By selling an object for Rs 900, a man earns a profit that is double the loss incurred when the object is sold for Rs 450. If he sells it at a profit of 20%, find the selling price of this object.

Options

A. 554
B. 618
C. 620
D. None of these

Answer

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

### Step 1: Understand the Problem
We know that selling an object for Rs 900 results in a profit that is double the loss incurred when the object is sold for Rs 450. We need to find the selling price when the object is sold at a profit of 20%.

### Step 2: Define Variables
Let:
- \( CP \) = Cost Price of the object
- \( L \) = Loss when sold for Rs 450
- \( P \) = Profit when sold for Rs 900

### Step 3: Set Up the Equations
From the problem, we know:
1. When sold for Rs 450, the loss incurred is \( L = CP - 450 \).
2. When sold for Rs 900, the profit is \( P = 900 - CP \).
3. The profit is double the loss: \( P = 2L \).

### Step 4: Substitute and Solve
Substituting the expressions for \( P \) and \( L \) into the equation \( P = 2L \):
\[ 900 - CP = 2(CP - 450) \]

### Step 5: Expand and Rearrange
Expanding the right side:
\[ 900 - CP = 2CP - 900 \]
Rearranging gives:
\[ 900 + 900 = 2CP + CP \]
\[ 1800 = 3CP \]

### Step 6: Solve for Cost Price
Dividing both sides by 3:
\[ CP = \frac{1800}{3} = 600 \]

### Step 7: Calculate Selling Price for 20% Profit
Now that we have the cost price, we need to find the selling price when there is a 20% profit:
\[ SP = CP + (20\% \text{ of } CP) \]
Calculating 20% of \( CP \):
\[ 20\% \text{ of } 600 = \frac{20}{100} \times 600 = 120 \]
Thus, the selling price is:
\[ SP = 600 + 120 = 720 \]

### Final Answer
The selling price of the object when sold at a profit of 20% is **Rs 720**.

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