A shopkeeper sold a TV set for Rs 17940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned if no discount was offered ?

Answer

To solve the problem step-by-step, we need to find out the percentage of profit earned if no discount was offered. Here’s how we can do it:

### Step 1: Determine the Marked Price (MP)
Given that the selling price (SP) after an 8% discount is Rs 17,940, we can express this relationship mathematically. The selling price is 92% of the marked price.

\[ SP = MP \times \left(1 - \frac{8}{100}\right) = MP \times 0.92 \]

Substituting the selling price:

\[ 17940 = MP \times 0.92 \]

To find the marked price (MP), we rearrange the equation:

\[ MP = \frac{17940}{0.92} \]

Calculating this gives:

\[ MP = 19500 \]

### Step 2: Determine the Cost Price (CP)
We know that the selling price is also related to the cost price (CP) through the profit percentage. The shopkeeper earned a profit of 19.6%, which means:

\[ SP = CP \times \left(1 + \frac{19.6}{100}\right) = CP \times 1.196 \]

Substituting the selling price:

\[ 17940 = CP \times 1.196 \]

To find the cost price (CP), we rearrange the equation:

\[ CP = \frac{17940}{1.196} \]

Calculating this gives:

\[ CP = 15000 \]

### Step 3: Calculate Profit if No Discount was Offered
If no discount was offered, the selling price would be equal to the marked price, which we found to be Rs 19,500. Now we can calculate the profit:

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 19500 - 15000 = 4500 \]

### Step 4: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]

Substituting the values we found:

\[ \text{Profit Percentage} = \left(\frac{4500}{15000}\right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = 30\% \]

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

---