The sum of the ages of father and his son is 60 years. After 15 years, father will be twice as old as his son. Their present ages are :

Correct option is B

Given:

The sum of the ages of a father and his son is 60 years. After 15 years, the father will be twice as old as his son. Find their present ages.

Solution:

Define Variables

Let the present age of the son be x years, and the present age of the father be y years.

From the given information, we can write two equations:

1. The sum of their ages is 60 years:

x + y = 60

2. After 15 years, the father will be twice as old as the son:

y + 15 = 2(x + 15)

Solve the Equations

From Equation (1), we can express y in terms of x:

y = 60 - x

Substitute y = 60 - x into Equation (2):

(60 - x) + 15 = 2(x + 15)

Simplify:

75 - x = 2x + 30

Combine like terms:

75 - 30 = 3x

45 = 3x

Solve for x:

x = 15

Find the Value of y

Substitute x = 15 into Equation (3):

y = 60 - x

y = 60 - 15

y = 45

Present age of the son x = 15 years.

Present age of the father y = 45 years.

After 15 years:

Son's age = 15 + 15 = 30

Father's age = 45 + 15 = 60

Since 60 = $$2 \times 30$$​, the solution is correct.

Final Answer:

The present ages are:

Father: 45 years.

Son: 15 years.