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Two trains viz A and B are running on parallel tracks and A is faster than B. If both are moving in same direction, A passes B in 5/3 minutes but when moving in opposite directions, A crosses B in 20 seconds. A's speed is how much percent more than B's speed?
- a)12.5%
- b)50%
- c)25%
- d)75%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two trains viz A and B are running on parallel tracks and A is faster ...
Let speed of A and B be a and b respectively.
Then,
⟹ (a + b) = 5(a − b)
⟹ 6b = 4a
i.e., if a=6, b=4
Then,
⟹ (a + b) = 5(a − b)
⟹ 6b = 4a
i.e., if a=6, b=4
Most Upvoted Answer
Two trains viz A and B are running on parallel tracks and A is faster ...
Understanding the problem:
The problem states that Train A is faster than Train B, and when they are moving in the same direction, A passes B in 5/3 minutes. When they are moving in opposite directions, A crosses B in 20 seconds.
Calculating speed:
Let the speed of Train A be x km/h and the speed of Train B be y km/h.
When they are moving in the same direction, the relative speed is x - y km/h. Therefore, in 5/3 minutes (or 100 seconds), A covers the length of B. This can be represented as:
(x - y) * 5/3 * 60 = y * 100
When they are moving in opposite directions, the relative speed is x + y km/h. Therefore, in 20 seconds, A covers the length of B. This can be represented as:
(x + y) * 20 = y * 20
Solving the equations:
From the first equation, we get:
5(x - y) = 3y
5x - 5y = 3y
5x = 8y
x = 8y/5
Substitute x = 8y/5 into the second equation:
(8y/5 + y) * 20 = y * 20
(13y/5) * 20 = y * 20
13y = 5y
y = 5
Therefore, B's speed is 5 km/h and A's speed is 8 km/h.
Calculating percentage increase:
The percentage increase in A's speed compared to B's speed is:
((8-5)/5) * 100 = 60%
Hence, A's speed is 60% more than B's speed, which is closest to option B - 50%.
The problem states that Train A is faster than Train B, and when they are moving in the same direction, A passes B in 5/3 minutes. When they are moving in opposite directions, A crosses B in 20 seconds.
Calculating speed:
Let the speed of Train A be x km/h and the speed of Train B be y km/h.
When they are moving in the same direction, the relative speed is x - y km/h. Therefore, in 5/3 minutes (or 100 seconds), A covers the length of B. This can be represented as:
(x - y) * 5/3 * 60 = y * 100
When they are moving in opposite directions, the relative speed is x + y km/h. Therefore, in 20 seconds, A covers the length of B. This can be represented as:
(x + y) * 20 = y * 20
Solving the equations:
From the first equation, we get:
5(x - y) = 3y
5x - 5y = 3y
5x = 8y
x = 8y/5
Substitute x = 8y/5 into the second equation:
(8y/5 + y) * 20 = y * 20
(13y/5) * 20 = y * 20
13y = 5y
y = 5
Therefore, B's speed is 5 km/h and A's speed is 8 km/h.
Calculating percentage increase:
The percentage increase in A's speed compared to B's speed is:
((8-5)/5) * 100 = 60%
Hence, A's speed is 60% more than B's speed, which is closest to option B - 50%.
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Two trains viz A and B are running on parallel tracks and A is faster than B. If both are moving in same direction, A passes B in 5/3 minutes but when moving in opposite directions, A crosses B in 20 seconds. As speed is how much percent more than Bs speed?a)12.5%b)50%c)25%d)75%Correct answer is option 'B'. Can you explain this answer?
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