Aman can run a distance in 190 seconds and Shakti can run the same distance in 200 seconds.if they start together by what distance can Aman beat Shakti in 1 km race?

Options

A. 48 m
B. 25 m
C. 24 m
D. 50 m

Answer

To solve the problem, we need to find out how much distance Aman can cover compared to Shakti in a 1 km race.

### Step-by-Step Solution:

1. **Determine the speeds of Aman and Shakti**:
- Aman takes 190 seconds to run a certain distance (let's assume it's 1 unit distance).
- Shakti takes 200 seconds to run the same distance.

To find their speeds, we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Let's assume the distance they both run is 1 unit. Therefore, the speeds are:
- Speed of Aman = \( \frac{1 \text{ unit}}{190 \text{ seconds}} \)
- Speed of Shakti = \( \frac{1 \text{ unit}}{200 \text{ seconds}} \)

2. **Convert their speeds to a common unit (km/h)**:
- To convert seconds to hours, we know that 1 hour = 3600 seconds.
- Speed of Aman in km/h:
\[ \text{Speed of Aman} = \frac{1 \text{ unit}}{190 \text{ seconds}} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} = \frac{3600}{190} \text{ km/h} \]
- Speed of Shakti in km/h:
\[ \text{Speed of Shakti} = \frac{1 \text{ unit}}{200 \text{ seconds}} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} = \frac{3600}{200} \text{ km/h} \]

3. **Calculate the speeds**:
- Speed of Aman:
\[ \text{Speed of Aman} = \frac{3600}{190} \approx 18.95 \text{ km/h} \]
- Speed of Shakti:
\[ \text{Speed of Shakti} = \frac{3600}{200} = 18 \text{ km/h} \]

4. **Find the time taken by both to complete 1 km**:
- Time taken by Aman to run 1 km:
\[ \text{Time} = \frac{1 \text{ km}}{\text{Speed of Aman}} = \frac{1}{\frac{3600}{190}} = \frac{190}{3600} \text{ hours} \approx 0.05278 \text{ hours} \approx 190 \text{ seconds} \]
- Time taken by Shakti to run 1 km:
\[ \text{Time} = \frac{1 \text{ km}}{\text{Speed of Shakti}} = \frac{1}{\frac{3600}{200}} = \frac{200}{3600} \text{ hours} \approx 0.05556 \text{ hours} \approx 200 \text{ seconds} \]

5. **Calculate the difference in time**:
- Difference in time = Time taken by Shakti - Time taken by Aman:
\[ \text{Difference} = 200 \text{ seconds} - 190 \text{ seconds} = 10 \text{ seconds} \]

6. **Calculate the distance Aman covers in that time**:
- Distance covered by Aman in 10 seconds:
\[ \text{Distance} = \text{Speed of Aman} \times \text{Time} = \frac{1 \text{ unit}}{190 \text{ seconds}} \times 10 \text{ seconds} = \frac{10}{190} \text{ units} \approx 0.05263 \text{ units} \]
- Since 1 unit represents 1 km, Aman beats Shakti by approximately 0.05263 km or 52.63 meters.

### Final Answer:
Aman can beat Shakti by approximately **52.63 meters** in a 1 km race.