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GATE 2022 CE (CE2) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The numerator and denominator of $3/4$ are increased by a positive integer x, and those of $15/17$ are decreased by x. The resulting fractions are equal. Find x.

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (C) 3

Explanation

Equate the modified fractions: $(3+x)/(4+x)=(15-x)/(17-x)$. Cross multiplication gives $51+14x-x^2=60+11x-x^2$.

Hence $3x=9$, so **x=3 (C)**. Both modified fractions then equal 6/7.