Question

Five years ago a man by 7 time oldest his son.After 5 year he will be twice oldest son. Find their present age.

Answer 1

Let us Assume That, Present age of man and his eldest son is x & y years.

Than,

Case ❶ :- (5 Years Ago.)

→ Father was = (x - 5) years old.

→ son was = (y - 5) years old.

A/q,

→ Father = 7 * son

→ (x - 5) = 7(y - 5)

→ x - 5 = 7y - 35

→ x - 7y = - 35 + 5

→ x - 7y = (-30) ---------- Eqn(1).

________________

Case ❷ :- (After 5 Years.)

→ Father will be = (x + 5) years old.

→ son will be = (y + 5) years old.

A/q,

→ Father = 2 * son

→ (x + 5) = 2(y + 5)

→ x + 5 = 2y + 10

→ x - 2y = 10 - 5

→ x - 2y = 5 ---------- Eqn(2).

________________

Subtracting Eqn.(2) from Eqn.(1) ,

→ (x - 7y) - (x - 2y) = (-30) - (5)

→ x - x - 7y + 2y = (-35)

→ (-5y) = (-35)

→ y = 7 .

Putting in Eqn.(1) Now,

→ x - 7*7 = (-30)

→ x - 49 = (-30)

→ x = (-30) + 49

→ x = 19.

Hence, Father Present age is 19 Years & his Eldest son Present age is 7 Years.

Answer 2

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

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

• Five years ago a man 7 times oldest by his son.
• After five years he will be twice the oldest son.

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

• Their present age

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

✧Let the age of man be x

✧and his son be y

☞Five years ago,

$\star{\sf{Age\: of\: Man=x-5}}$

$\star{\sf{Age\: of\: Son=7(y-5)}}$

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

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

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

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

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☞After Five years ,

$\star{\sf{Age \:of\: Man=x+5}}$

$\star{\sf{Age \:of \: Son=2(y+5)}}$

$\implies{\tt{x + 5 = 2(y + 5) }}$

$\implies{\tt{x + 5 = 2y + 10 }}$

$\implies{\tt{x = 2y + 10 - 5 }}$

$\boxed{\tt{x - 2y-5= 0......(2) }}$

__________________________________

According to the ques ,

$\implies{\tt{x = 7y -30 ...(3)}}$

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

$\implies{\tt{(7y-30) - 2y -5 = 0 }}$

$\implies{\tt{7y-30- 2y -5 = 0 }}$

$\implies{\tt{5y-35 = 0 }}$

$\implies{\tt{5y = 35}}$

$\implies{\tt{y = \frac{35}{5} }}$

$\implies\boxed{\tt{y = 7 }}$

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

$\implies{\tt{x = 7(7) -30}}$

$\implies{\tt{x = 49-30}}$

$\implies\boxed{\tt{x =19}}$

$\boxed{\tt{\purple{Present \: Age \: of \: Man \: = 19yrs }}}$

$\boxed{\tt{\purple{Present \: Age \: of \: Son\: = 7yrs }}}$