Question

age of father is 30 years more than that of his son, 5 years hence fathers age will be thrice of his sons age. find their present ages

Answer 1

Given that, age of father is 30 years more than that of his son.

☯ Let's consider that the age of his son be x.

$:\implies\sf Father's \ age = (x + 30)$

• After five years, age of son would be (x + 5).
• And, father's age would be (x + 35)

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⠀⠀$\underline{\bigstar\:\boldsymbol{According \ to \ Question\::}}$

• After five years, hence father's age will be thrice of his sons age.

$:\implies\sf 3(x + 5) = (x + 35) \\\\\\:\implies\sf 3x + 15 = x + 35 \\\\\\:\implies\sf 3x - x = 35 - 15\\\\\\:\implies\sf 2x = 20\\\\\\:\implies\sf x = \dfrac{\cancel{20}}{\cancel{\: 2}}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 10}}}}}$

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Now,

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• Present age of son, x = 10 years.
• Present age of his father (x + 30), = 30 + 10 = 40 years.

$\therefore\:{\underline{\sf{The\: Present \ ages \ of \ son \ and \ his \ father \ is \ {\textsf{\textbf{10 and 40 years.}}}.}}}$⠀

Answer 2

$\huge {\underline{\bf{Answer:}}}$

$\large \frak {\underline{\red{From \: the \: Above \: Question:}}}$

$\mapsto\sf{Present \: age \: of \: son \: = \bf x}$

${ \mapsto{\sf{Present \: age \: of \: his \: father \: = \bf x + 30}}}$

$\underline {\bf{After \: 5 \: years,}}$

$\mapsto\sf{Age \: of \: son \: = \bf x + 5}$

${ \mapsto{\sf{Age \: of \: his \: father \: = \bf x + 30 + 5 = x + 35}}}$

$\large \frak {\underline{\red{According \: to \: Question::}}}$

${ \implies{\sf{Age \: of \: son= \bf 3(x + 5) = Age \: of \: his \: father = \bf x + 35}}}$

${\implies \sf{3(x + 5) = x + 35}}$

${\implies \sf{3x + 15= x + 35}}$

${\implies \sf{3x - x= 35 - 15}}$

$\implies \sf{2x =20 }$

$\implies \sf{x = \frac{20}{2} }$

$\implies \sf{x = \cancel\frac{20}{2} = 10}$

$\underline {\bf{Then, }}$

${\rightarrow\sf{Present \: age \: of \: son \: = x = 10 years}}$

${ \mapsto{\sf{Present \: age \: of \: his \: father \: = x + 30 = 10 + 30 = 40years}}}$

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