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GATE 2025 CE (CE2) – Question 5

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

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:
(i) The sum of Yellow balls and twice the number of Violet balls is 50.
(ii) The sum of Violet and Green balls is 50.
(iii) The sum of Yellow and Red balls is 50.
(iv) The sum of Violet and twice the number of Red balls is 50.

Which one of the following Pie charts correctly represents the balls in the bag?

  1. V 10%, R 20%, Y 30%, G 40%
  2. V 40%, R 10%, Y 20%, G 30%
  3. V 30%, R 40%, Y 10%, G 20%
  4. V 20%, R 30%, Y 40%, G 10%

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Correct answer: (A) V 10%, R 20%, Y 30%, G 40%

Explanation

From (i), $Y = 50 - 2V$. From (iii), $R = 50 - Y = 2V$. Then (iv) gives $V + 4V = 50$, so $V = 10$, $R = 20$, $Y = 30$ and, from (ii), $G = 40$. The total is 100, so the shares are V 10%, R 20%, Y 30% and G 40%, which is option A.