A shopkeeper sold a TV set for Rs. 17,940 with a discount of `8%` and earned a profit of `19.6%`. What would been the percentage of profit earned if no discount was offered ?

Options

A. `24.8%`
B. `25%`
C. `26.4%`
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Selling Price (SP) and Discount
The selling price of the TV set is given as Rs. 17,940, and the discount offered is 8%.

### Step 2: Calculate the Marked Price (MP)
The formula to find the marked price when the selling price and discount are known is:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]
The discount can also be expressed as:
\[ \text{Discount} = \frac{\text{Discount Percentage}}{100} \times \text{Marked Price} \]
Thus, we can express the selling price as:
\[ \text{SP} = \text{MP} \times \left(1 - \frac{8}{100}\right) \]
Rearranging gives:
\[ \text{MP} = \frac{\text{SP}}{1 - \frac{8}{100}} \]
Substituting the values:
\[ \text{MP} = \frac{17940}{0.92} \]
Calculating this gives:
\[ \text{MP} = 19500 \]

### Step 3: Calculate the Cost Price (CP)
We know that the shopkeeper made a profit of 19.6%. The formula for calculating the cost price when the selling price and profit percentage are known is:
\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit Percentage}}{100}} \]
Substituting the values:
\[ \text{CP} = \frac{17940}{1 + \frac{19.6}{100}} \]
This simplifies to:
\[ \text{CP} = \frac{17940}{1.196} \]
Calculating this gives:
\[ \text{CP} \approx 15000 \]

### Step 4: Calculate the Profit Percentage if No Discount was Offered
If no discount was offered, the selling price would be equal to the marked price, which we calculated as Rs. 19,500. The profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values:
\[ \text{Profit} = 19500 - 15000 = 4500 \]
Now, we can calculate the profit percentage:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{4500}{15000}\right) \times 100 = 30\% \]

### Final Answer
If no discount was offered, the percentage of profit earned would be **30%**.

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