Two numbers are in the ratio of 2 : 3 and the product of their LCM and HCF is 96. The sum of the numbers is || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS
Two numbers are in the ratio of 2 : 3 and the product of their LCM and HCF is 96. The sum of the numbers is :
(A) 8
(B) 12
(C) 20
(D) 36
Solution:
To solve the problem, let's denote the two numbers as 2x and 3x, where x is a common factor.
We are given that the product of their LCM and HCF is 96. We can use the property that for any two numbers, the product of their LCM and HCF is equal to the product of the numbers themselves:
LCM(2x, 3x) × HCF(2x, 3x) = (2x) × (3x)
Let's denote the LCM as LCM and the HCF as HCF.
Thus,
LCM × HCF = 6x2
We are given that this product is 96:
6x2 = 96
Solving for x:
x2 = 96 / 6
x2 = 16
x = 4
Now we can find the two numbers:
2x = 2 × 4 = 8
3x = 3 × 4 = 12
The sum of the numbers is:
8 + 12 = 20
Thus, the answer is: 20
- This question was previously asked in the ADRE SLRC-2022 Paper III for the posts of Grade-III.
- Understanding and solving such questions enhances problem-solving skills.
- Practicing these types of questions is essential for effective preparation for competitive exams.
- It helps in familiarizing with the type of questions that can be asked in the exams.
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