Question

5 years ago mother was 7 times as old as her daughter 5 year hence his she will be 3 times as old as her daughter find their present ages

Answer 1

Hi ,

at present
________

mother's age = x years

daughters age = y years

5 years ago
_________

mother's age = ( x - 5 ) years

daughters age = ( y - 5 ) years

x- 5 = 7 ( y - 5 )

x = 7y - 35 + 5

x = 7y - 30 --- ( 1 )

after 5 years
__________

mother's age = ( x + 5 ) years

daughters age = ( y + 5 ) years

x + 5 = 3( y + 5 )

x = 3y + 15 - 5

x = 3y + 10 ------( 2 )

from ( 1 ) and ( 2 ) we get ,

7y - 30 = 3y + 10

7y - 3y = 10 + 30

4y = 40

y = 40 / 4

y = 10

put y = 10 in equation ( 1 ) , we get

x = 7× 10 - 30

x = 70 - 30

x = 40

Therefore ,

at present ,

mother's age = x = 40 years

daughters age = y = 10 years

I hope this helps you.

:)

Answer 2

Let daughter's and mother's present ages be x and y respectively.
As,5 years ago mother's age was 7 times her daughter's age, so,mother's will be y-5=7(x-5)
Similarly,5 years from now the mother's age will be y+5=3(x+5)
By solving both the equations we get x=10 & y=40.
So the present ages of mother and her daughter are 40 & 10 years respectively.