Question: Two trains are moving in the opposite directions on parallel tracks at the speeds of 64 km/hr and 96 km/hr respectively. The first train passes a telegraph post in 5 seconds whereas the second train passes the post in 6 seconds. What is the time taken by the trains to cross each other completely?
- 3 seconds
- \(4\frac45\)seconds
- \(5\frac3 5\)seconds
- \(5\frac45\)seconds
- 6 seconds
Correct Answer: C
Solution and Explanation:
Approach Solution 1:
In 5 seconds, the length of the train that passes through Telegraph will be.
\(L1=64*\frac{5}{3600}\)
Similarly
\(L2=96*\frac{6}{3600}\)
Trains take a certain amount of time to fully cross one another, which will be
\(\frac{l1+;2}{c1+v2}\)
\(\frac{96*\frac{6}{3600}+64*\frac{5}{3600}}{64+96}\)
\(\frac{96*\frac{6}{3600}+64*\frac{5}{3600}}{160}\)
\(\frac{896}{3600*160}\)hrs
Converting hrs to second
\(\frac{896}{160}\) seconds
\(5\frac{3}{5}\)seconds
Approach Solution 2:
There is another approach to answering this question:
Remember that we multiply \(\frac{5}{18}\) to convert km/hr to m/s
Now Length of First Train T1 = 64 * \(\frac{5}{18}\) * 5
Now Length of second Train T2 = 96* \(\frac{5}{18}\) * 6
Evaluating further Total crossing time, with T1 and T2 moving in opposing directions,will be
\(\frac{combined length}{speed}\)
\(\frac{64-5+96*6}{64+96}\)
\(\frac{896}{160}\)
\(5\frac{3}{5}\)seconds
“Two trains are moving in the opposite directions on parallel tracks at”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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