CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If x = 4ab/(a + b), where a ≠ b, then the value of (x + 2a)/(x − 2a) + (x + 2b)/(x − 2b) is:
The value is 2. Writing x/2a = 2b/(a+b) and applying componendo and dividendo gives (a+3b)/(b−a); the second term gives (3a+b)/(a−b). Combining over b−a yields (2b−2a)/(b−a), which equals 2.
- A1
- B2Correct
- C0
- D4
Explanation
x/(2a) = 2b/(a+b). By componendo and dividendo, (x+2a)/(x−2a) = (2b+a+b)/(2b−a−b) = (a+3b)/(b−a). Similarly x/(2b) = 2a/(a+b) gives (x+2b)/(x−2b) = (3a+b)/(a−b). Sum = [(a+3b) − (3a+b)]/(b−a) = (2b−2a)/(b−a) = 2. Option C forgets the sign change in the second denominator.
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