Question

the age of sona and Sonali are in the ratio 5 ratio 3..... 5 years hence the ratio of their ages will be 10 ratio 7 find their present age

Answer 1

Sona and Sonali 5:3 age
5 years later 10:7 age
5r:3r
5r+5/3r+5=10/7
cross multiply.
30r+50=35r+35
5r=15
r=3
Sona age 5*3=15
Sonali age 3*3=9

Hope this is correct

Answer 2

let the present age of Sona be x year
and present age of Sonali be y year
ATQ
$\frac{x}{y} = \frac{5}{3} \\ 3x = 5y \\ 3x - 5y = 0 \: \: \: \: \: \: \: \: \: .....(1)$
5 years hence
Sona's age = x + 5 year
Sonali's age= y +5 year
ATQ
$\frac{x \ + 5}{y + 5} = \frac{10}{7}$
7(x+5)= 10(y+5)
7x+35=10y+50
7x-10y=50-35
7x-10y=15 .......(2)

solving 1 and 2 for x and y
6x-10y=0
7x-10y=15

-x=-15
x=15
$y = \frac{3}{5} \times 15 \\ y = 3 \times 3 \\ y = 9$
Sona's age = 15 year
Sonali's age= 9 year