Question

the sum of father's age and twice the age of his son is 70 if we double the age of the father and add it to the age of his son the sum is 95 find their present engine

Answer 1

Let father's present age be x years

Let son's present age be y years

∴ A.T.Q. x+2y = 70 ------(i)

⇒ x = 70-2y -----(ii)

On doubling the age of the father and adding it to the age of his son the sum of their ages = 95 years

∴ 2x+y = 95 ------(iii)

⇒ 2(70-2y) + y = 95 { as x = 70-2y --------From equation (ii) }

⇒ 140 - 4y + y = 95

⇒ 140 - 95 = 3y

⇒ 3y = 45

⇒ y = 15 years

∴ Present age of son = 15 years

Putting y = 15 in (i) we get :

x + 2×15 = 70

⇒ x = 70-30

⇒ x = 40 years

∴ Present age of father is 40 years.

THANKS !

Answer 2

years.
and
The age of son be y years.

From 1st Condition
2x+y= 70 ------- I

From 2nd Condition
x+2y=95 -------- II

Multiplying equation I by 2
therefore, we get,
4x+2y=140 --------- III

Subtract equation II from III

4x + 2y = 140
- x + 2y = 95
–―-―--------------------
3x = 45
x = 45
----
3

X = 15

Substituting X=15 in equation II

x + 2y = 95 ---- II
(15) + 2y = 95
2y = 95-15
2y = 80
y = 80
-----
2

Y = 40

The present age of father is 40 years
and
The present age of son is 15 years.