A shopkeeper sells two articles, one of them with a profit of 10% for ₹ 1100 and another with a loss of 10% for ₹ 900. What will be the profit or loss percent?

Options

A. ₹ 1000
B. Neither profit nor loss
C. 20% profit
D. 20% loss

Answer

To solve the problem step by step, we need to calculate the cost price (CP) of each article and then determine the overall profit or loss percentage.

### Step 1: Calculate the Cost Price of the First Article
The first article is sold at a selling price (SP) of ₹1100 with a profit of 10%.

Profit percentage formula:
\[ \text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} \]

Let the cost price of the first article be \( CP_1 \).
Since the profit is 10%, we can express the selling price as:
\[ SP_1 = CP_1 + \text{Profit} \]
\[ SP_1 = CP_1 + CP_1 \times \frac{10}{100} \]
\[ SP_1 = CP_1 \left(1 + \frac{10}{100}\right) = CP_1 \times 1.1 \]

Now substituting the selling price:
\[ 1100 = CP_1 \times 1.1 \]

To find \( CP_1 \):
\[ CP_1 = \frac{1100}{1.1} = 1000 \]

### Step 2: Calculate the Cost Price of the Second Article
The second article is sold at a selling price of ₹900 with a loss of 10%.

Loss percentage formula:
\[ \text{Loss} = \text{Cost Price} \times \frac{\text{Loss Percentage}}{100} \]

Let the cost price of the second article be \( CP_2 \).
Since the loss is 10%, we can express the selling price as:
\[ SP_2 = CP_2 - \text{Loss} \]
\[ SP_2 = CP_2 - CP_2 \times \frac{10}{100} \]
\[ SP_2 = CP_2 \left(1 - \frac{10}{100}\right) = CP_2 \times 0.9 \]

Now substituting the selling price:
\[ 900 = CP_2 \times 0.9 \]

To find \( CP_2 \):
\[ CP_2 = \frac{900}{0.9} = 1000 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now we can calculate the total cost price (CP) and total selling price (SP):
\[ \text{Total CP} = CP_1 + CP_2 = 1000 + 1000 = 2000 \]
\[ \text{Total SP} = SP_1 + SP_2 = 1100 + 900 = 2000 \]

### Step 4: Determine Profit or Loss
Now we compare the total selling price and total cost price:
\[ \text{Total SP} = 2000 \]
\[ \text{Total CP} = 2000 \]

Since the total selling price is equal to the total cost price, there is no profit or loss.

### Step 5: Calculate Profit or Loss Percentage
Profit or Loss Percentage formula:
\[ \text{Profit or Loss Percentage} = \left(\frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit or Loss Percentage} = \left(\frac{2000 - 2000}{2000}\right) \times 100 = 0\% \]

### Final Answer
The shopkeeper has neither profit nor loss, so the profit or loss percentage is **0%**.

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