If the sum of LCM and HCF of two numbers is 260 and their LCM is 900 more than their HCF, then the product of two numbers is:

The correct option is B 194400
Let the HCF of the two numbers be x.
$\Rightarrow$ LCM = x + 900

Sum of LCM and HCF is 1260. (Given)
$\Rightarrow$ (x + 900) + x = 1260
$\Rightarrow$ 2x + 900 = 1260
$\Rightarrow$ x + 450 = 630
$\Rightarrow$ x = 180

$\therefore$ HCF = 180

$\Rightarrow$ LCM = 180 + 900 = 1080

Now, product of the two numbers = Product of their HCF and LCM
$\Rightarrow$ Product of the two numbers = 180 $\times$ 1080
$\Rightarrow$ Product of the two numbers = 194400