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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