Question

Five years ago a man was 7 times as old than his son. after 5 years he will be 3 times his sons age find their present age

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Five years ago a man was 7 times as old than his son. After 5 years he will be 3 times his son age.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

Their present age.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the present age of man be r years

Let the present age of son be m years

A/q

$\underbrace{\sf{5\:years\:agO\::}}}}$

The age of man = (r - 5) years

The age of son = (m - 5) years

So;

$\longrightarrow\rm{(r-5)=7(m-5)}\\\\\longrightarrow\rm{r-5=7m-35}\\\\\longrightarrow\rm{r-7m=-35+5}\\\\\longrightarrow\rm{r-7m=-30......................(1)}$

$\underbrace{\sf{After\:5\:years\::}}}}$

The age of man = (r + 5) years

The age of man = (m + 5) years

So;

$\longrightarrow\rm{(r+5)=3(m+5)}\\\\\longrightarrow\rm{r+5=3m+15}\\\\\longrightarrow\rm{r-3m=15-5}\\\\\longrightarrow\rm{r-3m=10}\\\\\longrightarrow\rm{r=10+3m......................(2)}$

Putting the value of r in equation (1),we get;

$\longrightarrow\rm{10+3m-7m=-30}\\\\\longrightarrow\rm{10-4m=-30}\\\\\longrightarrow\rm{-4m=-30-10}\\\\\longrightarrow\rm{-4m=-40}\\\\\longrightarrow\rm{m=\cancel{\dfrac{-40}{-4} }}\\\\\longrightarrow\rm{\pink{m=10\:years}}$

Putting the value of m in equation (2),we get;

$\longrightarrow\rm{r=10+3(10)}\\\\\longrightarrow\rm{r=10}+30}\\\\\longrightarrow\rm{\pink{r=40\:years}}$

Thus;

The present age of man will be r = 40 years.

The present age of son will be m = 10 years.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Five years ago a man was 7 times as old than his son.
• After 5 years the age of man will be 3 times the age of his son.

${\bf{\blue{\underline{To:Find:}}}}$

• Present age of man and his son

${\sf{\underline{\green{Now,}}}}$

✧Let the age of man be x

✧and his son be y

☞Five years ago,

$\star{\tt{Age\: of\: son=x-5}}$

$\star{\tt{Age\: of\: man=7(y-5)}}$

$\implies{\tt{x - 5 = 7(y - 5)}}$

$\implies{\tt{x - 5 = 7y - 35}}$

$\implies{\tt{x = 7y - 35 + 5}}$

${ \boxed{\tt{x - 7y + 30 = 0......(1)}}}$

☞After Five years ,

$\star{\tt{Age \:of\: Son=x+5}}$

$\star{\tt{Age \:of \:Man=3(y+5)}}$

$\implies{\tt{x + 5 = 3(y + 5) }}$

$\implies{\tt{x + 5 = 3y + 15 }}$

$\implies{\tt{x = 3y + 15 - 5 }}$

$\boxed{\tt{x - 3y - 10 = 0......(2) }}$

According to the ques ,

$\implies{\tt{x = 3y + 10 ...(3)}}$

${\bf{\blue{\underline{Put \:Value\: of \:x\: in \:equation\: (2)}}}}$

$\implies{\tt{x - 7y + 30 = 0 }} \\ \\ \implies{\tt{( 3y + 10) - 7y+ 30 = 0 }} \\ \\\implies{\tt{ - 4y + 10 + 30 = 0}} \\ \\ \implies{\tt{ y = 10 }}$

${\bf{\blue{\underline{Put \:Value\: of \:y\: in \:equation\: (3)}}}}$

$\implies{\tt{x = 3(10)+ 10 }}$

$\implies{\tt{x = 30+ 10 }}$

$\implies{\tt{x = 40}}$

$\boxed{\tt{\purple{Present \: Age \: of \: Man \: = 40yrs }}}$

$\boxed{\tt{\purple{Present \: Age \: of \: Son\: = 10yrs }}}$