# Shortcut Rules to Solve Problems on Time and Distance

## 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**

- If a certain distance is covered at x km/hr and the same distance is covered by y km/hr, then the average speed during the whole journey is

**Trick - 2**

- A person walking at a speed of x km/hr reaches his destination ${{x}_{1}}$ hrs late. Next time he increases his speed by y km/hr, but still he is late by ${{y}_{1}}$ hrs. The distance of his destination from his house is given by

$\left[
\left( {{x}_{1}}-{{y}_{1}} \right)\left( x+y \right)\frac{x}{y} \right]km$

**Trick - 3**

- If a person does a journey in T hours, and the first half at ${{S}_{1}}$ km/hr and the second half at ${{S}_{2}}$ km/hr, then the distance

$=\frac{2\times
time\times {{S}_{1}}\times {{S}_{2}}}{{{S}_{1}}+{{S}_{2}}}$

where, ${{S}_{1}}$ = speed during first half and

${{S}_{2}}$ = speed during second half of journey

**Trick - 4**

- The distance between two stations, A and B is D km. A train starts from A and moves towards B at an average speed of x km/hr. If an another train starts from B, t hours earlier than the train at A, and moves towards A at an average speed of y km/hr, then the distance from A, where the two trains meet is

$\left[
\left( D-ty \right)\left( \frac{x}{x+y} \right) \right]km$

**Trick - 5**

- If a train travelling x km an hour leaves a place and t hours later another train travelling y km an hour, where y>x, in the same direction, then they will be together after travelling $\left[ \frac{t\left( xy \right)}{y-x} \right]km$ from the starting place.

**Trick - 6**

- If the new speed of a person is $\frac{a}{b}$ of the usual speed, then the change in the time taken to cover the same distance is $\left( \frac{b}{a}-1 \right)\times $ usual time or, usual time is given by

$\left[
\frac{change\operatorname{in time}}{\left( \frac{b}{a}-1 \right)} \right]hrs$

**Questions for Practice****Q1. A man covers a certain distance by car driving at 70 km/hr and he returns back to the starting point riding on a scooter at 55 km/hr. Find his average speed for the whole journey.**

**Q2. A boy walking at a speed of 10 km/hr reaches his school 15 minutes late. Next time he increases his speed 2 km/hr, but still he is late by 5 minutes. Find the distance of his school from his house.**

**Q3. A mother car does a journey in 10 hrs, the first half at 21 km/hr and the second half at 24 km/hr. Find the distance.**

**Q4. The distance between two stations, Delhi and Amritsar is 450 km. A train starts at 4 pm from Delhi and moves towards Amritsar at an average speed of 60 km/hr. Another train starts from Amritsar at 3.20 pm and moves towards Delhi at an average speed of 80 km/hr. How far from Delhi will the two trains meet and at what time ?**

**Q5. A train travelling 25 km an hour leaves Delhi at 9 a.m. and another train travelling 35 km an hour starts at 2 p.m. in the same direction. How many km from Delhi will they be together ?**

**Q6. Walking**

**$\frac{3}{4}$ of his usual speed, a person is 10 min late to his office. Find his usual time to cover the distance.**

__Answers__**Answer 1. 61.6 km/hr**

**Answer 2. 10 km**

**Answer 3. 224 km**

**Answer 4. 6.50 p.m.**

**Answer 5.**

**$437\frac{1}{2}km$**

**Answer 6. 30 min**

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