If 3 times the mother's present age is 36 years more than 5 times her daughter's age, and 3 times the daughter's age is 4 years less than the mother's age, then what is the difference (in years) between the present ages of the mother and the daughter?

Correct option is C

Given:

3 times the mother's present age is 36 years more than 5 times her daughter's age.

3 times the daughter's age is 4 years less than the mother's age.

​Solution:​

Let the present age of the mother be m years and the present age of the daughter be d years.

From the first statement:
3m = 5d + 36 (Equation 1)
From the second statement:
3d = m - 4 (Equation 2)

From Equation 2: m = 3d + 4

Substitute ( m = 3d + 4 ) in Equation 1:
3(3d + 4) = 5d + 36
9d + 12 = 5d + 36
9d - 5d = 36 - 12
4d = 24
d = 6

Now, substitute d = 6 in m = 3d + 4:
m = 3(6) + 4 = 18 + 4 = 22

The difference in their ages:
m - d = 22 - 6 = 16  years