Neela, Saroj and Paulami start running around a circular stadium and complete one round in 10 seconds, 6 seconds and 14 seconds respectively. In how much time will they meet again at the starting point ?

Options

A. 3 minutes 30 seconds
B. 2 minutes 28 seconds
C. 4 minutes 45 seconds
D. 1 minute 40 seconds

Answer

To find out when Neela, Saroj, and Paulami will meet again at the starting point, we need to determine the least common multiple (LCM) of their individual times to complete one round.

1. **Identify the time taken by each runner:**
- Neela: 10 seconds
- Saroj: 6 seconds
- Paulami: 14 seconds

2. **Find the LCM of the three times:**
- First, we find the prime factorization of each time:
- 10 = 2 × 5
- 6 = 2 × 3
- 14 = 2 × 7

- Now, we take the highest power of each prime number:
- For 2: the highest power is \(2^1\) (from all three)
- For 3: the highest power is \(3^1\) (from 6)
- For 5: the highest power is \(5^1\) (from 10)
- For 7: the highest power is \(7^1\) (from 14)

3. **Calculate the LCM:**
- LCM = \(2^1 \times 3^1 \times 5^1 \times 7^1\)
- LCM = \(2 \times 3 \times 5 \times 7\)
- LCM = \(210\) seconds

4. **Convert seconds into minutes:**
- Since 1 minute = 60 seconds, we convert 210 seconds into minutes:
- \(210 \div 60 = 3\) minutes and \(30\) seconds.

Thus, Neela, Saroj, and Paulami will meet again at the starting point after **3 minutes and 30 seconds**.