Question

The age of the father is twice the sum of the ages of his two children. After 20 years , his age will be equal to the sum of the ages of his children. What is the father's age​

Answer 1

Required Answer:-

Let's consider the age of the father be x and the total sum of the ages of his children be y (Remember! two children).

According to condition-(1),

The age of the father is twice the sum of the ages of his two children. That means,

➙ Father's age = 2(Children's age)

➙ x = 2y -----(1)

According to condition-(2),

After 20 years, his age will be equal to the sum of the ages of his children. Then,

• Age of father after 20 yrs = x + 20
• Age of children = y + 40 (How?)

$\dag{\underline{ \red{ \sf{Twist \: in \: the \: question}}}}$

There are 2 children. After 20 years, each of their age will increase by 20 years. Then in total, there's an increase of 20 + 20 = 40 years.

Then,

➙ Father's age + 20 = Children's age + 40

➙ x + 20 = y + 40

Putting x = 2y from (1),

➙ 2y + 20 = y + 40

➙ 2y - y = 40 - 20

➙ y = 20

Then, x = 2*20 = 40.

Hence,

Age of the father = 40 years.

Answer 2

Given :

• The age of the father is twice the sum of the ages of his two children .
• After 20 years , his age will be equal to the sum of the ages of his children.

To find :

• What is the father's age ?

Solution :

Let , the age of father be a years

Let , the age of one of his children be b

Let , the other children be c

1 st method

$\sf x=2×(y+z) .$

After 20 years,

2nd method

$\sf (x+20)=(y+20)+(z+20)$

Equalities of value of 1st method and 2nd method :

Now,

Now, We will get

$\sf \red {2×(y+z) +20=y+z+40}$

$\sf2y+2z−y−z=40−20$

3rd method :

$\sf \green {y+z=20}$

Equalities of value of 3rd method and 1st method :

$\sf \blue {x=2×(20)}$

$\sf ⇒x=40$

$\sf \red {Age \: of \: father \: is \: 40 \: years.}$