Question

The present age of a father is 3 more than three
times the age of his son 3 years hence the
father's age
will be 10 more than twice the
son find their present age
​

Answer 1

Answer

The present age of son is 10 years and that of the father is 33 years

$\bf\large\underline{Given}$

• The present age of a father is 3 more than 3 times the age of son
• 3 years hence the father's age will be 10 more than twice the age of son

$\bf\large\underline{To \ Find}$

• The present ages of father and son

$\bf\large\underline{Solution}$

Let the present age of son be x years

Therefore , his father's age will be :(3 + 3x) years

$\sf \underline{\underline{Now , according \: to \: question}} :$

$\sf\implies 2(x + 3)+ 10 = 3 + 3x +3 \\\\ \sf\implies 2x + 6 + 10= 3x + 6 \\\\ \sf\implies 3x - 2x = 16 - 6 \\\\ \sf\implies x = 10$

Therefore , the present age of son is 10 years

And that of his father's :

$\sf\longrightarrow 3 + 3\times 10\\\\ \sf\longrightarrow 3 + 10\\\\ \sf\longrightarrow 33$

Therefore , the age of father is 33 years

Answer 2

★ Given : The present age of a father is three years more than three times the age of the son. Three years hence, father's age will be 10 years more than twice the age of the son.

$\rule{130}1$

★ Solution :

Let the age of son be x years and present age of father be (3x + 3) years.

$\rule{130}1$

After 3 years :

$\begin{lgathered}\bullet\:\:\textsf{Sons age = \textbf{x + 3}}\\\bullet\:\:\textsf{Father's age = 3x + 3 + 3 = \textbf{3x + 6}}\end{lgathered}$

$\rule{170}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf 3x + 6 = 10 + 2 ( x + 3) \\\\\\:\implies\sf 3x + 6 = 10 + 2x + 6\\\\\\:\implies\sf 3x + 6 = 16 + 2x\\\\\\:\implies\sf 3x - 2x = 16 - 6\\\\\\:\implies\sf x = 10$

$\rule{170}2$

☯$\underline{\boldsymbol{Present\: Age\:of\: Son\:\&\:Father:}}$

$\begin{lgathered}\bullet\:\:\textsf{Son age = x = \textbf{10 years}}\\\bullet\:\:\textsf{Father age = 3x + 3 = 3(10) + 3 = \textbf{33 years}}\end{lgathered}$