If the cost price of `4` toffees be equal to the selling price of `3` toffees then the gain% is

Options

A. `25%`
B. `30%`
C. `16 2/3%`
D. `37.1/3%`

Answer

To find the gain percentage when the cost price of 4 toffees is equal to the selling price of 3 toffees, we can follow these steps:

### Step-by-Step Solution:

1. **Let the Cost Price of 1 Toffee be X**:
- We denote the cost price of one toffee as \( X \).

2. **Calculate the Cost Price of 4 Toffees**:
- The cost price of 4 toffees is \( 4 \times X = 4X \).

3. **Set the Selling Price of 3 Toffees Equal to the Cost Price of 4 Toffees**:
- According to the problem, the selling price of 3 toffees is equal to the cost price of 4 toffees. Therefore, we have:
\[ \text{Selling Price of 3 Toffees} = 4X \]

4. **Calculate the Selling Price of 1 Toffee**:
- To find the selling price of one toffee, we divide the selling price of 3 toffees by 3:
\[ \text{Selling Price of 1 Toffee} = \frac{4X}{3} \]

5. **Calculate the Selling Price of 4 Toffees**:
- The selling price of 4 toffees will be:
\[ \text{Selling Price of 4 Toffees} = 4 \times \frac{4X}{3} = \frac{16X}{3} \]

6. **Calculate the Gain**:
- Gain is calculated as the selling price minus the cost price:
\[ \text{Gain} = \text{Selling Price of 4 Toffees} - \text{Cost Price of 4 Toffees} \]
- Substituting the values we found:
\[ \text{Gain} = \frac{16X}{3} - 4X \]
- To perform the subtraction, convert \( 4X \) into a fraction with the same denominator:
\[ 4X = \frac{12X}{3} \]
- Now, we can subtract:
\[ \text{Gain} = \frac{16X}{3} - \frac{12X}{3} = \frac{4X}{3} \]

7. **Calculate the Gain Percentage**:
- Gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
- The cost price of 4 toffees is \( 4X \):
\[ \text{Gain Percentage} = \left( \frac{\frac{4X}{3}}{4X} \right) \times 100 \]
- Simplifying this:
\[ \text{Gain Percentage} = \left( \frac{4}{3 \times 4} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = \frac{100}{3} \approx 33.33\% \]

### Final Answer:
The gain percentage is approximately **33.33%**.