Question

If twice the son's age in years is added to father's age the sum is 70. If twice the father's age is added to the son's age, the sum is 95. What are the ages of the father and the son
Message @Reaper

Answer 1

Answer:

The ages of father and son are 40 years and 15 years respectively.

Given:

• Twice the son's age in years is added to father's age the sum is 70.

• Twice the father's age is added to the son's age, the sum is 95.

To find:

• The ages of father and son.

Solution:

Let age of father be x years and son's age be y years.

According to the first condition.

x+2y=70...(1)

According to the second condition.

2x+y=95...(2)

Add equations (1) and (2), we get

x+2y=70

+

2x+y=95

____________

3x+3y=165

>> 3(x+y)=165

>> x+y=165/3

>> x+y=55...(3)

Subtract equation (2) from equation (1), we get

2x+y=95

-

x+2y=70

___________

x-y=25...(4)

Add equations (3) and (4), we get

x+y=55

+

x-y=25

__________

2x=80

>> x=80/2

>> x=40

Substitute x=40 in equation (3), we get

>> 40+y=55

>> y=55-40

>> y=15

The ages of father and son are 40 years and 15 years respectively.