An article when sold for Rs. 200 fetches 25 per cent profit. What would be the percentage profit/ loss if 6 such articles are sold for Rs. 1056 ?

Options

A. 10 per cent loss
B. 10 per cent profit
C. 5 per cent loss
D. 5 per cent profit

Answer

To solve the problem step by step, we need to find the cost price of one article first, then determine the selling price when 6 articles are sold, and finally calculate the profit or loss percentage.

### Step 1: Find the Cost Price (CP) of One Article
Given that when the article is sold for Rs. 200, it fetches a profit of 25%.

We can use the formula for selling price (SP) in terms of cost price (CP) and profit percentage:

\[ SP = CP + \left(\frac{Profit \%}{100} \times CP\right) \]

This can be rearranged to:

\[ SP = CP \times \left(1 + \frac{Profit \%}{100}\right) \]

Substituting the known values:

\[ 200 = CP \times \left(1 + \frac{25}{100}\right) \]
\[ 200 = CP \times 1.25 \]

Now, solving for CP:

\[ CP = \frac{200}{1.25} = 160 \text{ Rs.} \]

### Step 2: Find the Selling Price (SP) of 6 Articles
Now, we need to find the selling price of 6 articles. The total selling price given is Rs. 1056.

### Step 3: Calculate the Selling Price of One Article
To find the selling price of one article:

\[ SP \text{ of one article} = \frac{1056}{6} = 176 \text{ Rs.} \]

### Step 4: Determine Profit or Loss
Now we will calculate the profit or loss by comparing the selling price of one article with its cost price.

\[ \text{Profit} = SP - CP = 176 - 160 = 16 \text{ Rs.} \]

### Step 5: Calculate the Percentage Profit
To find the percentage profit, we use the formula:

\[ \text{Percentage Profit} = \left(\frac{Profit}{CP}\right) \times 100 \]

Substituting the values:

\[ \text{Percentage Profit} = \left(\frac{16}{160}\right) \times 100 = 10\% \]

### Final Answer
The percentage profit when 6 articles are sold for Rs. 1056 is **10%**.

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