Question

Seven years ago, father was seven times as old as his son was.Three years hence,he will be three times as old as his son. Find their present age.

Answer 1

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Answer 2

$\large\textsf{\textcolor{red}{Let the present age of :-}}$

$\large\leadsto\textsf{\textcolor{green}{Father be ' x ' years }}$

$\large\leadsto\textsf{\textcolor{green}{Son be ' y ' years }}$

$\large\textsf{\textcolor{red}{Seven years ago the age of :-}}$

$\large\leadsto\textsf{\textcolor{green}{Father is ( x - 7 ) years }}$

$\large\leadsto\textsf{\textcolor{green}{Son is ( y - 7 ) years }}$

$\large\textsf{\textcolor{red}{According to the given conditions :-}}$

$\large\therefore\textsf{\textcolor{green}{ 7 ( y - 7 ) = ( x - 7 )}}$

$\large\therefore\textsf{\textcolor{green}{ 7y - 49 = ( x - 7 )}}$

$\large\therefore\textsf{\textcolor{green}{ 7y - 49 + 7 = x}}$

$\large\therefore\textsf{\textcolor{green}{ 7y - 42 = x ...........( i )}}$

$\large\textsf{\textcolor{red}{After three years their age will be :-}}$

$\large\textsf{\textcolor{green}{Father's age will be ( x + 3 ) years}}$

$\large\textsf{\textcolor{green}{ Son's age will be ( y + 3 ) years}}$

$\large\textsf{\textcolor{red}{By the given conditions:-}}$

$\large\therefore\textsf{\textcolor{green}{3 ( y + 3 ) = ( x + 3 )}}$

$\large\therefore\textsf{\textcolor{green}{3y + 9 = x + 3}}$

$\large\therefore\textsf{\textcolor{green}{3y + 9 - 3 = x}}$

$\large\therefore\textsf{\textcolor{green}{3y + 6 = x .......... ( ii )}}$

$\large\textsf{\textcolor{red}{Combining ( i ) and ( ii )}}$

$\large\therefore\textsf{\textcolor{green}{7y - 42 = 3y + 6}}$

$\large\therefore\textsf{\textcolor{green}{ 7y - 3y = 6 + 42}}$

$\large\therefore\textsf{\textcolor{green}{4y = 48}}$

$\large\therefore\textsf{\textcolor{green}{y = 48/4}}$

$\large\therefore\textsf{\textcolor{green}{ y = 12 ........ ( iii )}}$

$\large\textsf{\textcolor{red}{Substituting the value of ' y ' in ( ii ) :-}}$

$\large\therefore\textsf{\textcolor{green}{3y + 6 = x}}$

$\large\therefore\textsf{\textcolor{green}{3 × 12 + 6 = x}}$

$\large\therefore\textsf{\textcolor{green}{36 + 6 = x}}$

$\large\therefore\textsf{\textcolor{green}{42 = x}}$

$\large\therefore\textsf{\textcolor{green}{x = 42}}$

$\large\boxed{\therefore\textsf{\textcolor{orange}{Present age of father = 42 years}}}$

$\large\boxed{\therefore\textsf{\textcolor{orange}{Present age of son = 12 years}}}$