Explanation:

Here's the explanation:

- Let initial number of children = n

- Initial average weight = 40 kg

- 5 children with average 36 kg join: New average stays same as when 5 children with 43.2 kg leave

- So, (Total weight with joiners) / (n + 5) = (Total weight with leavers) / (n - 5)

- Total initial weight = 40n

- After 5 joiners: (40n + 5×36) / (n + 5)

- After 5 leavers: (40n – 5×43.2) / (n – 5)

- Set both expressions equal:

(40n + 180) / (n + 5) = (40n – 216) / (n – 5)

- Cross-multiply and solve:

(40n + 180) × (n – 5) = (40n – 216) × (n + 5)

40n² + 180n – 200n – 900 = 40n² – 216n + 200n – 1080

40n² + 180n – 200n – 900 = 40n² – 216n + 200n – 1080

- Simplify:

40n² – 20n – 900 = 40n² – 16n – 1080

- 40n² cancels out:

–20n – 900 = –16n – 1080

–20n + 16n = –1080 + 900

–4n = –180

n = 45

- The correct answer is Option 1: 45.

- None of the other options fit the equation.