Today, age of the father is twice the sum of the ages of his 3 children. After 15 years father's age will be equal to the sum of the ages of his children. How old is the father 15 years from today?

Correct option is C

Given:

The father's age is twice the sum of the children's ages.

After 15 years, the father's age will equal the sum of the children's ages at that time.

Solution:

Let the current age of father be F, and the ages of three children be $$a$$, $$b$$ and $$c$$.​

The father's age is twice the sum of the children's ages:

F = 2($$a$$ +$$b$$ + $$c$$).

=> $$a$$ + $$b$$ + $$c$$ = $$\frac{F}{2}$$ (Equation 1)

After 15 years, the father's age will equal the sum of the children's ages at that time:

F+15 = ($$a$$ + 15) + ($$b$$ + 15) + ($$c$$ + 15)

=> F+15 = $$a$$ + $$b$$ + $$c$$ +  45

=> F = $$a$$ + $$b$$ + $$c$$ + 30 (Equation - 2)

From the first equation:

put the $$a$$ + $$b$$ + $$c$$ = $$\frac{F}{2}$$in the second equation.

Simplify:

=> F = $$\frac{F}{2}$$+ 30

=> F- $$\frac{F}{2}$$ = 30 => $$\frac{2F-F}{2}$$ = 30 => F =60

The father's age 15 years from today will be:

=> F+15 => 60+15 = 75 years

Thus the correct answer is (C)