Question

the sum of the ages of Seema and Gaurav is 31 yrs. After 10 yrs, the ratio of their ages will be 8:9. Find their present ages.

Answer 1

let seema's present age be x and gaurav's be y 
x+y=31
after 10 years
x+10:y+10=8:9
after solving these 2 eqns u will get teh answer as
x=14
and y =17

Answer 2

S + G = 31 years  - eq 1

S+ 10 : G+10 = 8 : 9

9 (S+10) = 8 ( G+10 )

9 S = - 10 + 8 G    -- eq 2

Multiply equation 1 by 8 and add to equation 2
17 S =  238

S = 14 years
G = 17 years