Discussion
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?
Answer: A
The correct pie chart is V 10%, R 20%, Y 30%, G 40%.
Check each chart against the four conditions, taking the percentages as counts out of 100:
- (i) Y + 2V = 30 + 20 = 50
- (ii) V + G = 10 + 40 = 50
- (iii) Y + R = 30 + 20 = 50
- (iv) V + 2R = 10 + 40 = 50
All four hold. Solving directly gives the same: (i) and (iv) give Y + 2V = V + 2R, so Y = 2R - V; with (iii), 3R - V = 50, and with (iv), V = 50 - 2R, so R = 20, V = 10, Y = 30 and G = 40. The total is 100, so the counts are also the percentages.
The other charts fail at once: V 40% and Y 20% give Y + 2V = 100; V 30%, Y 10% gives 70; V 20%, Y 40% gives 80.
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