In a 100 m race, A covers the whole distance in 36 seconds and B in 45 seconds. In this race, A beats B by

### Concept & Relative Distance In a race, the winner completes the full distance, while the loser covers a proportionally smaller distance in the winner's time. We calculate the distance the loser covers during the winner's time to find the winning margin. ### Step-by-Step Solution - **Given:** Distance = $100$ m, Time of $A$ = $36$ s, Time of $B$ = $45$ s. - $A$ finishes the race in $36$ seconds. - Speed of $B = \frac{\text{Distance}}{\text{Time of } B} = \frac{100}{45}$ m/s. - Distance covered by $B$ in $A$'s time ($36$ seconds) is: $$ \text{Distance} = \frac{100}{45} \times 36 = 100 \times \frac{4}{5} = 80 \text{ m} $$ - Therefore, $A$ beats $B$ by $100 - 80 = 20$ m. ### Exam Strategy & Shortcut Instead of calculating full speeds, use the ratio of times. $B$ takes $45$s for $100$m. In $36$s, $B$ covers $\frac{36}{45} = \frac{4}{5}$ of the track. $\frac{4}{5}$ of $100$ is $80$m. The gap is $20$m. ### Common Pitfall A common mistake is finding the difference in time ($9$ seconds) and subtracting it directly from distance options, confusing the units of measurement. ### Final Answer Therefore, the correct answer is **20 m**.