Niraj incurred a loss of 55 per cent on selling an article for Rs. 9,549 . What was the cost price of the article?

Options

A. Rs. 27,700
B. Rs. 25,600
C. Rs. 21,220
D. Rs. 29,000

Explanation

To find the cost price (CP) of the article that Niraj sold at a loss of 55%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss.
The formula for loss is given by:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Since Niraj incurred a loss of 55%, we can express this as:
\[ \text{Loss} = \frac{55}{100} \times \text{CP} \]
Thus, we can also express the Selling Price (SP) in terms of Cost Price (CP):
\[ \text{SP} = \text{CP} - \text{Loss} = \text{CP} - \frac{55}{100} \times \text{CP} = \text{CP} \left(1 - \frac{55}{100}\right) = \text{CP} \left(\frac{45}{100}\right) \]

### Step 2: Substitute the Selling Price (SP).
We know from the problem that the Selling Price (SP) is Rs. 9,549. Therefore, we can set up the equation:
\[ 9549 = \text{CP} \left(\frac{45}{100}\right) \]

### Step 3: Solve for Cost Price (CP).
To find CP, we rearrange the equation:
\[ \text{CP} = 9549 \times \frac{100}{45} \]
Now, calculate \( \frac{100}{45} \):
\[ \frac{100}{45} = \frac{20}{9} \]
Thus, we can rewrite the equation:
\[ \text{CP} = 9549 \times \frac{20}{9} \]

### Step 4: Perform the multiplication.
Now, calculate \( 9549 \times \frac{20}{9} \):
\[ \text{CP} = \frac{9549 \times 20}{9} \]
Calculating \( 9549 \times 20 = 190980 \):
\[ \text{CP} = \frac{190980}{9} \]
Now, divide \( 190980 \) by \( 9 \):
\[ \text{CP} = 21220 \]

### Final Answer:
The cost price of the article is Rs. 21,220.

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