Question : Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2700. The sum of the numbers is:
Option 1: 60
Option 2: 105
Option 3: 15
Option 4: 45
Correct Answer: 105
Solution :
Let the numbers be 3$x$ and 4$x$
Use: HCF × LCM = Product of the numbers
According to the question
⇒ HCF(3$x$, 4$x$) × LCM(3$x$,4$x$) = 2700
Now,
HCF(3$x$, 4$x$) = $x$
LCM(3$x$, 4$x$) = 12$x$
So,
⇒ $x× 12x = 2700$
⇒ $12x^{2} = 2700$
⇒ $x^{2} = \frac{2700}{12} = 225$
⇒ $x = \sqrt{225} = 15$
The numbers are $3x = 3 × 15 = 45$
⇒ $4x = 4 × 15 = 60$
The sum of the numbers = 45 + 60 = 105
Hence, the correct answer is 105.
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