Question

* The ages of A and I are in the ratio 5. 7. Eight years ago, their ages were in
ratio 7 13. Find their present ages
Let the presentes of A and be x and 7 years respectively​

Answer 1

Answer:

$let \: the \: present \: age \: of \: a \: and \: b \: \\ are \: x \: and \: y \: yrs$

$\frac{x}{y} = \frac{5}{7} (given)$

$7x = 5y \: \: equation \: 1$

$8 \: years \: ago.. \\ age \: of \: a =( x - 8)years$

$age \: of \: b = (y - 8)years$

$\frac{(x - 8)}{(y - 8)} = \frac{7}{13}$(given)

$13x - 7y = 48 \: \: equation \: 2$

$put \: value \: of \: x \: from \: equation \: 1$

$65y - 49y = 336$

$y = 21years$

$so \: x = \frac{5y}{7} \\ x = 15 \: years$

$therefore \: age \: of \: a = 15years$

$and \: age \: of \: b = 21 \: years$

Answer 2

Let the ages of A and I be 5x and 7x respectively.

After 8 years their ages will be in ratio 7:13.

A/Q,

$=>\frac{5x+8}{7x+8}=\frac{7}{13}$

$=>7(7x+8)=13(5x+8)$

$=>49x+56=65x+104$

$=>49x-65x=104-56$

$=>-16x=48$

$=>x=\frac{48}{16}=3$

$\huge\orange{hope\:it\:helps :)}$