Question

twice the son's age in years is added
to the age of his father, the sum is 90 if
twice the father's age in yours is added
to the age of the Son
the sum is 120
find their ages​

Answer 1

Let the age of son be x yrs

and the age of father be y yrs.

According to 1st scenario,

⇒ 2x + y = 90 ...eq.1

According to 2nd scenario,

⇒ 2y + x = 120 ...eq.2

Simply eq.1,

2x + y = 90

y = 90-2x ....eq.3

By substituting value of y in equation 2,

2y + x = 120

2(90-2x) + x = 120

180 - 4x +x = 120

3x = 180-120

3x = 60

x = 20

By substituting value of x in equation 3,

y = 90-2x

y = 90-2(20)

y = 90 - 40

y = 50

Therefore, son's age is 20 yrs and his father's age is 50 yrs.

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• If twice the son's age in years is added
• to the age of his father, the sum is 90.

• If twice the father's age in years is added to the age of the son the sum is 120.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present ages of father and son.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the common ratio between the ages be x

The present age of son be x

And the present age of father be y

According to the 1st condition:-

If twice the son's age is added to the age of his father, the sum is 90.

$\rm \implies2x + y = 90$

Multiplying the whole equation with 2

$\rm \implies2(2x + y = 90)$

$\rm \implies4x + 2y = 180.....(i)$

According to the 2nd condition:-

If twice the father's age is added to the age of the son the sum is 120.

$\rm \implies x + 2y = 120......(ii)$

Subtracting equation (ii) from (i)

$\rm \implies4x + 2y - (x + 2y)= 180 - 120$

$\rm \implies4x + 2y - x - 2y= 60$

$\rm \implies3x= 60$

$\rm \implies x= \dfrac{60}{ 3}$

$\rm \implies x= 20$

Substituting x = 20 in equation (ii)

$\rm \implies x + 2y= 120$

$\rm \implies 20+ 2y= 120$

$\rm \implies2y= 120 - 20$

$\rm \implies2y= 100$

$\rm \implies y= 50$

Therefore:-

The present age of son = 20 years

The present age of father = 50 years