A dealer buys a sofa set for Rs30000. At what price must he mark it so that after allowing a discount of 10%, he still makes a profit of 5%?

Options

A. Rs 37500
B. Rs 42450
C. Rs 35000
D. Rs 33000

Answer

To solve the problem, we need to determine the marked price (MP) of the sofa set such that after giving a discount of 10%, the dealer still makes a profit of 5% on the cost price (CP) of Rs. 30,000.

### Step-by-Step Solution:

1. **Calculate the Selling Price (SP) for a 5% Profit:**
- The cost price (CP) of the sofa set is Rs. 30,000.
- To find the selling price (SP) that gives a profit of 5%, we use the formula:
\[ SP = CP + (5\% \text{ of } CP) \]
- Calculate 5% of CP:
\[ 5\% \text{ of } 30000 = \frac{5}{100} \times 30000 = 1500 \]
- Now, calculate SP:
\[ SP = 30000 + 1500 = 31500 \]

2. **Determine the Marked Price (MP):**
- The dealer allows a discount of 10% on the marked price (MP).
- After the discount, the selling price (SP) is given by:
\[ SP = MP - (10\% \text{ of } MP) \]
- This can be rewritten as:
\[ SP = MP \times (1 - 0.10) = MP \times 0.90 \]
- We already calculated SP as Rs. 31,500, so we set up the equation:
\[ 31500 = MP \times 0.90 \]

3. **Solve for the Marked Price (MP):**
- Rearranging the equation gives:
\[ MP = \frac{31500}{0.90} \]
- Calculate MP:
\[ MP = 35000 \]

### Final Answer:
The marked price (MP) at which the dealer must sell the sofa set is **Rs. 35,000**.