The LCM of two numbers is 20 times their HCF. The sum of HCF ans LCM is 2520. If one of the number 480, the other number is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let HCF = }}x \cr & {\text{LCM = 20}}x \cr & {\text{sum of HCF + LCM = 2520}} \cr & \Rightarrow {\text{ }}x{\text{ }} + {\text{ }}20x{\text{ }} = {\text{ }}2520 \cr & \Rightarrow 21x = 2520 \cr & \Rightarrow x = 120 \cr & {\text{HCF = 120}} \cr & {\text{LCM = 120}} \times {\text{20 = 2400}} \cr & {\text{One number = 480}} \cr & {\text{Let another number = }}y \cr & y \times {\text{ }}480 = 120 \times 2400 \cr & y = \frac{{120 \times 2400}}{{480}} = 600 \cr} $$