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

Answer: (A)

127

Answer 2

Let's break the problem down:
Let's denote:

1. $S$ as the cost of the small box.
2. $L$ as the cost of the large box. So, $L = 2S$.
3. $w_s$ as the weight of chocolate in the small box.
4. $w_l$ as the weight of chocolate in the large box.
   5. Price per gram of chocolate in the small box = $\frac{S}{w_s}$.
   6. Price per gram of chocolate in the large box = $0.88(\frac{S}{w_s})$ (since it's 12% less than that in the small box).
   Now, from the large box pricing, $\frac{L}{w_l} = 0.88(\frac{S}{w_s})$
   Substitute $L$ in the above equation:
   $\frac{2S}{w_l} = 0.88 \times \frac{S}{w_s}$
   $\frac{2}{w_l} = 0.88 \times \frac{1}{w_s}$
   $w_l = 2.27w_s$
   This means the large box contains 2.27 times the weight of chocolate compared to the small box. Therefore, it exceeds the small box's weight by:
   $2.27 - 1 = 1.27$
   Or 127%.
   The percentage by which the weight of chocolate in the large box exceeds that in the small box is approximately 127%