)10
- c)15
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Trains A and B start traveling at the same time towards each other wit...
Given information:
- Train A and Train B start traveling towards each other simultaneously from stations X and Y, respectively.
- Train A reaches station Y in 10 minutes.
- Train B takes 9 minutes to reach station X after meeting Train A.
To find: Total time taken by Train B to travel from station Y to station X.
Approach:
Let's assume the distance between stations X and Y as 'd' and the speeds of Train A and Train B as 'vA' and 'vB', respectively.
Using the formula, speed = distance/time, we can write:
- vA = d/10 (Train A reaches station Y in 10 minutes)
- vB = d/tB (where tB is the time taken by Train B to travel from station Y to station X)
When Train A and Train B meet, the distance covered by both trains is equal to the distance between the two stations, i.e., d.
Using the formula, distance = speed × time, we can write:
- Distance covered by Train A in 9 minutes (before meeting Train B) = vA × 9
- Distance covered by Train B in 9 minutes (before meeting Train A) = vB × 9
Since both the trains cover the same distance when they meet, we can equate the above two equations to get:
vA × 9 = vB × 9
d/10 × 9 = d/tB × 9
tB = 10 minutes
Therefore, the total time taken by Train B to travel from station Y to station X is:
Time taken to meet Train A (at some point in between) + Time taken to travel from that point to station X
= 9 minutes + 10 minutes
= 19 minutes
Hence, the correct option is (c) 15.
- Train A and Train B start traveling towards each other simultaneously from stations X and Y, respectively.
- Train A reaches station Y in 10 minutes.
- Train B takes 9 minutes to reach station X after meeting Train A.
To find: Total time taken by Train B to travel from station Y to station X.
Approach:
Let's assume the distance between stations X and Y as 'd' and the speeds of Train A and Train B as 'vA' and 'vB', respectively.
Using the formula, speed = distance/time, we can write:
- vA = d/10 (Train A reaches station Y in 10 minutes)
- vB = d/tB (where tB is the time taken by Train B to travel from station Y to station X)
When Train A and Train B meet, the distance covered by both trains is equal to the distance between the two stations, i.e., d.
Using the formula, distance = speed × time, we can write:
- Distance covered by Train A in 9 minutes (before meeting Train B) = vA × 9
- Distance covered by Train B in 9 minutes (before meeting Train A) = vB × 9
Since both the trains cover the same distance when they meet, we can equate the above two equations to get:
vA × 9 = vB × 9
d/10 × 9 = d/tB × 9
tB = 10 minutes
Therefore, the total time taken by Train B to travel from station Y to station X is:
Time taken to meet Train A (at some point in between) + Time taken to travel from that point to station X
= 9 minutes + 10 minutes
= 19 minutes
Hence, the correct option is (c) 15.
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Community Answer
Trains A and B start traveling at the same time towards each other wit...
Here, we have the following:
Distance between stations X and Y = d units
Speed of train A = d/10 units/minutes
Speed of train B = d/Tb,
where Tb is total time taken by train B to cover distance d.
Let the trains meet after time T,
now, T + 9 = Tb (as mentioned in question, train B takes 9 minutes to reach other station after meeting the train).
So, we have the following:
Sum of distances covered by the 2 trains when they meet = distance between the two stations
=> T(d/10) + T(d/Tb) = d
=> T(d/10) + T(d/T+9) = d
=> T(T+9)/10(T+9) + 10T/10(T+9) = 1 (after taking d common on LHS and RHS)
=> T²+9T+10T = 10T+90
=> T²+9T-90 =0
=> (T-6)(T+15) = 0
Here, T = 6
Tb = 9 +T =9+6 = 15
Hence the answer is 15
Distance between stations X and Y = d units
Speed of train A = d/10 units/minutes
Speed of train B = d/Tb,
where Tb is total time taken by train B to cover distance d.
Let the trains meet after time T,
now, T + 9 = Tb (as mentioned in question, train B takes 9 minutes to reach other station after meeting the train).
So, we have the following:
Sum of distances covered by the 2 trains when they meet = distance between the two stations
=> T(d/10) + T(d/Tb) = d
=> T(d/10) + T(d/T+9) = d
=> T(T+9)/10(T+9) + 10T/10(T+9) = 1 (after taking d common on LHS and RHS)
=> T²+9T+10T = 10T+90
=> T²+9T-90 =0
=> (T-6)(T+15) = 0
Here, T = 6
Tb = 9 +T =9+6 = 15
Hence the answer is 15
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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer?
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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer?.
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X isa)6b)10c)15d)12Correct answer is option 'C'. Can you explain this answer?.
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