Simon purchased a bicycle for Rs. 6810. He had paid a VAT of 13.5%. The list price of the bicycle was

Options

A. Rs.6000
B. Rs.6140
C. Rs.6696.50
D. Rs.5970.50

Answer

To find the list price of the bicycle that Simon purchased for Rs. 6810 with a VAT of 13.5%, we can follow these steps:

### Step 1: Understand the relationship between the selling price and the list price
The selling price (SP) includes the list price (LP) plus the VAT applied to the list price. The formula can be expressed as:
\[ SP = LP + \text{VAT} \]

### Step 2: Express the VAT in terms of the list price
Since VAT is a percentage of the list price, we can express it as:
\[ \text{VAT} = \frac{13.5}{100} \times LP \]
Thus, the selling price can be rewritten as:
\[ SP = LP + \frac{13.5}{100} \times LP \]
\[ SP = LP \left(1 + \frac{13.5}{100}\right) \]
\[ SP = LP \left(\frac{100 + 13.5}{100}\right) \]
\[ SP = LP \left(\frac{113.5}{100}\right) \]

### Step 3: Rearrange the formula to find the list price
Now, we can rearrange the formula to find the list price (LP):
\[ LP = \frac{SP \times 100}{113.5} \]

### Step 4: Substitute the selling price into the formula
Now we can substitute the selling price (Rs. 6810) into the formula:
\[ LP = \frac{6810 \times 100}{113.5} \]

### Step 5: Calculate the list price
Now we perform the calculation:
\[ LP = \frac{681000}{113.5} \]
\[ LP \approx 6000 \]

### Conclusion
The list price of the bicycle is approximately Rs. 6000.

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