Charu purchased a dinner set at 3/10 th of its selling price and sold it at 10%more than its CP.Find the gain per cent.

Options

A. `15%`
B. `5%`
C. `9%`
D. `10%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Selling Price (SP)
Let the selling price of the dinner set be denoted as SP.

### Step 2: Calculate the Cost Price (CP)
According to the problem, Charu purchased the dinner set at \( \frac{3}{10} \) of its selling price. Therefore, we can express the cost price (CP) as:
\[ CP = \frac{3}{10} \times SP \]

### Step 3: Determine the Selling Price after Selling
Charu sold the dinner set at 10% more than its cost price. To find the selling price after selling (let's denote it as SP2), we calculate:
\[ SP2 = CP + 10\% \text{ of } CP \]
This can be rewritten as:
\[ SP2 = CP \times \left(1 + \frac{10}{100}\right) = CP \times \frac{110}{100} = 1.1 \times CP \]

### Step 4: Substitute CP in SP2
Now, substituting the expression for CP from Step 2 into the equation for SP2:
\[ SP2 = 1.1 \times \left(\frac{3}{10} \times SP\right) \]
\[ SP2 = \frac{1.1 \times 3}{10} \times SP = \frac{3.3}{10} \times SP = \frac{33}{100} \times SP \]

### Step 5: Calculate the Profit
Now, we can calculate the profit made by Charu:
\[ \text{Profit} = SP2 - CP \]
Substituting the values we have:
\[ \text{Profit} = \left(\frac{33}{100} \times SP\right) - \left(\frac{3}{10} \times SP\right) \]
To simplify, convert \( \frac{3}{10} \) to a fraction with a denominator of 100:
\[ \frac{3}{10} = \frac{30}{100} \]
Thus,
\[ \text{Profit} = \left(\frac{33}{100} \times SP\right) - \left(\frac{30}{100} \times SP\right) = \frac{3}{100} \times SP \]

### Step 6: Calculate Gain Percentage
The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{\frac{3}{100} \times SP}{\frac{3}{10} \times SP}\right) \times 100 \]
The \( SP \) cancels out:
\[ \text{Gain Percentage} = \left(\frac{\frac{3}{100}}{\frac{3}{10}}\right) \times 100 \]
This simplifies to:
\[ \text{Gain Percentage} = \left(\frac{3}{100} \times \frac{10}{3}\right) \times 100 = \left(\frac{10}{100}\right) \times 100 = 10\% \]

### Final Answer
The gain percentage is **10%**.

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