Two numbers P and Q are such that P : Q = x : y. If 1 is added to both the numbers, the ratio becomes 7 : 10. If 3 is added to both the numbers, the ratio becomes 3 : 4. What is (x + y) : (x - y) equal to ?
- A. -5 ✓
- B. -3
- C. 3
- D. Cannot be determined due to insufficient data
Correct Answer: A. -5
Explanation
We have (P+1)/(Q+1) = 7/10 \implies 10P - 7Q = -3 and (P+3)/(Q+3) = 3/4 \implies 4P - 3Q = -3. Solving these linear equations gives P = 6 and Q = 9. The ratio x : y = 6 : 9 = 2 : 3. Thus, (x+y)/(x-y) = (2+3)/(2-3) = -5.
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