Question

the sum of ages of the father and son is 80 years.if 10 years ago the age of the father was 3 times that of his son.find the present age of his son.

Answer 1

Let age of father be x
And age of son be y

From the question;
x+y=80
=>x=80-y —>(1)

TEN YEARS AGO:-

Fathers age = x-10
Son age = y-10

From the question;
X-10=3(y-10)
X-10=3y-30
X-3y= -20 —>(2)

Put (1) in (2)

80-y-3y= -20
-4y =-80-20
X=100/4=25

Son age = 25
Fathers age = 55

Hope you this is right

Answer 2

The present age of the son is 25 years old

Given:

Sum of ages = 80 years

10 years ago father's age was 3 times his son's.

To find:

The present age of the son.

Solution:

Let us assume the age of the son as X and the age of the father as Y.

As we know the sum of the ages of father and son is 80 years

So, X + Y = 80

Y = 80 - X

Given that 10 years ago the age of the father was 3 times that of the son.

10 years ago their ages were X - 10 and Y - 10

So, Y - 10 = 3 (X - 10) + 10

Y = 3 (X - 10) + 10

Y = 3X -30 + 10

Y = 3X - 20

Let us equate the two equations in place of Y

3X - 20 = 80 - X

4X = 80 + 20

4X = 100

X = 25

The age of the father can be calculated through one of the equations.

X + Y = 80

25 + Y = 80

Y = 55

The age of the father is 55 years.

Therefore the age of the son is 25 years old.

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