Question: Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in the opposite direction. Find the speed of the faster train.

1. 30 kmph
2. 35 kmph
3. 42 kmph
4. 50 kmph
5. 84 kmph

Answer: C
Solution and Explanation:
Approach Solution 1:
To solve this GMAT problem-solving question, you must use the information given in the question. The problems in this group come from many different areas of mathematics. This one has a lot to do with speed and distance.
The options are set up in a way that makes it hard to pick the best one. The candidates must know the right way to get the response they need. Only one of the five choices given is correct.
Given in the question that if two trains are moving in the same direction and are each 100 meters long, it takes them 60 seconds and 10 seconds, respectively, to cross each other. Find the faster train's speed.
- Assume that trains move at speeds S1 and S2.
Total Distance = the combined length of both trains Time taken: T1 = 60 seconds; T2 = 10 seconds. 100+100 = 200 m.
- S1+S2 = 200/10 => 20 m/s .…
- S1-S2 = 200/60 => 10/3 m/s .…
- By adding (1) and (2), we obtain S1 = 35/3 m/s and S2 = 25/3 m/s.
- The faster train's speed (in Kmph) is 35/3*18/5 = 42 Kmph.
C is the correct answer.

Approach Solution 2:
To solve this GMAT problem-solving question, you must use the information given in the question. The problems in this group come from many different areas of mathematics. This one has a lot to do with algebra.
The options are set up in a way that makes it hard to pick the best one. The candidates must know the right way to get the response they need. Only one of the five choices given is correct.
Given in the question that if two trains are moving in the same direction and are each 100 meters long, it takes them 60 seconds and 10 seconds, respectively, to cross each other. Find the faster train's speed.
Let v1 and v2 be the difference between the two speeds, such that v1> v2
Same direction: If we consider v2 to be stationary, the faster train's speed is functionally equal to v1 - v2. To completely pass the slower train, the quicker train must travel 200 meters (since each train is 100 meters long).
200/ (v1-v2) = 60
The speed of the opposing train is effectively v1 + v2 if we assume either as stationary.
We have v1 + v2 = 20 m/s and v1 - v2 = 10/3 m/s from these two equations we can get,
2*v1 = 70/3 m/s and v1 = 35/3 m/s
After converting this value to km/hr we will get an answer as 42 km/hr
C is the correct answer.

Approach Solution 3:
Given in the question that if two trains are moving in the same direction and are each 100 meters long, it takes them 60 seconds and 10 seconds, respectively, to cross each other. Find the faster train's speed.
In both circumstances, the distance is the same.
60 x 200/relative speed (In the same direction)
200/x - y = 60
x - y = 200/60
= 10/3————-(1)
200/x + y = 10
x + y = 20 ————- (2)
Taking into account equations (1) and (2), 2 x = 20 + 10/3
2 x = 60 + 10/3
x = 35/3(18/5) = 42 KMPH
C is the correct answer.

“Two trains, each 100 meters long take 60 seconds to cross each other" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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