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CA Foundation · Quantitative Aptitude · Equations

A fraction becomes 3/5 when 1 is added to both its numerator and denominator, and becomes 1/2 when 1 is subtracted from both. What is the sum of the numerator and denominator of the original fraction?

The sum is 14. The conditions give 5x − 3y = −2 and y = 2x − 1, which solve to x = 5 and y = 9. The original fraction is 5/9, and both conditions check out: 6/10 = 3/5 and 4/8 = 1/2.

  1. A14Correct
  2. B13
  3. C12
  4. D16

Explanation

Let the fraction be x/y. Then 5(x + 1) = 3(y + 1) gives 5x − 3y = −2, and 2(x − 1) = y − 1 gives y = 2x − 1. Substituting: 5x − 6x + 3 = −2, so x = 5 and y = 9. Check: 6/10 = 3/5 and 4/8 = 1/2. The sum is 14.

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