Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
- 3:1
- 1:3
- 3:2
- 2:3
- 5:3
“Two Trains Running in Opposite Directions Cross a Man Standing on the Platform”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation
Approach Solution 1:
Explanation:
Let us consider that
- r = speed of train 1,
- s = speed of train 2,
- t = the length of train 1, and
- u = the length of train 2.
We know that speed x time = distance covered.
Considering the above formula to solve the problem, we have
- r x 27 = t
- s x 17 = u And
- (r + s) x 23 = t + u
If we add the first two equations, we have: 27r + 17s = t + u.
If we simplify the third equation, we have 23r + 23s = t + u.
Since both new equations are equal to t + u, we can equate them:
27r + 17s = 23r + 23s
4r = 6s
r/s = 6/4 = 3/2
=> 3:2
Hence, the correct option is C.
Correct Answer: C.
Approach Solution 2:
Explanation:
We will solve this problem using the S=D/T rule.
We can get the lengths of each train (thinking of it as the distance here).
Therefore, for Train 1
Let X be speed
The distance becomes (D=T*S, 27X)
For train 2 it will be 17Y
We know that the time of them combined is 23 then their combined speed would be
S=D/T >> T=D/S
23=(27X+17Y)/(x+y)
27x+17y = 23 x+23y
4x=6y
X/Y = 6/4 = 3/2
Hence, the ratio is 3:2
Correct Answer: C.
Approach Solution 3:
Explanation:
Let the man stand at their meeting point in the beginning.
After 17 secs, train II would have crossed him and Train I would have another 10secs to go. Train II helps getting down these 10 secs to 6 secs
These 10 seconds are covered in the ratio 6:4, so 3:2
We will follow the weighted average method.
t27/t17
= (23-17) / (27-23)
=6/4
=3/2
Correct Answer: C
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