Question

9 years ago ,a grandfather's age was 9 times his grandson's age at that time.After 15 years , his age will be thrice his grandson's age.Find their present ages?

Answer 1

let the present age of the grand son be 'X' and grand father's age be 'Y'
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9 years age
grand son's age = (x - 9)
grand father's age = (y - 9)

By first condition

y - 9  = 9 ( x - 9)
y - 9 = 9x - 81
9x - y = 72----------------------- (1)

After 15 years

the age of grandson = ( x + 15)
the age of the grand father = (y +15)

by second condition

y + 15 = 3 ( x + 15)
y + 15 = 3x + 45
3x - y  = (- 30 ) --------------------- (2)

Subtract  (1) and ( 2)

9X - y = 72
3x - y = (-30)
-      +        +
--------------------
6 x = 102
x = 102/6 = 17

put x in (1 )

9 (17) - y = 72
153 - 72 = y
y = 81

grand son's present age = 17 years
and grand father's age = 81 years

Answer 2

Let the grandpa's present age be x years and the grandson's present age be y years.
Grandpa's age before 9 years=x-9 years
Grandson's age before 9 years=y-9 years
Given,at that time,Grandpa's age was 9 times the grandson's age.
so,x-9=9(y-9)
or,x-9=9y-81
or,x=9y-81+9=9y-72
Grandpa's age after 15 years=x+15 years
Grandson's age after 15 years=y+15 years
Given.at that time,Grandpa's age is 3 times the grandson's age.
so,x+15=3(y+15)
or,x+15=3y+45
or,x=3y+45-15=3y+30
it is proved above that x=9y-72.Also x=3y+30
Therefore,if x=3y+30
then, also 9y-72=3y+30(proved above)
or,9y-3y=30+72
or,6y=102
or,y=102/6=17
Grandson's present age=17 years
Grandpa's present age=3y+30=3*17+30=51+30=81 years