Question

The present ages of Parul and Sonia are in the ratio 5:7. If Parul was 9 years older and Sonia 9 years younger, the age of Parul would have been twice the age of Sonia. Find their ages.​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

Ratio of ages of Parul and Sonia = 5:7

When,Parul was 9 years older and Sonia was 9 years younger

the age of Parul would have been twice the age of Sonia i.e 2 times.

To find :

Age of Parul and Sonia

Solution :

Let age of Parul = x

and Age of Sonia = y

Ratio = 5:7

$\frac{x}{y} = \frac{5}{7} \\ x = \frac{5}{7} \: y...(i)$

According to Question

$⟶(x+9)=2(y−9)$

$⟶x+9=2y−18$

$⟶27=2y−x$

Insering value of x

$⟶27=2y− \frac{5}{7} y$

$⟶27= \frac{14 - 5}{7} y$

$⟶27= \frac{9}{7} y$

$⟶y = \frac{27 \times 7}{9}$

$⟶y = 21 \: years$

Insert value of y in equation (i)

$⟶x = \frac{5}{7} y$

$⟶x = \frac{5}{7} \times 21$

$⟶x = 15 \: years$

$\therefore$

Age of Parul = 15 years.

Age of Sonia = 21 years.