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

• A. 127
• B. 135
• C. 124
• D. 144

Answer 1

The Correct Option is A

Define the following variables:

• \(S\) represents the cost of the small box.
• \(L\) represents the cost of the large box, with \(L = 2S\).
• \(w_s\) is the weight of chocolate in the small box.
• \(w_l\) is the weight of chocolate in the large box.

Step 1: Calculate Price per Gram of Chocolate

The price per gram of chocolate in the small box is calculated as: \[ \frac{S}{w_s} \] The price per gram of chocolate in the large box is 12% less than in the small box, which can be expressed as: \[ 0.88 \times \frac{S}{w_s} \]

Step 2: Formulate and Solve the Equation for the Large Box

Based on the large box pricing, we establish the equation: \[ \frac{L}{w_l} = 0.88 \times \frac{S}{w_s} \] Substitute \(L = 2S\) into the equation: \[ \frac{2S}{w_l} = 0.88 \times \frac{S}{w_s} \] Simplify the equation: \[ \frac{2}{w_l} = 0.88 \times \frac{1}{w_s} \] Solve for \(w_l\): \[ w_l = 2.27w_s \]

Step 3: Conclusion

This result indicates that the large box contains 2.27 times the weight of chocolate compared to the small box. The excess weight of chocolate in the large box over the small box is: \[ 2.27 - 1 = 1.27 \] This equates to 127%.

Final Answer:

The percentage increase in the weight of chocolate in the large box compared to the small box is approximately \( \boxed{127\%} \).