The cost price of a shirt is Rs 262.40. At what price should it be marked so as to gain 14% after allowing a 18% discount on the marked price?

Options

A. Rs 364.80
B. Rs 356
C. Rs 358.40
D. Rs 352

Answer

To find the marked price (MP) of the shirt that allows for a 14% profit after an 18% discount, we can follow these steps:

### Step 1: Identify the given values
- Cost Price (CP) = Rs. 262.40
- Profit Percentage = 14%
- Discount Percentage = 18%

### Step 2: Calculate the Selling Price (SP)
To achieve a profit of 14% on the cost price, we can calculate the selling price (SP) using the formula:
\[ SP = CP + (Profit \% \times CP) \]
Substituting the values:
\[ SP = 262.40 + \left( \frac{14}{100} \times 262.40 \right) \]
\[ SP = 262.40 + 36.736 = 299.136 \]

### Step 3: Relate Selling Price to Marked Price
The selling price (SP) is related to the marked price (MP) and the discount given. The formula for this relationship is:
\[ SP = MP - (Discount \% \times MP) \]
This can be rewritten as:
\[ SP = MP \times \left(1 - \frac{Discount \%}{100}\right) \]
Substituting the discount percentage:
\[ SP = MP \times \left(1 - \frac{18}{100}\right) = MP \times 0.82 \]

### Step 4: Set up the equation
Now we can set the two expressions for SP equal to each other:
\[ 299.136 = MP \times 0.82 \]

### Step 5: Solve for Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{299.136}{0.82} \]
Calculating this gives:
\[ MP = 364.00 \]

### Conclusion
The marked price should be Rs. 364.00 to achieve a 14% profit after allowing an 18% discount.