# Shortcut Rules to Solve Problems on Trains

## Effective for IBPS PO - SBI PO Exam

Here we will start a series of Quantitative Aptitude Shortcut Tricks for your upcoming SBI - IBPS - SSC and Other Government Competitive Exams. We will try to cover up all topics of the quantitative Aptitude Sections from which question was generally asked.

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Trick - 1

• Two trains are moving in the same direction at x km/hr and y km/hr (where x>y). If the faster train crosses a man in the slower train in 't' seconds, then the length  of the faster train is given by

$\left[ \frac{5}{18}\left( x-y \right)t \right]metres$
Trick - 2
• A train running at x km/hr takes ${{t}_{1}}$ seconds to pass a platform. Next it takes ${{t}_{2}}$ seconds to pass a man walking at y km/hr in the opposite directions, then the length of the train is $\left[ \frac{5}{18}\left( x+y \right){{t}_{2}} \right]$ meters and that of the platform is

$\frac{5}{18}\left[ x\left( {{t}_{1}}-{{t}_{2}} \right)-y{{t}_{2}} \right]metres$
Trick - 3
• If L metres long train crosses a bridge or a platform  of length ${{L}_{1}}$ metres in T seconds, then the time taken by train to cross a  pole is given by

$\left( \frac{L\times T}{L+{{L}_{1}}} \right)\sec onds$
Trick - 4
• Two trains of the same length but with different speeds pass a static pole in ${{t}_{1}}$ seconds and ${{t}_{2}}$ respectively. They are moving in the opposite directions. The time they will taken to cross each other is given by

$\left( \frac{2{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}} \right)$second
Trick - 5
• Two trains of the length ${{l}_{1}}$ and ${{l}_{2}}$ metres respectively with different speeds pass a static pole in ${{t}_{1}}$ seconds and ${{t}_{2}}$ seconds respectively. When they are moving in the same direction, they will cross each other in

$\left[ \frac{\left( {{l}_{1}}+{{l}_{2}} \right){{t}_{1}}{{t}_{2}}}{{{t}_{2}}{{l}_{1}}-{{t}_{1}}{{l}_{2}}} \right]\sec onds$
Trick - 6
• Two stations A and B are D km apart on a straight line. A train starts from A and travels towards B at x km/hr. Another train, starting from B 't' hours earlier, travels towards A at y km/hr. The time after which the train starting from A will meet the train starting from B is

$\left( \frac{D-ty}{x+y} \right)hours$

Questions for Practice

Q1. Two trains are moving in the same direction at 50 km/hr and 30 km/hr. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train.

Q2. A train running at 25 km/hr takes 18 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 5 km/hr in the opposite directions. Find the length of the train and that of the platform.

Q3. 120 metres long train crosses a tunnel of length 80 metres in 20 seconds. Find the time for train to cross a  man standing on a platform of length 130 metres.

Q4. Two trains of the same length but with different speeds pass a static pole in 4 seconds and 5 seconds respectively. In what time will they cross each when they are moving in the opposite directions.

Q5. Two trains of the length 100m and 125m respectively with different speeds pass a static pole in 4 seconds and 7 seconds respectively. In what time will they  cross each other when they are moving in the same direction ?

Q6.
Two stations A and B are 110 km apart on a straight line. A train starts from A and travels towards B at 40 km/hr. Another train, starting from B 2 hours earlier, travels towards A at 50 km/hr. when will the first train meet to the second train ?

Answer 4. $4\frac{4}{9}$ seconds
Answer 6. $6\frac{2}{3}$ minutes 