Question

7 years ago the ratio of the ages of a and b is 5 by 7 if product of present ages is 616 find the ratio of present eges

Answer 1

Answer:

Step-by-step explanation:

let the ages of a and b before 7 years are x and y

from given information

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

∴7x=5y

∴x=$\frac{5}{7} y$

after 7 years ages of a and b will be x+7 and y+7 respectively.

now product of their ages is 616

∴(x+7)×(y+7)=616

∴xy+7y+7x+49=616

∴xy+7y+7x=567

but   x=$\frac{5}{7} y$  

∴    ($\frac{5}{7} y$ )y+7y+7×($\frac{5}{7} y$ )=567

∴$5y^{2}+84y-3969=0$

∴$y=\frac{-84\pm \sqrt{84^{2}-4\times 5\times (-3969)}}{2\times 5}$

∴y=21

we will neglect negative value as age can not be in negative

∵x=$\frac{5}{7} y$

∴x=15

ratio of their present ages = $\frac{x+7}{y+7}$

=$\frac{15+7}{21+7}$

=$\frac{22}{28}$