Question

a man is 30 times older than his son.18 years later he will be only trice as old as his son.what is man's present age ​

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\sf\textsf{Given}\\\underline{\textit{Statement-1:}}\\\sf\textsf{A man is 30 times older than his son}\\\underline{\textit{Statement-2:}}\\\sf\textsf{18 years later, he will be only thrice}\\\sf\textsf{as old as his son}$

$\underline{\LARGE{\texttt{Step-1:}}}}$

$\sf\textsf{Assume a variable for Present Ages of Man and His Son}$



$\sf\textsf{Let the Present Age of Son be \textbf{x\: years}}$

$\sf\textsf{Let Present Age of Man be \textbf{y\: years}}$



$\underline{\LARGE{\texttt{Step-2:}}}}$

$\sf\textsf{Rewrite Statement-1}$



$\textsf{y= 30x}$ ———[1]



$\underline{\LARGE{\texttt{Step-3:}}}}$

$\sf\textsf{Note the Age of Man and his son after 18 years}$



$\begin{aligned}\sf\textsf{Age of Man after 18 years} &\; \sf\textsf{= Present Age of Man + 18} \\\\\sf\textsf{Age of Son after 18 years} &\; \sf\textsf{= Present Age of Son + 18}\\\\\implies \textsf{Age of Man after 18 years} & =\; \textbf{y + 18}\\\\\implies \sf\textsf{Age of Son after 18 years}&=\; \textbf{x+18}\end{aligned}$



$\underline{\LARGE{\texttt{Step-4:}}}}$

$\sf\textsf{Rewrite Statement-2}$



$\begin{aligned} \sf{(y+18)} &\; = \sf3(x+18)\\\\\implies \sf y +18 &\; = \sf 3x + 54\\\\\implies y-3x &\; = \sf54-18 \\\\\implies \sf y -3x &\; = \sf36\end{aligned}$

$\sf\textsf{y -3x = 36}$ ———[2]



$\underline{\LARGE{\texttt{Step-5:}}}}$

$\sf\textsf{Substitute [1] in [2]}$



$\sf\textsf{(30x) -3x = 36}\\\\\implies \sf\textsf{27x = 36}\\\\\implies \sf\textsf{x= \dfrac{36}{27} }\\\\\implies \sf\textsf{x = \dfrac{4}{3} (= 1.3)}$



$\underline{\LARGE{\texttt{Step-6:}}}}$

$\sf\textsf{Find the Age of the Father}$



$\sf\textsf{From [1],}$

$\sf\textsf{y = 30 \left(\dfrac{4}{3}\right) }\\\\\sf\textsf{y = 10 \times 4}\\\\\sf\textsf {y = 40}$




$\therefore$

$\blacksquare \: \: \textsf{The Present Age of Man = \LARGE{\underline{\Large{\textbf{40\: years}}}}}$