Question

the ages of somya and yaseenare in the ratio 5:7. if somya were 9 years older and yaseen 9 years younger , the age of somya would have been twice the age of yaseen. find their ages​

Answer 1

let age of Sonya =x years

age of yaseen=y years

ratio x:y=5:7

x/y=5/7

by cross multiplication we get,

7x=5y

7x-5y=0........(1)

from given condition we get,

x+9=2(y-9)

x+9=2y-18

x-2y+9+18=0

x-2y+27=0

x-2y=-27........(2)

we get two equations,

7x-5y=o........(1)

x-2y=-27........(2)

multiply equation (1)by 7

7x-14y=-189......(3)

subtract equation (3) and(2)

7x-14y=-189.......(3)

7x-5y=0........(1)

-9y=-189

y=21

put y=21 in (1)

7x-5*21=0

7x-105=0

7x=105

x=15

there age is somya=x=15 years

and age of yaseen=y=21 years