Question : Two numbers are in the ratio of 4 : 3. The product of their HCF and LCM is 2700. The difference between the numbers is:
Option 1: 15
Option 2: 30
Option 3: 25
Option 4: 105
Correct Answer: 15
Solution :
Ratio of Two numbers = 4 : 3
HCF × LCM = 2700
Product of two numbers = Product of their HCF and LCM
Let the numbers be $4x$ and $3x$ respectively
⇒ $x × 12x = 2700$
⇒ $12x^2 = 2700$
⇒ $x^2 = 225$
⇒ $x = 15$
Difference between the numbers is $=4x - 3x = x = 15$
Hence, the correct answer is 15.
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