If the cost price of 16 tables be equal to the selling price of 12 tables, the gain per cent is

Options

A. `33(1)/(3)%`
B. `20%`
C. `30%`
D. `15%`

Answer

To find the gain percentage when the cost price of 16 tables is equal to the selling price of 12 tables, we can follow these steps:

### Step 1: Define the Cost Price (CP) of One Table
Let the cost price of one table be \( X \).

### Step 2: Calculate the Cost Price of 16 Tables
The cost price of 16 tables will be:
\[ \text{Cost Price of 16 tables} = 16 \times X = 16X \]

### Step 3: Relate Cost Price of 16 Tables to Selling Price (SP) of 12 Tables
According to the problem, the cost price of 16 tables is equal to the selling price of 12 tables:
\[ \text{Selling Price of 12 tables} = 16X \]

### Step 4: Calculate the Selling Price of One Table
Now, we can find the selling price of one table:
\[ \text{Selling Price of 12 tables} = 12 \times \text{Selling Price of one table} \]
Let the selling price of one table be \( Y \). Therefore:
\[ 12Y = 16X \implies Y = \frac{16X}{12} = \frac{4X}{3} \]

### Step 5: Calculate the Gain
The gain can be calculated as:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]
For one table:
\[ \text{Gain} = Y - X = \frac{4X}{3} - X = \frac{4X}{3} - \frac{3X}{3} = \frac{X}{3} \]

### Step 6: Calculate Gain Percentage
The gain percentage is given by the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{\frac{X}{3}}{X} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
The gain percentage is \( 33.33\% \).

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