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GATE 2019 CE (CE2) – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

From 2001 to 2011 the populations of states X and Y increased by x% and y%, with x > y. P is the ratio of X’s population to Y’s in a given year. Find the percentage increase in P.

  1. $x/y$
  2. $x-y$
  3. $100(x-y)/(100+x)$
  4. $100(x-y)/(100+y)$

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Correct answer: (D) $100(x-y)/(100+y)$

Explanation

The new population ratio divided by the original is $(100+x)/(100+y)$. Subtract one and multiply by 100: $$\%\text{ increase}=\frac{100(x-y)}{100+y}.$$ Answer **D**; initial population sizes cancel.