A merchant changed his trade discount from 25% to 15%. This would increase selling price by

Options

A. `3(1)/(3)%`
B. `6(1)/(6)%`
C. `13(1)/(3)%`
D. `16(1)/(3)%`

Answer

To solve the problem of how much the selling price increases when the trade discount changes from 25% to 15%, we can follow these steps:

### Step 1: Define the Market Price
Let’s assume the market price (MP) of the item is 100 rupees.

### Step 2: Calculate Selling Price with 25% Discount
When the trade discount is 25%, the selling price (SP1) can be calculated as follows:
- Discount = 25% of 100 = 25 rupees
- Selling Price (SP1) = Market Price - Discount = 100 - 25 = 75 rupees

### Step 3: Calculate Selling Price with 15% Discount
Now, when the trade discount is changed to 15%, the new selling price (SP2) can be calculated:
- Discount = 15% of 100 = 15 rupees
- Selling Price (SP2) = Market Price - Discount = 100 - 15 = 85 rupees

### Step 4: Calculate the Increase in Selling Price
To find the increase in selling price, we subtract the old selling price from the new selling price:
- Increase in Selling Price = SP2 - SP1 = 85 - 75 = 10 rupees

### Step 5: Calculate the Percentage Increase
To find the percentage increase in selling price, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Old Selling Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{10}{75} \right) \times 100 = \frac{1000}{75} = \frac{40}{3} \approx 13.33\% \]

### Final Answer
The increase in selling price is approximately **13.33%**.

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