Question

The sum of the ages of a father and son is 52 years.Five years ago, the age of
the father was five times the age of the son. Find their present age?​

Answer 1

Answer:

Let the age of father be x and his son be y.

According to the question;

x + y = 52 ..... (i)

5 years ago,

Father's age = x - 5

Son's age = y - 5

So, the equation will be :-

x - 5 = 5(y - 5)

⇒ x - 5 = 5y - 25

⇒ x - 5y = - 25 + 5

⇒ x - 5y = - 20 ...... (ii)

Subtracting equation (i) and (ii),

x + y - ( x - 5y ) = 52 - (-20)

⇒ x + y - x + 5y = 52 + 20

⇒ 6y = 72

⇒ y =72/6

⇒ y = 12

Putting the value of y in (i),

x + y = 52

⇒ x + 12 = 52

⇒ x = 52 - 12

⇒ x = 40

Hence,

• Father's age = 40 years
• Son's age = 12 years

_______________________

Answer 2

The present ages of the father and son is 44 years and 8 years respectively.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here, according to the given information, we are given that,

The sum of the ages of a father and son is 52 years.

This means that, the age of the father is x and the age of the son is (52-x).

Five years ago, the age of the father was (x-5).

Then, we get,

$x-5 = 5(52-x).$

Or, $x-5 = 260-5x$

Or, $6x = 265$

Or, x = 44.

Then, the age of the son = 52 - 44 = 8.

Hence, the present ages of the father and son is 44 years and 8 years respectively.

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