The HCF and LCM of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is = ?

A. 12

B. 48

C. 84

D. 108

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let the numbers be }}x{\text{ and 4}}x \cr & {\text{Then ,}}x \times 4x = 84 \times 21 \cr & \Leftrightarrow {x^2}{\text{ = }}\left( {\frac{{84 \times 21}}{4}} \right) \cr & \Leftrightarrow x{\text{ = 21 }} \cr & {\text{Hence larger number}} \cr & {\text{ = 4}}x \cr & {\text{ = 84}} \cr} $$