Correct Answer: 63

Solution : Let's denote the two numbers as $2x$ and $7x$ (where $x$ is a positive integer)
The product of the two numbers is equal to the product of their HCF and LCM:
⇒ $(2x)(7x)$ = HCF $\times$ LCM
Given,
HCF = 9 and the LCM = 126
⇒ $(2x)(7x)=9\times126$
⇒ $14x^2=1134$
⇒ $x^2=81$
⇒ $x=9$
$\therefore$ Larger number = 7 × 9 = 63
Hence, the correct answer is 63.