Question

The ratio of the age of father and son in a family is 11: 6. If the age of the
mother is added to the age of the son then the ratio becomes 11: 16. If the
age of the son is 30 years, what is the age of the mother?
(a) 25 years (6) 50 years (c) 15 years (d) 45 years​

Answer 1

Answer:

25 years is your answer

Step-by-step explanation:

hope you got it

Answer 2

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

$\sf The \: ratio \: of \: the \: age \: of \: father \: and \: son \: in \: a \: family \: is \: 11: 6$

$\sf If \: the \: age \: of \: the \: mother \: is \: added \: to \: the \: age \: of \: the \: son :$

$\sf \implies Then, the \: ratio \: becomes \: 11: 16$

$\sf Real \: age \: of \: son = 30 \: years.$

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

$\sf \implies Age \: of \: mother = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf Let \: us \: assume \: that,$

$\sf \implies Age \: of \: father \: be \: 11x$

$\sf \implies Age \: of \: son \: be \: 6x$

$\sf \implies Age \: of \: mother \: be \: y$

$\bf \underline{ Now}, \sf according \: to \: question,$

$\sf \implies \bf \dfrac{11x}{6x + y} = \dfrac{11}{16}$

$\sf \implies 11(6x + y) = 16(11x)$

$\sf \implies 11(6x + y) = 176x$

$\sf \implies 66x +11y = 176x$

$\sf \implies 11y = 176x - 66x$

$\sf \implies 11y = 110x$

$\sf \implies y = \cancel \dfrac{110x}{11}$

$\sf \implies y = 10x$

$\bf \underline{ Now},$

$\sf Since, age \: of \: son \: is \: 30 \: years.$

$\sf \implies 6x = 30$

$\sf \implies x = \cancel \dfrac{30 }{6}$

$\sf \implies x = 5$

$\bf \underline{ Therefore},$

$\sf \implies Age \: of \: mother \: (y) = \bf 10(x) = 10 \times5= 50 \: years$