Averages , Ratio and Proportion Question 10 - CAT 2021
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:
Step-by-Step Explanation
Let the price of the small box be PS = 100 and the price of the large box be PL = 200.
Let their weights be WS and WL.
- Formulate the price-per-gram relationship:
Price per gram (Small) = 100/WS
Price per gram (Large) = 200/WL
The price per gram of the large box is 12% less than that of the small box:
200/WL = 0.88 × (100/WS)
2/WL = 0.88/WS
WL/WS = 2/0.88 = 200/88 = 25/11
- Calculate the percentage weight increase:
Percentage Increase = ((25 − 11)/11) × 100% = (14/11) × 100% ≈ 127.27% ≈ 127%
Correct Option: B