The MP of a camera is 3/2 of the CP and SP is 9/10 of MP. Find the percentage profit or loss.

Options

A. 25% profit
B. 35% profit
C. 33.33 % loss
D. none of these

Answer

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

### Step 1: Understand the given relationships
- **MP (Marked Price)** of the camera is given as \( \frac{3}{2} \) of the **CP (Cost Price)**.
- **SP (Selling Price)** is given as \( \frac{9}{10} \) of the **MP**.

### Step 2: Express MP in terms of CP
Let the **CP** be \( x \).
Then, the **MP** can be expressed as:
\[ MP = \frac{3}{2} \times CP = \frac{3}{2} \times x = \frac{3x}{2} \]

### Step 3: Express SP in terms of CP
Now, substituting the expression for MP into the SP formula:
\[ SP = \frac{9}{10} \times MP = \frac{9}{10} \times \frac{3x}{2} = \frac{27x}{20} \]

### Step 4: Calculate Profit
To find the profit, we need to subtract the CP from the SP:
\[ \text{Profit} = SP - CP = \frac{27x}{20} - x \]
To perform the subtraction, express \( x \) with a common denominator:
\[ x = \frac{20x}{20} \]
Thus,
\[ \text{Profit} = \frac{27x}{20} - \frac{20x}{20} = \frac{7x}{20} \]

### Step 5: Calculate Percentage Profit
The percentage profit can be calculated using the formula:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Profit} = \left( \frac{\frac{7x}{20}}{x} \right) \times 100 = \left( \frac{7}{20} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage Profit} = \frac{700}{20} = 35\% \]

### Final Answer
The percentage profit is **35%**.

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