A and B start running at the same time and from the same point around a circle. If A can complete one round in 40 seconds and B in 50 seconds, how many seconds will they take to reach the starting point simultaneously ?

Options

A. 10
B. 200
C. 90
D. 2000

Answer

To solve the problem of when A and B will reach the starting point simultaneously, we need to find the least common multiple (LCM) of the time it takes each of them to complete one round.

### Step-by-Step Solution:

1. **Identify the time taken by A and B**:
- A completes one round in **40 seconds**.
- B completes one round in **50 seconds**.

2. **Find the LCM of 40 and 50**:
- To find the LCM, we can use the prime factorization method.
- **Prime factorization**:
- 40 = \(2^3 \times 5^1\)
- 50 = \(2^1 \times 5^2\)

3. **Determine the LCM using the highest powers of each prime**:
- For the prime number 2, the highest power is \(2^3\) (from 40).
- For the prime number 5, the highest power is \(5^2\) (from 50).
- Therefore, the LCM is calculated as:
\[ \text{LCM} = 2^3 \times 5^2 = 8 \times 25 = 200 \]

4. **Conclusion**:
- A and B will reach the starting point simultaneously after **200 seconds**.

### Final Answer:
The time taken for A and B to reach the starting point simultaneously is **200 seconds**.

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