# Races and games - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Races and Games is a common topic in Quantitative Aptitude which involves questions related to time, distance, speed, and acceleration. Here are some basic formulas, shortcuts, rules, tricks, and tips for solving Races and Games problems:

1. Speed formula: Speed = ${\text"Distance"}/{\text"Time"}$. If the distance is 'D' and the time taken is 'T', then the speed is given by the formula: Speed = $D/T$.

2. Time formula: Time = ${\text"Distance"}/{\text"Speed"}$. If the distance is 'D' and the speed is 'S', then the time taken is given by the formula: Time = $D/S$.

3. Distance formula: Distance = Speed x Time. If the speed is 'S' and the time taken is 'T', then the distance covered is given by the formula: Distance =$S × T$.

4. If the speed of a person is 'S1' and the speed of another person is 'S2', then the time taken by both persons to cover the same distance is inversely proportional to their speeds. i.e. $(\text"Time taken by Person 1")/(\text"Time taken by Person 2")$ = $(S2)/(S1)$.

5. If two persons A and B start at the same time from two points 'P' and 'Q' respectively and after crossing each other, A takes 't1' hours to reach Q, and B takes 't2' hours to reach P, then the ratio of their speeds is given by the formula: ${S1}/{S2}$ = $√({t2}/{t1})$.

6. If a person covers a certain distance at 'S1' km/hr and the same distance at 'S2' km/hr, then the average speed during the whole journey is given by the formula: (2S1S2)/(S1+S2) km/hr.

7. If the speed of a person is increased by 'x'%, then the time taken to cover the same distance is decreased by $(x/100)$%.

8. If the speed of a person is decreased by 'x'%, then the time taken to cover the same distance is increased by $(x/100)$%.

9. If the ratio of the speeds of two persons A and B is 'm:n', then the ratio of the time taken by them to cover the same distance is 'n:m'.

10. If the speed of a person is 'S' km/hr, and he covers a distance of 'D' km in 'T' hours, then the average speed during the whole journey is given by the formula: Average Speed = 2SD/(S+2×D) km/hr.

These formulas, shortcuts, rules, tricks, and tips can help you solve Races and Games problems quickly and accurately. However, understanding the underlying concepts and practicing regularly are essential for mastering this topic.

Races and games practice test

 Online Test - 1 (Races and games) TAKE TEST Number of questions : 20  |  Time : 30 minutes
 Online Test - 2 (Races and games) TAKE TEST Number of questions : 20  |  Time : 30 minutes