A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father’s and the mother’s age is 51 years. What is the age of the son ?

The correct option/answer is 3 years.

Let us solve this problem step-by-step by setting up algebraic equations based on the relationships given in the question.

Step 1: Define the variables
Let the age of the son be represented by the variable $x$ (in years).

Step 2: Express the parents' ages in terms of the son's age
Based on the problem statement:
1. The father is nine times as old as his son. Therefore, the father's age is:
$\mathrm{Father\text{'}s\; Age}=9x$
2. The mother is eight times as old as the son. Therefore, the mother's age is:
$\mathrm{Mother\text{'}s\; Age}=8x$

Step 3: Set up the equation using the sum of their ages
We are given that the sum of the father's and the mother's age is 51 years. We can write this as:
$\left(9x\right)+\left(8x\right)=51$

Step 4: Solve for $x$
Combine the like terms on the left side of the equation:
$17x=51$
Now, divide both sides by 17 to find the value of $x$:
$x=\frac{51}{17}$
$x=3$

Thus, the age of the son is 3 years.