Races and Games: Key Concepts
| No. | Term | Definition / Description |
| 1 | Race | A contest of speed in running, riding, driving, sailing, or rowing. |
| 2 | Race Course | The ground or path on which the contest takes place. |
| 3 | Starting Point | The specific point from which a race begins. |
| 4 | Winning Point (Goal) | The point set to mark the end of the race. |
| 5 | Winner | The first person to reach the winning point. |
| 6 | Dead Heat Race | A race where all contestants reach the goal at exactly the same time. |
Understanding “Starts” and “Beats”
These concepts are crucial for solving aptitude problems involving two contestants (A and B).
| Scenario | Meaning | Mathematical Interpretation |
| A gives B a start of $x$ metres | B starts $x$ metres ahead of A. | To finish a 100m race: A covers 100m, B covers (100 – $x$)m. |
| A beats B by $x$ metres | A reaches the goal while B is still $x$ metres away. | While A runs 100m, B runs (100 – $x$)m. |
| A beats B by $t$ seconds | A reaches the goal $t$ seconds before B. | A’s time = $T$; B’s time = $T + t$. |
| Game of 100 | A contest where the first to score 100 points wins. | The winner is the one who reaches 100 first. |
| A gives B $x$ points | A scores 100 points while B scores only $(100 – x)$ points. | Ratio of scores = $100 : (100 – x)$. |
Example Calculation
If in a 100m race, A gives B a start of 12m, the distances covered are:
- Distance covered by A: $100\text{ m}$
- Distance covered by B: $100 – 12 = 88\text{ m}$
