Question : The HCF and the LCM of two numbers are 5 and 175, respectively. If the ratio of the two numbers is 5 : 7, the larger of the two numbers is _______.
Option 1: 35
Option 2: 25
Option 3: 45
Option 4: 75
Correct Answer: 35
Solution : Given: HCF of the two numbers = 5 LCM = 175 Let the two numbers be $5x$ and $7x$ We know that, The product of the two numbers = HCF × LCM ⇒ $5x \times 7x = 5 \times 175$ ⇒ $x^2 = \frac{175}{7}$ ⇒ $x^2 = 25$ ⇒ $x = 5$ The larger number is $7x=7\times5=35$ Hence, the correct answer is 35.
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