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CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms

If x = 4ab/(a + b), with a ≠ b and a, b ≠ 0, then the value of (x + 2a)/(x − 2a) + (x + 2b)/(x − 2b) is:

The value is 2. Writing x/2a = 2b/(a + b) and x/2b = 2a/(a + b) and applying componendo-dividendo gives (a + 3b)/(b − a) and (3a + b)/(a − b). Their sum simplifies to 2. Check with a = 1, b = 3: x = 3, giving 5 − 3 = 2.

  1. A2Correct
  2. B1
  3. C0
  4. D4

Explanation

x/(2a) = 2b/(a + b), so by componendo-dividendo (x + 2a)/(x − 2a) = (2b + a + b)/(2b − a − b) = (a + 3b)/(b − a). Similarly x/(2b) = 2a/(a + b) gives (b + 3a)/(a − b). Sum = [(a + 3b) − (b + 3a)]/(b − a) = (2b − 2a)/(b − a) = 2. Test a = 1, b = 3: x = 3; (3+2)/(3−2) = 5 and (3+6)/(3−6) = −3; sum 2.

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