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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 = ?

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 = ? Correct Answer 1100

$$\eqalign{ & {\text{Let HCF = }}x \cr & {\text{LCM = 44}}x \cr & {\text{given HCF + LCM}} \cr & = 44x + x = 45x \cr & 45x = {\text{ }}112{\text{5}} \cr & x = \frac{{1125}}{{45}} = 25 \cr & \therefore {\text{HCF}} = {\text{25}} \cr & {\text{LCM = 25}} \times {\text{44}} \cr & {\text{also given that one number}} \cr & {\text{ = 25}} \cr & {\text{Let another number = }}y \cr & \therefore 25y = 25 \times 25 \times 44 \cr & y = \frac{{25 \times 25 \times 44}}{{25}} \cr & y = 1100 \cr} $$

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