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

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

Answer 2

Hi friend,

Let Aman's present age be x years.

And his son's present age be y years.

Their age after 6 years::

Aman's age = x+6

His son's age = y+6

After 6 years,aman 's age will be three times the age of his Son

x+6 = 3(y+6)

x+6 = 3y+18

x-3y = 18-6

x-3y = 12 -------(1)

Their age before 3 years:-

Aman's age = x-3

His son's age = y-3

Three years ago he was nine times as old as his son.,

x- 3 = 9 ( y - 3 )

x - 3 = 9y - 27

x - 9y = -27 + 3

x - 9y = -24 --------(2)

(1) - (2)

x - 3y = 12
- (x - 9y = -24)
––––––––––––
6y = 36

y = 36/6

y = 6

x-3y = 12

x-3(6) = 12

x - 18 = 12

x = 12+18

x = 30

Therefore,

Present age of Aman = 30 years

Present age of his son = 6 years

Hope it helps...