If the cost price of 5 bananas be equal to the selling price of 3 bananas, then gain per cent is

Options

A. `33.1/3%`
B. `15%`
C. `50%`
D. `40%`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Define the Cost Price of One Banana:**
Let the cost price (CP) of one banana be \( x \).

2. **Calculate the Cost Price of 5 Bananas:**
The cost price of 5 bananas will be:
\[ \text{Cost Price of 5 Bananas} = 5 \times x = 5x \]

3. **Set Up the Selling Price of 3 Bananas:**
According to the problem, the cost price of 5 bananas is equal to the selling price (SP) of 3 bananas. Therefore:
\[ \text{Selling Price of 3 Bananas} = 5x \]

4. **Calculate the Selling Price of One Banana:**
The selling price of one banana can be calculated as:
\[ \text{Selling Price of 1 Banana} = \frac{\text{Selling Price of 3 Bananas}}{3} = \frac{5x}{3} \]

5. **Calculate the Gain for One Banana:**
Gain can be calculated using the formula:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]
For one banana, this becomes:
\[ \text{Gain} = \frac{5x}{3} - x \]
To simplify this, we need a common denominator:
\[ \text{Gain} = \frac{5x}{3} - \frac{3x}{3} = \frac{5x - 3x}{3} = \frac{2x}{3} \]

6. **Calculate the Gain Percentage:**
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Cost Price}} \times 100\right) \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left(\frac{\frac{2x}{3}}{x} \times 100\right) \]
Simplifying this:
\[ \text{Gain Percentage} = \left(\frac{2}{3} \times 100\right) = \frac{200}{3} \approx 66.67\% \]

### Final Answer:
The gain percentage is approximately \( 66.67\% \).