Three tables are purchased for Rs 2500 each. First is sold at a profit of 8%, the second is sold at a loss of 3%. If their average selling price is Rs 2575, find the profit per cent on the third.

Options

A. 0.06
B. 0.05
C. 0.04
D. 0.08

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Selling Price of the First Table
The first table is sold at a profit of 8%.

- Cost Price (CP) of the first table = Rs 2500
- Profit Percentage = 8%

The Selling Price (SP) can be calculated using the formula:
\[ SP = CP + \left(\frac{Profit \%}{100} \times CP\right) \]
Substituting the values:
\[ SP_1 = 2500 + \left(\frac{8}{100} \times 2500\right) = 2500 + 200 = 2700 \]

### Step 2: Calculate the Selling Price of the Second Table
The second table is sold at a loss of 3%.

- Cost Price (CP) of the second table = Rs 2500
- Loss Percentage = 3%

The Selling Price (SP) can be calculated using the formula:
\[ SP = CP - \left(\frac{Loss \%}{100} \times CP\right) \]
Substituting the values:
\[ SP_2 = 2500 - \left(\frac{3}{100} \times 2500\right) = 2500 - 75 = 2425 \]

### Step 3: Calculate the Average Selling Price
The average selling price of the three tables is given as Rs 2575.

Using the formula for average:
\[ \text{Average SP} = \frac{SP_1 + SP_2 + SP_3}{3} \]
Substituting the known values:
\[ 2575 = \frac{2700 + 2425 + SP_3}{3} \]

### Step 4: Solve for SP_3
To find SP_3, we multiply both sides by 3:
\[ 2575 \times 3 = 2700 + 2425 + SP_3 \]
Calculating the left side:
\[ 7725 = 2700 + 2425 + SP_3 \]
Now, combine the known selling prices:
\[ 7725 = 5125 + SP_3 \]
Subtract 5125 from both sides:
\[ SP_3 = 7725 - 5125 = 2600 \]

### Step 5: Calculate the Profit Percentage on the Third Table
Now, we need to find the profit percentage on the third table.

- Cost Price (CP) of the third table = Rs 2500
- Selling Price (SP) of the third table = Rs 2600

Profit can be calculated as:
\[ \text{Profit} = SP - CP = 2600 - 2500 = 100 \]

Now, the profit percentage can be calculated using the formula:
\[ \text{Profit \%} = \left(\frac{Profit}{CP} \times 100\right) \]
Substituting the values:
\[ \text{Profit \%} = \left(\frac{100}{2500} \times 100\right) = 4\% \]

### Final Answer
The profit percentage on the third table is **4%**.

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