Explanation:

Let one woman, one man and one children can complete w, m and c units of work in one day
From question
xw × 2y = 1.5mx × y = 2xc × 3y
2w = 1.5m = 6c
Let 2w = 1.5m = 6c = k
So,
w : m : c = 3 : 4 : 1 or 3a : 4a : a (let)
Total work = 45/2×8(1w+1m+1c)
=45/2×8×8a = 1440 a units
According to question
9m × (y + 20) = 1440a
9 × 4 a (y + 20) = 1440 a
y = 20
So, x × w × 2y = 1440 a
x × 3 a × 2 × 20 = 1440 a
x = 12

work completed by 36 women in 4 days
= 36 × 3 a × 4 = 432 a units
After 4 days
Remaining work = 1008 a units
Now in one day work completed by 6 women and 8 men = 32 a + 18 a = 50 a units
Required time = (1008a/50a+4) days =24(4/25) days