When a shopkeeper allows 36% discount on the retail price of his product, he earns a profit of 8.8%. Find the discount percentage given by shopkeeper if he intended to earn 34.3% profit by selling same product?

Options

A. `24%`
B. `22%`
C. `21%`
D. `19%`

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript and break it down into clear steps.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The shopkeeper allows a 36% discount on the retail price and earns an 8.8% profit.
- We need to find the discount percentage if he intends to earn a 34.3% profit.

2. **Assume the Cost Price (CP)**:
- Let the cost price (CP) of the product be ₹100.

3. **Calculate the Selling Price (SP) for 8.8% Profit**:
- Since the profit is 8.8%, the selling price (SP) can be calculated as:
\[ SP = CP + (Profit \% \times CP) = 100 + (8.8\% \times 100) = 100 + 8.8 = ₹108.8 \]

4. **Calculate the Retail Price (RP)**:
- The shopkeeper gives a 36% discount on the retail price. This means:
\[ SP = RP \times \left(1 - \frac{Discount \%}{100}\right) \]
- Substituting the known values:
\[ 108.8 = RP \times \left(1 - \frac{36}{100}\right) = RP \times 0.64 \]
- Rearranging to find RP:
\[ RP = \frac{108.8}{0.64} = ₹170 \]

5. **Calculate the Selling Price for 34.3% Profit**:
- To earn a 34.3% profit, the new selling price (SP) will be:
\[ SP = CP + (Profit \% \times CP) = 100 + (34.3\% \times 100) = 100 + 34.3 = ₹134.3 \]

6. **Calculate the New Discount Percentage**:
- Let the new discount percentage be \(D\). The selling price can also be expressed as:
\[ SP = RP \times \left(1 - \frac{D}{100}\right) \]
- Substituting the known values:
\[ 134.3 = 170 \times \left(1 - \frac{D}{100}\right) \]
- Rearranging gives:
\[ 1 - \frac{D}{100} = \frac{134.3}{170} \]
- Calculating the right side:
\[ 1 - \frac{D}{100} = 0.79 \]
- Therefore:
\[ \frac{D}{100} = 1 - 0.79 = 0.21 \]
- Thus, multiplying by 100 gives:
\[ D = 21\% \]

### Conclusion:
The discount percentage given by the shopkeeper if he intends to earn a 34.3% profit is **21%**.