A shopkeeper sells an article for Rs18000 after allowing 16% discount and still manages to gain 32% profit. If he sold the article at 9% discount on MP, then what will be his profit %?

Options

A. `33.33%`
B. `43%`
C. `45%`
D. `40%`

Answer

To solve the problem step by step, we will follow the reasoning and calculations outlined in the video transcript.

### Step 1: Determine the Mark Price (MP)
Let the Mark Price (MP) be \( X \).

Given that a 16% discount is allowed on the MP, the Selling Price (SP) after discount is given as Rs 18,000.

The formula for Selling Price after discount is:
\[ SP = MP \times \left(1 - \frac{\text{Discount \%}}{100}\right) \]
Substituting the values:
\[ 18000 = X \times \left(1 - \frac{16}{100}\right) \]
\[ 18000 = X \times \frac{84}{100} \]
To find \( X \):
\[ X = \frac{18000 \times 100}{84} \]
Calculating \( X \):
\[ X = \frac{1800000}{84} = 21428.57 \text{ (approximately)} \]

### Step 2: Determine the Cost Price (CP)
We know that the shopkeeper gains a profit of 32%. The Selling Price (SP) is Rs 18,000.

The formula for Selling Price in terms of Cost Price (CP) and profit percentage is:
\[ SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]
Substituting the values:
\[ 18000 = CP \times \left(1 + \frac{32}{100}\right) \]
\[ 18000 = CP \times \frac{132}{100} \]
To find \( CP \):
\[ CP = \frac{18000 \times 100}{132} \]
Calculating \( CP \):
\[ CP = \frac{1800000}{132} = 13636.36 \text{ (approximately)} \]

### Step 3: Calculate New Selling Price with 9% Discount
Now, we need to find the new Selling Price if the shopkeeper sells the article at a 9% discount on the Mark Price (MP).

Using the previously calculated MP:
\[ MP = 21428.57 \]
The new Selling Price (SP) with a 9% discount is:
\[ SP = MP \times \left(1 - \frac{9}{100}\right) \]
Substituting the values:
\[ SP = 21428.57 \times \frac{91}{100} \]
Calculating the new SP:
\[ SP = 21428.57 \times 0.91 = 19500 \text{ (approximately)} \]

### Step 4: Calculate Profit Percentage
Now we can calculate the profit percentage using the new Selling Price and the Cost Price.

The formula for profit percentage is:
\[ \text{Profit \%} = \frac{SP - CP}{CP} \times 100 \]
Substituting the values:
\[ \text{Profit \%} = \frac{19500 - 13636.36}{13636.36} \times 100 \]
Calculating the profit:
\[ \text{Profit} = 19500 - 13636.36 = 5863.64 \]
Now substituting back into the profit percentage formula:
\[ \text{Profit \%} = \frac{5863.64}{13636.36} \times 100 \approx 43\% \]

### Final Answer
The profit percentage when the article is sold at a 9% discount on the Mark Price is approximately **43%**.

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