## Shortcut Rules to Solve Problems on Train - 3

## 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**

- A train with x km/hr crosses a bridge in T seconds. Another train L metres shorter crosses the same bridge at y km/hr. Time taken by the second train to cross the bridge is given by

$\left[ \frac{x}{y}T-\frac{L}{y\times \frac{5}{18}}
\right]\sec onds.$

**Trick – 2**

- A train meets with an accident $'{{t}_{1}}'$ hours after starting, which detains it for ‘t’ hours, after which it proceeds at $\frac{x}{y}$ of its original speed. It arrives at the destination $'{{t}_{2}}'$ hours late. Had the accident taken place ‘d’ km farther along the railway line, the train would have arrived only $'{{t}_{3}}'$ hours late. The original speed of the train is given by

$\left[
\frac{d\left( 1-\frac{x}{y} \right)}{\frac{x}{y}\left( {{t}_{2}}-{{t}_{3}}
\right)} \right]$ km/hr and The length
of the trip is given by $\left(
\frac{d}{{{t}_{2}}-{{t}_{3}}} \right)\left[ {{t}_{2}}+{{t}_{1}}\left(
\frac{y}{x}-1 \right) \right]km$

**Trick – 3**

- A train covers a distance between station A and B in T1 hours. If the speed is reduced by x km/hr, it will cover the same distance in T2 hours, then the distance between the two station A and B is $\left( \frac{x{{T}_{1}}{{T}_{2}}}{{{T}_{2}}-{{T}_{1}}} \right)km$ and the speed of the train is given by

$\left( \frac{x{{T}_{2}}}{{{T}_{2}}-{{T}_{1}}} \right)km/hr.$

**Trick - 4**

- Two trains are moving in opposite 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

$\frac{5}{18}(x+y)t$
metres

**Trick - 5**

- A train L1 metres in length passes a pole in T1 seconds and another train of the length L2 metres travelling in the same direction in T2 seconds. The speed of the second train is

$\frac{18}{5}\left[
{{L}_{1}}\left( \frac{{{T}_{2}}-{{T}_{1}}}{{{T}_{1}}{{T}_{2}}}
\right)-\frac{{{L}_{2}}}{{{T}_{2}}} \right]km/hr$ OR $\left[
{{L}_{1}}\left( \frac{{{T}_{2}}-{{T}_{1}}}{{{T}_{1}}{{T}_{2}}}
\right)-\frac{{{L}_{2}}}{{{T}_{2}}} \right]m/\sec $

**Trick - 6**

- A train L1 metres in length passes a pole in T1 sec and another train of the same length L2 metres travelling in opposite direction in T2 seconds. Then, the speed of the second train is

$\left[
{{L}_{1}}\left( \frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}{{T}_{2}}}
\right)+\frac{{{L}_{2}}}{{{T}_{2}}} \right]m/\sec $ or $\left[
{{L}_{1}}\left( \frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}{{T}_{2}}}
\right)+\frac{{{L}_{2}}}{{{T}_{2}}} \right]\frac{18}{5}km/hr$

**Questions for Practice****Q1. A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/hr. Find the time taken by the second train to cross the bridge.**

**Q2. . A train meets with an accident 3 hours after starting, which detains it for 1 hours, after which it proceeds at 75% of its original speed. It arrives at the destination 4 hours late. Had the accident taken place 150 km farther along the railway line, the train would have arrived only $3\frac{1}{2}$ hours late. Find the length of the trip and the speed of the train.**

**Q3 A train covers a distance between station A and B in 45 mins. If the speed is reduced by 5 km/hr, it will cover the same distance in 48 mins. What is the distance between the two station A and B (in km)? Also find the speed of the train.**

**Q4. Two trains are moving in opposite direction at 50 km/hr and 40 km/hr. The faster train crosses a man in the slower train in 3 seconds. Find the length of the faster train.**

**Q5. A train 96 metres in length passes a pole in 6 seconds and another train of the length 144 metres travelling in the same direction in 24 seconds. Find the speed of the second train.**

**Q6. A train 100 metres in length passes a pole in 10 sec and another train of the same length travelling in opposite direction in 8 sec. Find the speed of the second train.**

__Answers__**Answer 1. 64 sec**

**Answer 2. 1500 km**

**Answer 3. 60 km**

**Answer 4. 75 m**

**Answer 5.**

**$21\frac{3}{5}km/hr$**

**Answer 6. 54 km/hr**

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