A person makes a profit of `17%` after allowing `10%` discount on its marked price. If he gives `14%` discount on the marked price, then his profit percent is:

Options

A. `11.8`
B. `14.6`
C. `10.5`
D. `23.8`

Answer

To solve the problem step by step, let's define the variables and use the information given in the question.

### Step 1: Define Variables
Let:
- \( CP \) = Cost Price
- \( MP \) = Marked Price
- \( SP \) = Selling Price

### Step 2: Determine Selling Price with 10% Discount
When a 10% discount is given on the marked price, the selling price can be calculated as:
\[ SP = MP \times \left(1 - \frac{10}{100}\right) = MP \times 0.90 \]

### Step 3: Profit Calculation with 17% Profit
According to the problem, the profit is 17% when selling at this price:
\[ SP = CP \times \left(1 + \frac{17}{100}\right) = CP \times 1.17 \]

### Step 4: Set Up the Equation
Now we can equate the two expressions for selling price:
\[ MP \times 0.90 = CP \times 1.17 \]

### Step 5: Express Marked Price in Terms of Cost Price
Rearranging the equation gives:
\[ \frac{MP}{CP} = \frac{1.17}{0.90} \]
Calculating this gives:
\[ \frac{MP}{CP} = \frac{117}{90} = \frac{13}{10} \]
This means:
\[ MP = \frac{13}{10} \times CP \]

### Step 6: Determine Selling Price with 14% Discount
Now, if a 14% discount is given on the marked price, the new selling price becomes:
\[ SP = MP \times \left(1 - \frac{14}{100}\right) = MP \times 0.86 \]

### Step 7: Substitute Marked Price
Substituting \( MP \) from Step 5 into the selling price equation:
\[ SP = \left(\frac{13}{10} \times CP\right) \times 0.86 = \frac{13 \times 0.86}{10} \times CP \]
Calculating this gives:
\[ SP = \frac{11.18}{10} \times CP = 1.118 \times CP \]

### Step 8: Calculate Profit
Now we can calculate the profit:
\[ \text{Profit} = SP - CP = (1.118 \times CP) - CP = 0.118 \times CP \]

### Step 9: Calculate Profit Percentage
Profit percentage can be calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{0.118 \times CP}{CP}\right) \times 100 = 11.8\% \]

### Final Answer
Thus, the profit percentage when a 14% discount is given on the marked price is:
**11.8%**

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