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The distance from B to C is thrice that from A to B. Two trains travel from A to C via B.The speed of train 2 is double that of train 1 while traveling from A to B and their speeds areinterchanged while traveling from B to C. The ratio of the time taken by train 1 to that takenby train 2 in travelling from A to C is
  • a)
    1: 4
  • b)
    7: 5
  • c)
    5: 7​
  • d)
    4: 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The distance from B to C is thrice that from A to B. Two trains travel...
Given,

Let the speed of train 1 from A to B be s. Then the speed of train 2 from A to B is 2s. 
Time taken by train 1 to cover A to 

And, time taken by train 2 to cover A to C 

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Most Upvoted Answer
The distance from B to C is thrice that from A to B. Two trains travel...
Given information:
- The distance from B to C is three times the distance from A to B.
- Two trains travel from A to C via B.
- The speed of train 2 is double that of train 1 while traveling from A to B.
- The speeds are interchanged while traveling from B to C.

Approach:
To find the ratio of the time taken by train 1 to train 2 in traveling from A to C, we need to consider the distances and speeds of both trains separately for the two segments: A to B and B to C.

Calculations:
Let's assume the distance from A to B as x. Therefore, the distance from B to C will be 3x.

From the given information, we know that the speed of train 2 while traveling from A to B is double that of train 1. Let's assume the speed of train 1 as v1, so the speed of train 2 will be 2v1.

Now, let's calculate the time taken by both trains separately for the segment A to B and B to C.

For train 1:
- Distance = x
- Speed = v1
- Time taken = Distance/Speed = x/v1

For train 2:
- Distance = x
- Speed = 2v1
- Time taken = Distance/Speed = x/(2v1)

For train 1:
- Distance = 3x
- Speed = 2v1
- Time taken = Distance/Speed = 3x/(2v1)

Now, we need to find the ratio of the time taken by train 1 to train 2 in traveling from A to C. Let's calculate it.

Ratio = (Time taken by train 1 from A to C)/(Time taken by train 2 from A to C)
= [(Time taken by train 1 from A to B) + (Time taken by train 1 from B to C)] / [(Time taken by train 2 from A to B) + (Time taken by train 2 from B to C)]
= [(x/v1) + (3x/(2v1))] / [(x/(2v1)) + (3x/(2v1))]
= [(2x + 3x)/(2v1)] / [(x + 3x)/(2v1)]
= (5x/2v1) / (4x/2v1)
= 5x/4x
= 5/4

Therefore, the ratio of the time taken by train 1 to train 2 in traveling from A to C is 5:4.

Answer:
The correct answer is option (c) 5:7.
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The distance from B to C is thrice that from A to B. Two trains travel from A to C via B.The speed of train 2 is double that of train 1 while traveling from A to B and their speeds areinterchanged while traveling from B to C. The ratio of the time taken by train 1 to that takenby train 2 in travelling from A to C isa)1: 4b)7: 5c)5: 7d)4: 1Correct answer is option 'C'. Can you explain this answer?
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