Sajal purchased some car parts for Rs.20776 including VAT at 12%. What is the original cost of these spare parts?

Answer

To find the original cost of the car parts purchased by Sajal, we can follow these steps:

### Step 1: Understand the Problem
Sajal purchased car parts for Rs. 20,776, which includes a VAT of 12%. We need to find the original cost of the car parts before VAT was added.

### Step 2: Set Up the Formula
The formula to find the original price (Cost Price, CP) when you know the Selling Price (SP) and the VAT percentage is:
\[ CP = \frac{SP}{1 + \frac{VAT\%}{100}} \]
Where:
- SP = Selling Price (including VAT)
- VAT% = VAT percentage

### Step 3: Substitute the Values
Here, the Selling Price (SP) is Rs. 20,776 and the VAT% is 12. We can substitute these values into the formula:
\[ CP = \frac{20,776}{1 + \frac{12}{100}} \]

### Step 4: Simplify the Denominator
Calculate \(1 + \frac{12}{100}\):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

### Step 5: Calculate the Original Cost
Now substitute this back into the formula:
\[ CP = \frac{20,776}{1.12} \]
Now perform the division:
\[ CP = 18,554.46 \]

### Step 6: Round Off
Since we are dealing with currency, we can round it off to the nearest rupee:
\[ CP \approx 18,554 \]

### Final Answer
The original cost of the spare parts is approximately Rs. 18,554.

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