If x:y = 1:3, then the ratio (7x² + 3xy) : (2xy + y²) is

Quantitative Aptitude ·Previously asked in JKSSB Sub Inspector (Executive) 2022

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Question

If x:y = 1:3, then the ratio (7x² + 3xy) : (2xy + y²) is

  1. A. 10:3
  2. B. 16:5
  3. C. 16:7
  4. D. 16:15 (Correct answer)

Correct Answer

Option D — 16:15

Detailed Solution & Explanation

The correct answer is 16:15.

Key Points

  • Given x:y = 1:3, let x = 1 and y = 3. Numerator: 7x^2 + 3xy = 7(1)^2 + 3(1)(3) = 7 + 9 = 16. Denominator: 2xy + y^2 = 2(1)(3) + (3)^2 = 6 + 9 = 15. Therefore the ratio (7x^2 + 3xy) : (2xy + y^2) = 16 : 15.