After selling 72 article a man losses SP of 12 article. If the CP of article is 980. Find the SP of article

Options

A. 720
B. 1020
C. 840
D. 880

Answer

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

### Step 1: Understand the given information
- The cost price (CP) of one article is Rs 980.
- After selling 72 articles, the man incurs a loss equivalent to the selling price (SP) of 12 articles.

### Step 2: Calculate the total cost price of 72 articles
To find the total cost price of 72 articles, we multiply the cost price of one article by the number of articles sold:
\[ \text{Total CP of 72 articles} = \text{CP of one article} \times \text{Number of articles sold} = 980 \times 72 \]
\[ \text{Total CP of 72 articles} = 70560 \]

### Step 3: Determine the loss incurred
The loss incurred is equal to the selling price of 12 articles. To find the selling price of 12 articles, we need to first find the selling price of one article.

Let the selling price of one article be \( SP \). Then, the selling price of 12 articles will be:
\[ \text{SP of 12 articles} = 12 \times SP \]

### Step 4: Set up the equation for loss
According to the problem, the loss incurred is equal to the total cost price minus the total selling price:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} \]
Given that the loss is equal to the selling price of 12 articles, we can write:
\[ \text{Loss} = 12 \times SP \]
Thus, we have:
\[ \text{Total CP} - \text{Total SP} = 12 \times SP \]

### Step 5: Substitute the values
Now substituting the values we have:
\[ 70560 - (72 \times SP) = 12 \times SP \]

### Step 6: Combine like terms
Rearranging the equation gives:
\[ 70560 = 72 \times SP + 12 \times SP \]
\[ 70560 = 84 \times SP \]

### Step 7: Solve for SP
Now, we can find the selling price of one article:
\[ SP = \frac{70560}{84} \]
\[ SP = 840 \]

### Conclusion
The selling price of one article is Rs 840.

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