Question

I the present age of A and B are in the ratio 7:5. 10 years later, their ages will be in the ratio 9:7. find their present ages.

Answer 1

QUESTION

I the present age of A and B are in the ratio 7:5. 10 years later, their ages will be in the ratio 9:7. find their present ages.


Answer


Let present age of A=x years

Let present age of B=y years

so , it's ratio become


$\frac{x}{y} = \frac{7}{5}$
on cross multiply

$5x = 7y$

$x = \frac{7y}{5}$



After 10 years


Age of A= x+10 years

Age of B= y+10 years



SO, ratio of ages after 10 year




$\frac{x + 10}{y + 10} = \frac{9}{7}$
on cross multiply


$7x + 70 = 9y + 90$


$7x - 9y = 90 - 70$


$7x - 9y = 20$

put value of x



$7 \frac{7y}{5} - 9y = 20$



$49y - 45y = 20 \times 5$


$4y = 100$



$y = 25 \: years$



so

$x = \frac{7y}{5}$



$x = \frac{7 \times 25}{5}$


$x = 35 \: years$




HENCE


Age of A= 35years

Age of B=25years