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

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%

Answer 2

Let's assume the following:
Selling price of the large boxes be Rs.200
Selling price of the small boxes be Rs.100
Now. let's consider the following:
Large box has L grams of Chocolate
Small box has S grams of Chocolate

Now, the relation between the selling price per gram of chocolate can be represented as :
\(\frac{200}{L}=0.88\times\frac{100}{S}\)

By solving the above relation , we get the ratio of the amount of chocolates in each box :
\(\frac{L}{S}=\frac{25}{11}\)

Now , the percentage by which weight of chocolate in the large box exceeds that in the small box :
\((\frac{25}{11}-1)\times100\)
≈ 127%
Therefore, the correct option is (A) : 127.