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1. 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 = ?

A. 400

B. 480

C. 520

D. 600

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}

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