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

If a/b = c/d, then by componendo and dividendo, which of the following is always true (assuming no denominator is zero)?

Componendo and dividendo states that if a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d). It follows by adding and subtracting 1 on both sides and then dividing the two results, so the signs match on both sides.

  1. A(a + b)/(a − b) = (c + d)/(c − d)Correct
  2. B(a + b)/(a − b) = (c − d)/(c + d)
  3. C(a + b)/(c + d) = (a − b)/(d − c)
  4. D(a + c)/(a − c) = (b − d)/(b + d)

Explanation

Adding 1 to both sides of a/b = c/d gives (a+b)/b = (c+d)/d. Subtracting 1 gives (a−b)/b = (c−d)/d. Dividing the first by the second gives (a+b)/(a−b) = (c+d)/(c−d). Option B inverts one side, so it is wrong.

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