Question

My father's age 5 years ago plus twice my age now gives 65. My age 5 years ago plus three times my father's age now gives 130. What is my father's age?​

Answer 1

Let father's present age be x and your present age be y

Father's age five years ago= x-5

your age five years ago= y-5

Case 1, (x-5) + 2y= 65

x + 2y= 70 (eqn. 1)

Case 2, y - 5 + 3x = 130

3x + y= 135 (eqn. 2)

Eqn 1 is x+2y=65

y= 65/2 - x/2 (eqn 3)

Putting 3 in 2

3x + 65/2 - x/2= 135

6x/2 - x/2 +65/2 =135

5x/2 + 65/2= 135

5x + 65 = 135 × 2

5x= 270-65=205

x= 41

Putting the value of x in eqn 3

y= 65/2-41/2

y=24/2

y=12

(This part was not asked in the question)

Ans- Father's present age is 41

Answer 2

let the father's age be x

father's age 5 years ago = x-5

let your present age be y

then your age 5 years ago= y-5

now according to question,

=>x-5+2y=65

=>x+2y=70-------1

next

=y-5+3x= 130

=3x+y=135-------2 ×2

subtracting 2 from 1

x+2y=. 70

6x+2y=.270

-. -. -

-------------------

-5x. =. -200

5x = 200

x=200/5

x= 40

so age of dad = x. = 40 y/o