Question

if twice the sons ages in years is added to father age the sum is 70.But if twice the father ages is added to the son age the sum is 95.find the ages of father and son

Answer 1

let the age of the father be x and the age of the son be y

according to the conditions,

2y+x=70 ..............(1)

2x+y=95 ..............(2)

multiplying equation (1) into 2 we get 

subtracting equation (2) from equation (3)

4y+2x=140 .........(3)

 y+2x=  95

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

3y     = 45

y=15 ..................(4)

substituting (4) in (2) we get

15 +2x=95

2x=80

x=40.

Therefore the age of the father is 40yrs and that of the son is 15 yrs

Answer 2

⠀⠀⠀☯ Let father's age (in years) be x and that of son's be y.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

★ If twice the sons ages in years is added to father age the sum is 70.

$:\implies\sf x + 2y = 70$

★ If twice the father ages is added to the son age the sum is 95.

$:\implies\sf 2x + y = 95$

This system of equations may be written as,

• x + 2y - 70 = 0

• 2x + y - 95 = 0

⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ By Cross multiplication method,

$:\implies\sf \dfrac{x}{2 \times - 95 - (-70)} = \dfrac{- y}{1 \times - 95 - 2 \times - 70} = \dfrac{1}{1 \times 1 - 2 \times 2}$

$\qquad \qquad \quad:\implies\sf \dfrac{x}{- 190 + 70} = \dfrac{- y}{- 95 + 140} = \dfrac{1}{-3}$

$\qquad \qquad\quad \qquad:\implies\sf \dfrac{x}{- 120} = \dfrac{y}{- 45} = \dfrac{1}{- 3}$

$\qquad \qquad \quad:\implies\sf \dfrac{x}{- 120} = \dfrac{1}{- 3}\;and\;\dfrac{y}{- 45} = \dfrac{1}{- 3}$

$\qquad \qquad \qquad:\implies\sf x = \dfrac{- 120}{- 3}\;and\;y = \dfrac{- 45}{- 3}$

$\qquad \qquad \qquad \quad:\implies\sf \purple{x = 40\;and\;y = 15}$

$\therefore$ Hence, father's age is 40 years and the son's age is 15 years.