# 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?

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by shra28

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by shra28

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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

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