At what price should a shirt , costing Rs. 602, be marked so that there is a profit of `10%` when it is sold by given `14%` discount on its marked price /

Options

A. Rs. 700
B. Rs. 770
C. Rs. 660
D. Rs. 750

Answer

To find the marked price of the shirt that costs Rs. 602, ensuring a profit of 10% after applying a 14% discount, we can follow these steps:

### Step 1: Understand the given values
- Cost Price (CP) = Rs. 602
- Profit Percentage = 10%
- Discount Percentage = 14%

### Step 2: Calculate the Selling Price (SP) for a 10% profit
To find the Selling Price (SP) that includes a 10% profit on the Cost Price, we use the formula:
\[ SP = CP + (Profit \% \times CP) \]
Calculating the profit:
\[ Profit = 10\% \text{ of } 602 = \frac{10}{100} \times 602 = 60.2 \]
Now, calculate SP:
\[ SP = 602 + 60.2 = 662.2 \]

### Step 3: Relate Selling Price to Marked Price (MP)
The Selling Price (SP) can also be expressed in terms of the Marked Price (MP) and the discount:
\[ SP = MP - (Discount \% \times MP) \]
This can be rewritten as:
\[ SP = MP \times \left(1 - \frac{Discount \%}{100}\right) \]
Substituting the discount percentage:
\[ SP = MP \times \left(1 - \frac{14}{100}\right) = MP \times \left(\frac{86}{100}\right) \]

### Step 4: Set up the equation
Now we can set the two expressions for SP equal to each other:
\[ 662.2 = MP \times \left(\frac{86}{100}\right) \]

### Step 5: Solve for Marked Price (MP)
To find MP, rearrange the equation:
\[ MP = \frac{662.2}{\frac{86}{100}} = 662.2 \times \frac{100}{86} \]
Calculating this gives:
\[ MP = 662.2 \times \frac{100}{86} \approx 770 \]

### Conclusion
Thus, the marked price of the shirt should be approximately Rs. 770.

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