# Shortcut Rules to Solve Problems on Trains

## Effective for IBPS PO - SBI PO Exam

**Dear Reader,**

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

**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 ?

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 ?

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 ?

__Answers__**Answer 1. 100 m**

**Answer 2. 25 m**

**Answer 3. 12 sec**

**Answer 4.**

**$4\frac{4}{9}$ seconds**

**Answer 5. 31.5 sec**

**Answer 6.**

**$6\frac{2}{3}$ minutes**

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