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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

Let the present age of the grand son be 'X' and grand father's age be 'Y' <span class="_wysihtml5-temp-placeholder"></span> 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

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