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 of the shirt so that a profit of 14% is achieved after allowing an 18% discount, we can follow these steps:

### Step 1: Calculate the Selling Price (SP)
The cost price (CP) of the shirt is given as Rs. 262.40. To find the selling price that includes a profit of 14%, we can use the formula:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

First, we need to calculate the profit:

\[ \text{Profit} = \text{CP} \times \frac{14}{100} = 262.40 \times \frac{14}{100} = 36.736 \]

Now, we can find the selling price:

\[ \text{SP} = 262.40 + 36.736 = 299.136 \]

### Step 2: Relate Selling Price to Marked Price
Let the marked price (MP) be \( x \). Since there is an 18% discount on the marked price, the selling price can also be expressed as:

\[ \text{SP} = \text{MP} - \text{Discount} \]

The discount is 18% of the marked price:

\[ \text{Discount} = \text{MP} \times \frac{18}{100} = x \times \frac{18}{100} = 0.18x \]

Thus, we can write:

\[ \text{SP} = x - 0.18x = 0.82x \]

### Step 3: Set Up the Equation
Now we can set the two expressions for the selling price equal to each other:

\[ 0.82x = 299.136 \]

### Step 4: Solve for Marked Price
To find the marked price \( x \), we divide both sides by 0.82:

\[ x = \frac{299.136}{0.82} \]

Calculating this gives:

\[ x \approx 364.80 \]

### Conclusion
The marked price of the shirt should be Rs. 364.80 to achieve a 14% profit after allowing an 18% discount.

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