A takes 4 mins 50 secs. while B takes 5 mins. to complete the race. A beats B by `(33) 1/3` metres. Find the length of the course-

Options

A. 1.1 km
B. 100 m
C. 10 km
D. 1000 m

Answer

To solve the problem, we need to find the length of the course based on the information given about the times taken by A and B, and the distance by which A beats B.

### Step-by-step Solution:

1. **Convert A's Time to Seconds:**
- A takes 4 minutes 50 seconds to complete the race.
- Convert this to seconds:
\[ \text{Time taken by A} = 4 \times 60 + 50 = 240 + 50 = 290 \text{ seconds} \]

2. **Convert B's Time to Seconds:**
- B takes 5 minutes to complete the race.
- Convert this to seconds:
\[ \text{Time taken by B} = 5 \times 60 = 300 \text{ seconds} \]

3. **Calculate the Time Difference:**
- The time difference between A and B is:
\[ \text{Time difference} = \text{Time taken by B} - \text{Time taken by A} = 300 - 290 = 10 \text{ seconds} \]

4. **Distance A Beats B:**
- A beats B by \(33 \frac{1}{3}\) meters, which can be converted to an improper fraction:
\[ 33 \frac{1}{3} = \frac{100}{3} \text{ meters} \]

5. **Calculate B's Speed:**
- B covers the distance of \( \frac{100}{3} \) meters in 10 seconds. Therefore, B's speed is:
\[ \text{Speed of B} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{100}{3}}{10} = \frac{100}{30} = \frac{10}{3} \text{ meters per second} \]

6. **Calculate the Total Length of the Course:**
- Since B takes 300 seconds to complete the race, we can find the total length of the course using B's speed:
\[ \text{Length of the course} = \text{Speed of B} \times \text{Time taken by B} = \frac{10}{3} \times 300 = 1000 \text{ meters} \]

### Final Answer:
The length of the course is **1000 meters**.