Question

Q. The sum of the ages of a father and his son is 40 years.If they both live on till the son becomes as old as the father is now the sum of their ages will be 96 years.Find their present ages.

Answer 1

Answer:

The sum of the ages of a father and his son is 40 years.If they both live until

the son becomes as old as the father is now, the sum of their ages will be 96 years .

Find their present ages.

:

Let f = father's age

Let s = son's age

:

Write an equation for each statement.

"The sum of the ages of a father and his son is 40 years.'

f + s = 40

s = (40-f)

:

If they both live until the son becomes as old as the father is now, the sum of their ages will be 96 years. "

f + f + (f-s) = 96

2f + (f-s) = 96

3f - s = 96

3f -(40-f) = 96

3f - 40 + f = 96

4f = 96 + 40

4f = 136

f = 136/4

f = 34 is father's age

then

40 - 34 = 6 yrs is son's age

:

:

Check this: the dif in their ages 34-6 = 28;

34 + 28 + 6 + 28 = 96

Answer 2

Step-by-step explanation:

let the father age be x and son age be y.

Now,The sum of the ages of a father be 40

i.e x+y = 40

or, x = 40 -y.................1

and

if the age of the sum is equation to the fathers age,the son of the age is 96years.

i.e x + (x-y) + y +(x-y) = 96

or, x + x -y + y +x - y = 96

or, 3x - y = 96.............(ii)

Put value of x from equation (i) in equation (ii), we get,

or,3(40−y)−y=96

or,120−3y−y=96

or,120−4y=96

or,120−96=4y

or,24=4y

∴y = 6

Put value of y in equation (i), we get,

or,x=40−6

∴x=34

So, (x,y) = (34,6)

Therefore, the required present ages of the father and the son are 34 years and 6 years, respectively.