By selling a table for Rs. 2700 a man gets 10% loss, and then at what price (in Rs.) should he sell to gain 33 `1/3` %?

Options

A. 3000
B. 3300
C. 3600
D. 4000

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the table based on the given selling price (SP) and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 33⅓%.

### Step 1: Determine the Cost Price (CP)

Given:
- Selling Price (SP) = Rs. 2700
- Loss Percentage = 10%

When there is a loss of 10%, the selling price is 90% of the cost price.

This can be expressed as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
\[ 2700 = CP \times \left(1 - \frac{10}{100}\right) \]
\[ 2700 = CP \times 0.90 \]

Now, we can solve for CP:
\[ CP = \frac{2700}{0.90} \]
\[ CP = 3000 \]

### Step 2: Calculate the Selling Price for a 33⅓% Profit

Now that we have the cost price, we need to find the selling price that would give a profit of 33⅓%.

Profit percentage of 33⅓% can be expressed as:
\[ Profit\% = \frac{1}{3} \text{ or } 33.33\% \]

This means that the selling price (SP) will be:
\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
\[ SP = 3000 \times \left(1 + \frac{33.33}{100}\right) \]
\[ SP = 3000 \times \left(1 + \frac{1}{3}\right) \]
\[ SP = 3000 \times \frac{4}{3} \]

Now, calculate the selling price:
\[ SP = 3000 \times \frac{4}{3} = 4000 \]

### Final Answer
The selling price to gain a profit of 33⅓% should be Rs. 4000.

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