Question : The LCM of the two numbers is 44 times their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is:
Option 1: 1100
Option 2: 975
Option 3: 900
Option 4: 800
Correct Answer: 1100
Solution : Let the HCF = X So, the LCM = 44X Given: HCF + LCM = 1125 or, X + 44X = 1125 or, 45X = 1125 or, X = $\frac{1125}{45}$ = 25 So, HCF is 25. LCM is 44X = 44 × 25 = 1100 Given one number is 25. Let the other number be Y. 1st number × 2nd number = LCM × HCF ⇒ 25 × Y = 1100 × 25 ⇒ Y = $\frac{1100 × 25}{25}$ = 1100 So, the other number is 1100. Hence, the correct answer is 1100.
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