When an article is sold at 7/8th of its selling price, there is a loss of 37%. What will be the profit percentage when the same article is sold at 19/12th of its selling price ?

Options

A. `12.5%`
B. `14%`
C. `15%`
D. `16.66%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the article be ₹100.

**Hint:** Start by assuming a simple value for the cost price to make calculations easier.

### Step 2: Calculate the Selling Price (SP) at a Loss of 37%
If there is a loss of 37%, the selling price can be calculated as:
\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} \]
\[ \text{Loss} = 37\% \text{ of CP} = 37\% \text{ of } 100 = 37 \]
Thus,
\[ \text{SP} = 100 - 37 = 63 \]

**Hint:** Remember that a loss means the selling price is less than the cost price.

### Step 3: Determine the Selling Price at 7/8th of the Selling Price
We know that the article is sold at \( \frac{7}{8} \) of its selling price. Therefore:
\[ \text{SP at } \frac{7}{8} = \frac{7}{8} \times 63 \]
Calculating this gives:
\[ \text{SP at } \frac{7}{8} = \frac{7 \times 63}{8} = \frac{441}{8} = 55.125 \]

**Hint:** When calculating fractions, multiply the numerator by the value and then divide by the denominator.

### Step 4: Calculate the Selling Price at 19/12th of the Selling Price
Now, we need to find the selling price when the article is sold at \( \frac{19}{12} \) of its selling price:
\[ \text{SP at } \frac{19}{12} = \frac{19}{12} \times 63 \]
Calculating this gives:
\[ \text{SP at } \frac{19}{12} = \frac{19 \times 63}{12} = \frac{1197}{12} = 99.75 \]

**Hint:** Again, multiply and then divide to find the selling price at the new fraction.

### Step 5: Calculate the Profit
Now, we can calculate the profit made when selling at \( \frac{19}{12} \):
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
\[ \text{Profit} = 99.75 - 100 = -0.25 \]

**Hint:** Profit is calculated by subtracting the cost price from the selling price.

### Step 6: Calculate the Profit Percentage
To find the profit percentage, use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Since the profit is negative:
\[ \text{Profit Percentage} = \left( \frac{-0.25}{100} \right) \times 100 = -0.25\% \]

**Hint:** Profit percentage can be negative if there is a loss.

### Final Answer
The profit percentage when the same article is sold at \( \frac{19}{12} \) of its selling price is **-0.25%**.