Question

The age of a father is equal to twice the age of his two sons. If the elder son is 8 years older than the younger son, find the age of the younger son if the age of the father is 52 years?
(a) 9 years
(b) 4 years
(c) 6 years
(d) 8 years​

Answer 1

Answer:

9 years

Step-by-step explanation:

As per the provided information in the given question, we have:

• Age of father is twice the age of his two sons.
• Elder son is 8 years older than the younger son.
• Age of father is 52 years.

We've been asked to calculate the age of younger son.

Let us suppose the age of father as x, age of elder son as y and age of younger son as z.

– Now, according to the question, the age of father is equal to twice the age of his two sons. According to our assumption,

$\twoheadrightarrow\quad\sf{x=2(y+z)}$

Here, the age of father, x is 52 years. So, we can equate the value.

$\twoheadrightarrow\quad\sf{52=2(y+z)}$

Transposing 2 from RHS to LHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{y+z=\dfrac{52}{2}}$

Performing division.

$\twoheadrightarrow\quad\sf{y+z=26\qquad\qquad\qquad\left\lgroup\begin{matrix} \sf{{eq} ^{n} \: (1)} \end{matrix}\right\rgroup \]}$

We've calculated the sum of age of elder son and younger son that is 26.

It is also given that, the elder son is 8 years older than younger son.

$\twoheadrightarrow\quad\sf{y=z+8\qquad\qquad\qquad\quad\left\lgroup\begin{matrix} \sf{{eq} ^{n} \: (2)} \end{matrix}\right\rgroup \]}$

Equating value of y from eqⁿ (2) to eqⁿ (1).

$\twoheadrightarrow\quad\sf{z+8+z=26}$

Bringing like terms together.

$\twoheadrightarrow\quad\sf{2z+8=26}$

Transposing 8 from LHS to RHS. It's sign will get change.

$\twoheadrightarrow\quad\sf{2z=26-8}$

Performing subtraction.

$\twoheadrightarrow\quad\sf{2z=18}$

Transposing 2 from LHS to RHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{z=\dfrac{18}{2}}$

Performing division.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{z=9\; years}}}}$

❝ Therefore age of younger son is 9 years. ❞