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1. The LCM of two numbers is 44 times of their of HCF. The sum of the LCM and HCF is 1125. If one number is 25 then the other number is = ?

A. 1100

B. 975

C. 900

D. 800

Solution:

\begin{aligned} Let HCF  = x \\ LCM  =  44 x \\ given HCF + LCM \\ = 44 x + x = 45 x \\ 45 x = 1125 \\ x = \frac{1125}{45} = 25 \\ ∴ HCF = 25 \\ LCM  =  25 \times 44 \\ also given that one number \\ =  25 \\ Let another number  = y \\ ∴ 25 y = 25 \times 25 \times 44 \\ y = \frac{25 \times 25 \times 44}{25} \\ y = 1100 \end{aligned}

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