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Multiple Choice Questions

The product of two numbers is 2160 and their HCF is 12 If tbe sum of the squares of t...........

Quantitative Aptitude (CDS) LCM, HCF

The product of two numbers is 2160 and their HCF is 12. If tbe sum of the squares of the squares of the two numbers is 4896, tben what is tbe mean of the two numbers ?

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2023 CDS -1 MATH

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Explanation:

- We know two numbers have a product of 2160 and an HCF of 12.
- True numbers can be represented as 12x and 12y, where HCF is common.
- Therefore, 144xy (12x * 12y) equals 2160. Simplifies to xy = 15.
- Also, the sum of squares (12x)^2 + (12y)^2 equals 4896.
- Simplifying: 144(x^2 + y^2) = 4896; therefore, x^2 + y^2 = 34.
- Use identity: (x + y)^2 = x^2 + y^2 + 2xy; gives us (x + y)^2 = 64.
- Solving gives x + y = 8.
- Mehr (mean) of numbers 12x, 12y is: (12(x + y))/2 = 48.

**Option 3: 48** ✅

**YOUR ANSWER IS RIGHT**

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