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CAT 2021 Quant Question [Slot 1] with Solution 20

Question
Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to
  1. 144
  2. 127
  3. 135
  4. 124
Option: 2
Solution:
Let the selling price of the Large and Small boxes of chocolates be Rs.200 and Rs.100 respectively. Let us consider that the Large box has \(L\) grams of chocolate while the Small box has \(S\) grams of chocolate.
The relation between the selling price per gram of chocolate can be represented as: \(\frac{{200}}{L} = 0.88 \times \;\frac{{100}}{S}\)
On solving we obtain the ratio of the amount of chocolate in each box as: \(\frac{L}{S} = \frac{{25}}{{11}}\)
The percentage by which the weight of chocolate in the large box exceeds that in the small box = \(\left( {\frac{{25}}{{11}} - 1} \right) \times \;100 \approx \;127\% \)
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