Total work in boy-days = 9 x 360 = 3240; man-days = 18 x 72 = 1296; woman-days = 12 x 162 = 1944.
Combined rate of 4 men + 12 women + 10 boys (per day) = 4/1296 + 12/1944 + 10/3240.
Using LCM 19440: 60/19440 + 120/19440 + 60/19440 = 240/19440 = 1/81.
So they finish in 81 days.