Two numbers are in the ratio $3:4$. The product of their HCF and LCM is $2028$. The sum of the numbers will be

1. Let the two numbers be $3x$ and $4x$, where $x$ represents their Highest Common Factor (HCF).2. We know the fundamental relationship:
$$\text{Product of two numbers}=\text{HCF}\times \text{LCM}$$
Substituting the given values into the formula:
$$(3x)\times (4x)=2028$$
$$12x^2=2028$$
$$x^2=\frac{2028}{12}=169$$
$$x=\sqrt{169}=13$$
The two numbers are:
$$\text{First number}=3\times 13=39$$
$$\text{Second number}=4\times 13=52$$
The sum of these two numbers is:
$$\text{Sum}=39+52=91$$