Question

Ajay purchased a computer for Rs 34650 which includes \(12 \%\) rebate on the marked price and \(5 \%\) sales tax on the remaining price. What is the marked price of the computer? (1) \(\mathrm{Rs} 35000\) (2) \(\mathrm{Rs} 37500\) (3) \(\mathrm{Rs} 40000\) (4) \(\mathrm{Rs} 42500\)

Short answer

Answer: The marked price of the computer is Rs 37500.

Step-by-step solution

Determine the price reduction due to the rebate

First, let the marked price of the computer be \(x\). The price reduction due to the \(12 \%\) rebate would be \(0.12x\).

Determine the price before tax

After receiving the \(12 \%\) rebate, the remaining price would be \(x - 0.12x = 0.88x\).

Determine the price increase due to sales tax

Next, we need to determine the price increase due to the \(5 \%\) sales tax on the remaining price. The added tax on \(0.88x\) would be \(0.05(0.88x) = 0.044x\).

Calculate the final price formula

The final price Ajay paid for the computer is the price before tax plus the price increase due to sales tax. So the final price is \(0.88x + 0.044x = 0.924x\). We know that the final price is also Rs 34650, so we have this equation: \(0.924x = 34650\)

Solve for x

Now, we just need to solve for \(x\), which represents the marked price of the computer. \(x = \frac{34650}{0.924} = 37500\)

Verify the answer with the given options

The value of \(x\) that we found is Rs 37500. This matches option (2), so the marked price of the computer is \(\boxed{\mathrm{Rs \, 37500}}\).

Key concepts

Rebate Calculation

When you hear about a rebate, it refers to a reduction in price offered by the seller. Rebates are frequently used as a sales promotion tactic to increase the sale of a product. In the context of our exercise, a 12% rebate is provided on the marked price of a computer.

To calculate the rebate amount, you simply take the marked price and multiply it by the rebate percentage. The formula looks like this: Rebate Amount = Marked Price \times Rebate Percentage. Using our exercise as an example: if the marked price is represented by the variable \(x\), then the rebate amount will be \(0.12x\).

After applying the rebate, to find the reduced price before tax, subtract the rebate amount from the marked price: Price Before Tax = Marked Price - Rebate Amount. So for our case, it will be \(x - 0.12x = 0.88x\). Understanding the rebate calculation is crucial as it affects the final sale price before taxes are applied.

Sales Tax Impact on Price

Sales tax is a tax imposed by the government on the sale of goods and services. It is typically expressed as a percentage of the sale price paid by the consumer, which means the actual monetary value of the tax depends on the final selling price of the product after any discounts or rebates.

When a sales tax is applied, it increases the end price paid by the consumer. To calculate the sales tax amount, multiply the price before tax by the sales tax rate: Sales Tax Amount = Price Before Tax \times Sales Tax Rate. From our problem, after a 12% rebate, we apply a 5% sales tax to the remaining amount: the tax added would be \(0.05(0.88x) = 0.044x\).

To determine the final price a customer will pay, which includes the sales tax, simply add the sales tax amount to the price before tax: Final Price = Price Before Tax + Sales Tax Amount. In the exercise, this calculation resulted in the equation \(0.88x + 0.044x = 0.924x\) to represent the final price including the sales tax.

Price Before Tax

The 'price before tax', also known as the 'net price', is the amount after all discounts, rebates, and markdowns are applied but before any sales tax is added.

It represents the actual amount that the seller receives for the product. To find out the price before sales tax, you initially start with the marked price and adjust it for any reductions: Price Before Tax = Marked Price - Discounts and Rebates.

For instance, in the exercise Ajay faced, we calculated the price before tax to be \(0.88x\), where \(x\) was the original marked price and 0.88 is the remaining percentage of the marked price after applying a 12% rebate.

Understanding the concept of 'price before tax' is important for several reasons, including budgeting and understanding the actual base price of a product or a service. It is a key step in determining the final price after factoring in the sales tax, which is critical for both consumers and businesses alike.