Since the product of the children is 36, all the ages are factors of 36.
Factors of 36 are: 2,3,4,6,9,12,18,36
Since there are twins, one number is repeated two times.
If 2 gets repeated, then ages will be 2,2,9 (possible)
If 3 gets repeated, then ages will be 3,3,4 (possible)
If 4 gets repeated, then ages will be 4,4, 36/16 (not possible since the twins are elder but it is given that younger are twins)
So two possible solutions are
2+2+9 = 13
3+3+4 = 10
The room number can be 13 or 10.