Question

Q3. The present 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. Find the age of the father.​

Answer 1

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Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

Present age of Father be 'x' years

and

Sum of the present ages of two children be 'y' years.

According to first condition

The present age of the father is twice the sum of the ages of his two children.

$\bf :\longmapsto\:x = 2y - - - (1)$

According to second condition

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

After 20 years,

Age of father be 'x + 20' years

and

Sum of the ages of two children = y + 40 years.

Thus,

$\rm :\longmapsto\:x + 20 = y + 40$

$\rm :\longmapsto\:2y+ 20 = y + 40 \: \: \: \: \: \: \: \: \: \: \{ \because \: x \: = \: 2y \}$

$\rm :\longmapsto\:2y - y = 40 - 20$

$\rm :\longmapsto\:y = 20$

On substituting the value of y in equation (1), we get

$\rm :\longmapsto\:x = 2 \times 20 = 40$

Hence,

• The present age of Father is 40 years

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

Understand all the words used in stating the problem.

Understand what you are asked to find.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown.

Clearly state what the variable represents.

3. Carry out the plan and solve the problem.