Profit obtained on selling an article for Rs 310 is equal to the loss incurred on selling that article for Rs 230. What will be the loss percent age when selling price is R 180 ?

Options

A. 33`1/3`
B. 16`2/3`
C. 32`1/3`
D. 20`1/2`

Answer

To solve the problem step by step, we will follow the given information and derive the necessary values.

### Step 1: Understand the given information
We know that:
- Selling Price (SP1) = Rs 310 (where profit is made)
- Selling Price (SP2) = Rs 230 (where loss is incurred)
- The profit from selling at Rs 310 is equal to the loss from selling at Rs 230.

### Step 2: Define the Cost Price (CP)
Let the Cost Price (CP) be \( x \).

### Step 3: Set up the equations
From the information given:
- Profit when sold for Rs 310:
\[ \text{Profit} = SP1 - CP = 310 - x \]
- Loss when sold for Rs 230:
\[ \text{Loss} = CP - SP2 = x - 230 \]

Since the profit is equal to the loss, we can set up the equation:
\[ 310 - x = x - 230 \]

### Step 4: Solve for CP
Now, we will solve the equation:
\[ 310 - x = x - 230 \]
Adding \( x \) to both sides:
\[ 310 = 2x - 230 \]
Adding 230 to both sides:
\[ 310 + 230 = 2x \]
\[ 540 = 2x \]
Dividing both sides by 2:
\[ x = 270 \]

### Step 5: Calculate the loss when selling price is Rs 180
Now we need to find the loss when the selling price is Rs 180:
- Selling Price (SP3) = Rs 180
- Loss = CP - SP3 = 270 - 180 = Rs 90

### Step 6: Calculate the loss percentage
The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{90}{270} \right) \times 100 \]
Calculating:
\[ \text{Loss Percentage} = \frac{1}{3} \times 100 = 33.33\% \]
This can be written as \( 33 \frac{1}{3} \% \).

### Final Answer
The loss percentage when selling price is Rs 180 is \( 33 \frac{1}{3} \% \).

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