At present age of father is 3 years more than three times of the age of the son. After three years , the age of father age will be 10 years more than twice the age of the son. Now find their present age.

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At present age of father is 3 years more than three times of the age of the son. After three years , the age of father age will be 10 years more than twice the age of the son. Now find their present age.

Let’s the present ages of the father as a years and that of his son’s age as b years.

According to the question,,

The present age of father is three years more than three times the age of the son.

So, the equation formed is

$a=3b+3$

$a-3b-3=0$ …….. (i)

Now from the question it’s given as,

After 3 bears, father’s age will be $(a+3)$ years and son’s age will be $(b+3)$ years.

Therefore, the relation between their ages after 3 years is given below

$a+3=2(b+3)+10$

$a-2b-13=0$ …….. (ii)

Now, solving (i) and (ii), we get the solution

Using cross-multiplication method, then

$\begin{array}{l} \frac{A}{{( - 3) \times ( - 13) - ( - 2) \times ( - 3)}} = \frac{{ - B}}{{1 \times ( - 13) - 1 \times ( - 3)}} = \frac{1}{{1 \times ( - 2) - 1 \times ( - 3)}}\\ \frac{A}{{39 - 6}} = \frac{{ - B}}{{ - 13 + 3}} = \frac{1}{{ - 2 + 3}}\\ \frac{A}{{33}} = \frac{{ - B}}{{ - 10}} = 1\\ \frac{A}{{33}} = \frac{B}{{10}} = 1 \end{array}$