Question : The LCM of the two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is:
Option 1: 5
Option 2: 25
Option 3: 100
Option 4: 125
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Correct Answer: 25
Solution : Let LCM = L and HCF = H, then Given: L = 4H The sum of LCM and HCF = 125 ⇒ H + 4H = 125 ⇒ 5H = 125 ⇒ H =$\frac{125}{5}$ ⇒ H = 25 ∴ L = 4 × 25 = 100 2 nd number = $\frac{L× H}{100}$ = $\frac{100× 25}{100}$ = 25 Hence, the correct answer is 25.
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