The marked price of a trouser is Rs 3510. The shopkeeper allows a discount of 40% and gains 17%. If no discount is allowed, then what will be the profit percentage?

Options

A. `69.8`
B. 95
C. 85
D. `74.6`

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Identify the given values
- Marked Price (MP) = Rs 3510
- Discount = 40%
- Gain Percentage = 17%

### Step 2: Calculate the Selling Price (SP) after the discount
The Selling Price (SP) can be calculated using the formula:
\[ SP = MP \times \left(1 - \frac{Discount}{100}\right) \]
Substituting the values:
\[ SP = 3510 \times \left(1 - \frac{40}{100}\right) \]
\[ SP = 3510 \times \left(1 - 0.4\right) \]
\[ SP = 3510 \times 0.6 \]
\[ SP = 2106 \]

### Step 3: Relate Selling Price and Cost Price using Gain Percentage
The relationship between Selling Price (SP), Cost Price (CP), and Gain Percentage is given by:
\[ SP = CP \times \left(1 + \frac{Gain\ Percentage}{100}\right) \]
We know SP = 2106 and Gain Percentage = 17%, so:
\[ 2106 = CP \times \left(1 + \frac{17}{100}\right) \]
\[ 2106 = CP \times 1.17 \]

### Step 4: Calculate the Cost Price (CP)
To find CP, rearrange the equation:
\[ CP = \frac{2106}{1.17} \]
Calculating this gives:
\[ CP \approx 1800 \]

### Step 5: Calculate Profit when no discount is allowed
If no discount is allowed, the Selling Price will be equal to the Marked Price:
\[ SP = MP = 3510 \]
Now, we can calculate the profit:
\[ Profit = SP - CP \]
\[ Profit = 3510 - 1800 \]
\[ Profit = 1710 \]

### Step 6: Calculate Profit Percentage
Profit Percentage can be calculated using the formula:
\[ Profit\ Percentage = \left(\frac{Profit}{CP}\right) \times 100 \]
Substituting the values:
\[ Profit\ Percentage = \left(\frac{1710}{1800}\right) \times 100 \]
Calculating this gives:
\[ Profit\ Percentage \approx 95\% \]

### Final Answer
The profit percentage if no discount is allowed is **95%**.

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