Explanation
Work done by 12 children in 16 days = 1 (full work)
Work done by 1 child in 16 days = 1/12
Work done by 1 child in 1 day = 1/(12 × 16) = 1/192
Work done by 8 adults in 12 days = 1
Work done by 1 adult in 12 days = 1/8
Work done by 1 adult in 1 day = 1/(8 × 12) = 1/96
Work done by 16 adults in 3 days = 16 × 3 × (1/96) = 1/2
Remaining work = 1 - 1/2 = 1/2
Now, 6 adults and 4 children work together:
Work done by 6 adults in 1 day = 6 × 1/96 = 6/96 = 1/16
Work done by 4 children in 1 day = 4 × 1/192 = 4/192 = 1/48
Total work done per day = (1/16 + 1/48) = (3 + 1)/48 = 4/48 = 1/12
Days required = (1/2) ÷ (1/12) = 6 days