GMAT Problem Solving - Two Trains Running in Opposite Directions Cross a Man Standing on the Platform

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:

  1. 3:1
  2. 1:3
  3. 3:2
  4. 2:3
  5. 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

Suggested GMAT Problem Solving Samples

Fees Structure

CategoryState
General15556

In case of any inaccuracy, Notify Us! 

Comments


No Comments To Show