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 = ?

1400
2480
3520
4600

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let HCF  = x \\ LCM  =  20 x \\ sum of HCF + LCM  =  2520 \\ \Rightarrow x + 20 x = 2520 \\ \Rightarrow 21 x = 2520 \\ \Rightarrow x = 120 \\ HCF  =  120 \\ LCM  =  120 \times 20 = 2400 \\ One number  =  480 \\ Let another number  = y \\ y \times 480 = 120 \times 2400 \\ y = \frac{120 \times 2400}{480} = 600 \end{aligned}

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