A shopkeeper sells T.V. for Rs 17940 after giving discounts of 8% and earns profit of 19.6% . If he had not given the discount then find its profit %?

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the given information
The shopkeeper sells a TV for Rs. 17,940 after giving a discount of 8% and earns a profit of 19.6%. We need to find the profit percentage if no discount was given.

### Step 2: Calculate the Marked Price (MP)
Let the marked price (MP) be \( x \).
Since the shopkeeper gives an 8% discount, the selling price (SP) can be calculated as:
\[ SP = MP - \text{Discount} = x - 0.08x = 0.92x \]
Given that the selling price (SP) is Rs. 17,940, we can set up the equation:
\[ 0.92x = 17940 \]
To find \( x \), we divide both sides by 0.92:
\[ x = \frac{17940}{0.92} \approx 19500 \]
So, the marked price (MP) is Rs. 19,500.

### Step 3: Calculate the Cost Price (CP)
We know that the profit percentage is 19.6%. The relationship between the cost price (CP), marked price (MP), and profit percentage can be expressed as:
\[ CP = \frac{MP \times (100 - \text{Profit \%})}{100} \]
Substituting the values we have:
\[ CP = \frac{19500 \times (100 - 19.6)}{100} = \frac{19500 \times 80.4}{100} = 15678 \]
So, the cost price (CP) is Rs. 15,678.

### Step 4: Calculate the Selling Price (SP) without Discount
If the shopkeeper had not given any discount, the selling price would be equal to the marked price:
\[ SP = MP = 19500 \]

### Step 5: Calculate the Profit
Now, we can calculate the profit when selling at the marked price:
\[ \text{Profit} = SP - CP = 19500 - 15678 = 3822 \]

### Step 6: Calculate the Profit Percentage
Finally, we can find the profit percentage using the formula:
\[ \text{Profit \%} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \left(\frac{3822}{15678}\right) \times 100 \approx 24.4\% \]

### Conclusion
If the shopkeeper had not given the discount, the profit percentage would be approximately **24.4%**.

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