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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