Question

Five years hence, a mother's age will be three times that of her daughter's and five years ago. the mother was $7$ times as old as the daughter was. Find their present ages.

Answer 1

Let mother present age is x & daughter present age is y.

$5+x=3(y+5)$ …………$\left(1\right)$

and $5$ years ago

$x-5=7(y-5)$ ……….$\left(2\right)$

$5+x=3y+15$

$(-)x-5=7y-35$

___________________

$10=-4y+50$

$4y=40$

$y=10$

from $\left(1\right)$

$5+x=3(y+5)$

$5+x=3(10+5)$

$5+x=45$

$x=40$

$\therefore$ Mother's present age $=40$

Daughter's present age $=10$.