A trade purchased a gift box for Rs 150. What should be the marked price on the gift box so that after allowinga discount of 10%, he makes a profit of 10%.

Options

A. Rs 180
B. Rs 183.33
C. Rs 186.6
D. Rs 190

Answer

To find the marked price on the gift box so that after allowing a discount of 10%, the trader makes a profit of 10%, we can follow these steps:

### Step 1: Determine the Cost Price (CP)
The cost price of the gift box is given as Rs. 150.

### Step 2: Calculate the Selling Price (SP) for a 10% Profit
To find the selling price that gives a profit of 10%, we use the formula:
\[ SP = CP + (Profit \% \times CP) \]
Here, the profit percentage is 10%. Therefore:
\[ SP = 150 + (10\% \times 150) \]
\[ SP = 150 + (0.10 \times 150) \]
\[ SP = 150 + 15 = 165 \]

### Step 3: Calculate the Marked Price (MP) Considering the Discount
The selling price (SP) is related to the marked price (MP) through the discount. If the trader allows a discount of 10%, then:
\[ SP = MP - (Discount \times MP) \]
The discount is 10%, so:
\[ SP = MP - (0.10 \times MP) \]
This can be simplified to:
\[ SP = MP \times (1 - 0.10) = MP \times 0.90 \]

### Step 4: Substitute the Selling Price into the Equation
We already calculated the selling price (SP) as Rs. 165. Now we can substitute this into the equation:
\[ 165 = MP \times 0.90 \]

### Step 5: Solve for Marked Price (MP)
To find the marked price, we rearrange the equation:
\[ MP = \frac{165}{0.90} \]
\[ MP = 183.33 \]

### Conclusion
The marked price on the gift box should be approximately Rs. 183.33.

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