Question

two year ago father 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 age​

Answer 1

let the present age of father=x years

let the present age of son=y years

2 years ago

the age of father=(x-2)years

the age of son=(y-2)years

A.T.Q

x-2=3(y-2)

x-2=3y-6

x-3y=-6+2

x-3y=-4..................(1.)

2 years hence

the age of father=(x+2)years

the age of son=(y+2)years

Again A.T.Q

2(x+2)=5(y+2)

2x+4=5y+10

2x-5y=10-4

2x-5y=6..........................(2.)

from eq. 1 and 2.

(see in attachment.)

Answer 2

Two years ago age of father was three times as old as his son.

Let age of son 2 years ago be "M" years.

So,

Age of father = (3M) years

So,

Present age of son = Age of son 2 years ago + 2

= (M + 2) years

Present age of father = Age of father 2 years ago + 2

= (3M + 2) years

Two years hence,

Now,

Age of son after 2 years = Present age of son + 2

= M + 2 + 2

= (M + 4) years

Age of father after 2 years = Present age of father + 2

= 3M + 2 + 2

= (3M + 4) years

According to question,

Two years hence, twice his age will be equal to five times that of his son.

=> 2(3M + 4) = 5(M + 4)

=> 6M + 8 = 5M + 20

=> 6M - 5M = 20 - 8

=> M = 12

Present age of son = M + 2

= 12 + 2

= 14 years

Present age of father = 3M + 2

= 3(12) + 2

= 36 + 2

= 38 years