Question

Two years ago, farther was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their present ages.

Answer 1

let son present age be x

2 years ago ,x -2 years
father 2 years ago, 3x -6 years
father's present age= 3x-6+2= 3x-4

two years hence ,
son x+2
father 3x-2

according to condition,
2(3x-2)= 5(x+2)
6x-4=5x+10
x=14

present age of son and father are 14 and 38 respectively

Answer 2

let us take current age of father as X and as of son as Y
as per 1st statement the equation will be
X-2 = 3(Y-2)
X-2 = 3Y-6
multiply this by 2 we will get
2X-6Y = -8
as per 2nd statement the equation will be
2(X+2) = 5(Y+2)
2X-5Y = 6
solve the 2 equation we will get
Y = 14
put this in the 1st or 2nd equation we will get
X = 38