Question

The father’s age is six times his son’s age. Four years hence, the age of the father will be four

times his son’s age. The present ages (in years) of the son and the father are, respectively

(a) 4 and 24 (b) 5 and 30 (c) 6 and 36 (d) 3 and 24​

Answer 1

Given that:

• The father’s age is six times his son’s age.

Let present ages of:

• Son = x years
• Father = 6x years

Four years hence,

• The age of the father will be four times his son’s age.

After four years:

• Son's age = (x + 4) years
• Father's age = (6x + 4) years

According to the question.

Father's age = 4(Son's age)

ㅤ↠ㅤ6x + 4 = 4(x + 4)

ㅤ↠ㅤ6x + 4 = 4x + 16

ㅤ↠ㅤ6x - 4x = 16 - 4

ㅤ↠ㅤ2x = 12

ㅤ↠ㅤx = 12/2

ㅤ↠ㅤx = 6

Present ages of:

• Son = 6 years
• Father = 6x = 6(6) = 36 years

Hence,

• (c) 6 years and 36 years is the required answer.

Answer 2

$\bf\bigstar\: How \: to \: solve\:such \: Questions :$

1. Firstly we have to Understand this problem.
2. Then We also have to Understand that what we are asked to find and then we have to Translate this problem to an equation.
3. We will Assign a variable (or variables) like 'a' and 'b' to represent the unknown and
4. Then we will Carry out the plan and solve the problem by using substitution or elimination method to solve this problem

$\small \text{Step 1 ) Understand the problem}$

$\bf\bigstar\: Information \: provided \: with \: us ,$

• The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age.

$\small \text{Step 2) Understand what we are going to find out}$

$\bf\bigstar\:What \: we \: have \: to \: find ,$

• The present ages (in years) of the son and the father

$\small \text{★Step 3) Translate the problem to an equation by assigning variable}$

$\small \text{(or variables) like (a) and (b) to represent the unknown}$

$\bf\bigstar\:Consider,$

• We have to assume that Suppose 'a 'year be the present age of father and 'b 'be the present age of son

$\small \text{Step 4) Carry out the plan to solve this problem}$

• Four year hence it has relation by given condition

$\rm\implies \: (a+ 4) = 4(b + 4)$

• By simplifying it we get :

$\rm\implies \: (a+ 4) = 4(b + 16)$

Now We have first equation :

$\rm\implies \: (a - 4 \: b) =12 \: \: ...\: \: \: (1)$

Here we get second equation :

• We know that Father's age is 6 times son's age so

$\rm\implies \: a = 6 \: b \: ...\: \: \: (2)$

$\small \text{Step 5) By using substitution method solve this problem}$

• On putting the value of 'a ' from equation (2) in equation (1) we get ,

$\rm\implies \: 6 \: b - 4 \: b = 12$

$\rm\implies \: 2 \: b = 12$

$\rm\implies \: b \: = \dfrac{12}{2}$

$\rm\implies \: b \: = 6 \: years$

• By placing value of b = 6 in equation (2) we get ,

$\rm\implies \: a = 6 \: b \:$

$\rm\implies \: a = 6 \: \times 6$

$\rm\implies \: a = 36 \: years$

$\bf\bigstar\:Therefore ,$

• So present age of father is 36 years and age of son is 6 years

• So option c) 6 and 36 years is correct

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