If the cost price of `18` mangoes is the same as the selling price of `16` mangoes, find the gain percent.

Options

A. Gain `= "Rs. 2"`
Gain `% = 12.5%`
B. Gain `= "Rs. 12"`
Gain `% = 32.5%`
C. Gain `= "Rs. 8"`
Gain `% = 15%`
D. Gain `= "Rs. 7"`
Gain `% = 12.5%`

Answer

To find the gain percent when the cost price of 18 mangoes is the same as the selling price of 16 mangoes, we can follow these steps:

### Step-by-Step Solution:

1. **Let the Cost Price of 1 Mango be x**:
We assume the cost price (CP) of one mango is \( x \).

2. **Calculate the Total Cost Price of 18 Mangoes**:
The total cost price of 18 mangoes will be:
\[ \text{Total CP} = 18 \times x = 18x \]

3. **Let the Selling Price of 1 Mango be y**:
We assume the selling price (SP) of one mango is \( y \).

4. **Calculate the Total Selling Price of 16 Mangoes**:
The total selling price of 16 mangoes will be:
\[ \text{Total SP} = 16 \times y = 16y \]

5. **Set the Cost Price Equal to the Selling Price**:
According to the problem, the cost price of 18 mangoes is equal to the selling price of 16 mangoes:
\[ 18x = 16y \]

6. **Find the Selling Price of 1 Mango**:
Rearranging the equation to find \( y \):
\[ y = \frac{18x}{16} = \frac{9x}{8} \]

7. **Calculate the Gain**:
Gain is defined as the selling price minus the cost price. Thus, the gain for one mango is:
\[ \text{Gain} = y - x = \frac{9x}{8} - x = \frac{9x}{8} - \frac{8x}{8} = \frac{x}{8} \]

8. **Calculate the Gain Percent**:
Gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percent} = \left( \frac{\frac{x}{8}}{x} \right) \times 100 = \frac{1}{8} \times 100 = 12.5\% \]

### Final Answer:
The gain percent is **12.5%**.