Question

Six years hence, aman 's age will be three times the age of his Son and Three years ago he was nine times as old as his son. Find their present age.

Answer 1

Let Aman's age be x and his son's age be y
A.T.Q,
x+6=3 (y+6)
x=3y+18-6
x-3y=12 eq 1
x-3=9 (y-3)
x=9y-27+3
x-9y=-24 eq 2
on substracting eq 2 from eq 1-
( x-3y)-(x-9y)=12-(-24)
=>x-3y-x+9y=12+24
=>6y=36
=>y=6
on putting value of y in eq 1-
x-(3×6)=12
=>x=12+18
x=30
Therefore aman's age is 30 yrs and his son's age is 6 yrs.

Answer 2

Hi there !!

Present ages :-
Aman's age = x
Son's age = y

Their ages after 6 yrs :-
Aman's age = x + 6
Son's age = y + 6

Given :-
x  + 6 = 3 [ y+ 6]
x + 6 = 3y + 18
x - 3y  = 18 - 6
x - 3y = 12    --------> [1]

Their ages three years ago :-
Aman's age = x - 3
Son's age = y - 3

Given :-
x-  3 = 9 [ y - 3 ]
x - 3 = 9y - 27
x - 9y = -27 + 3
x - 9y = -24          -----> [2]

subtracting equations 1 and 2 ,

           x - 3y = 12
  -        x - 9y = -24   
 -------------------------------------
       6y = 36
     
y = 36/6
y = 6

Put this value in equation [1]

x - 3y = 12
x - 18 = 12
x = 12 + 18
x = 30

Present age of Aman = 30yrs
Present age of son = 6yrs