Question

The sum of the age of father and the son is 65 year . the quotient obtained by dividing the age of son by the age of father is 10/3 .find their ages.​

Answer 1

$\sf\large\underline\purple{Let:-}$

$\rm{\implies The\:age\:of\: father=x}$

$\rm{\implies The\:age\:of\: son=y}$

$\sf\large\underline\purple{To\: Find:-}$

$\rm{\implies The\:age\:of\: father\:and\:son=?}$

$\sf\large\underline\purple{Solution:-}$

• To calculate the age of father and son ,at first we have to set up equation as per the given clue in the question then solve those equation. By solving we get the value of x and y:-]

$\sf\small\underline\red{Given\:in\:case\:(i):-}$

• The sum of the age of father and the son is 65 year:-]

$\tt{\implies Father\:_{(age)}+Son\:_{(age)}=65}$

$\tt{\implies x+y=65------(i)}$

$\sf\small\underline\red{Given\:in\:case\:(ii):-}$

• The quotient obtained by dividing the age of son by the age of father is 10/3:-]

$\tt{\implies \dfrac{y}{x}=\dfrac{10}{3}}$

$\tt{\implies 10x=3y}$

$\tt{\implies 10x-3y=0------(ii)}$

• In eq (i) multiplying by 10 then subract from eq (ii):-]

$\tt{\implies 10x+10y=650}$

$\tt{\implies 10x-3y=0}$

• By solving we get here:-]

$\tt{\implies 13y=650}$

$\tt{\implies y=50}$

• Now putting the value of y=50 in eq (i):-]

$\tt{\implies x+y=65}$

$\tt{\implies x+50=65}$

$\tt{\implies x=65-50}$

$\tt{\implies x=15}$

$\sf\large{Hence,}$

$\bf{\implies The\:age\:of\: father=50\: years}$

$\bf{\implies The\:age\:of\: son=15\: years}$

Answer 2

Son= 15

Father = 50

See image above...