Question

Ramu purchased a motorcycle at a price of Rs 37800 which includes the sales tax. If the rate of sales tax is \(8 \%\), then what is the list price of the motorcycle? (1) Rs 31000 (2) Rs 33000 (3) Rs 35000 (4) Rs 37000

Short answer

Answer: The list price of the motorcycle is approximately Rs 35000.

Step-by-step solution

Determine the sales tax amount

To find the amount of sales tax paid on the motorcycle, we can use the formula: Sales tax amount = (Rate of sales tax / 100) * List price Since we want to find the list price, let's call it x. We know that the rate of sales tax is \(8 \%\). The formula for sales tax amount can be written as: Sales tax amount = 0.08 * x Now, we know that the total price paid for the motorcycle is Rs 37800, which includes the list price and sales tax amount. Therefore, we can write the equation: Total price = List price + Sales tax amount 37800 = x + 0.08 * x

Find the list price

Now, we can solve the equation to find the list price (x): 37800 = x + 0.08 * x 37800 = 1x + 0.08x 37800 = 1.08x To find x, divide both sides of the equation by 1.08: x = 37800 / 1.08 x ≈ 35000 Therefore, the list price of the motorcycle is approximately Rs 35000, which is option (3).

Key concepts

Sales Tax in Mathematics

Understanding how sales tax works is essential for both consumers and businesses. It's an additional amount of money calculated as a percentage of the product's selling price. In mathematics, the process of determining sales tax is straightforward once the tax rate is known.

Using the exercise as an example, a motorcycle's final purchase price includes the sales tax. If the tax rate is given, we can backtrack to find the original list price before tax was added. This is commonly done via an equation where the total cost equals the list price plus the product of the list price and the tax rate (represented as a decimal).

The real-world application of this concept helps consumers understand how much they are actually paying for a product, and businesses set appropriate prices while accounting for tax inclusion in their total sales.

Percentages in Mathematics

Percentages are ubiquitous in mathematics and everyday life. They represent a fraction of 100 and are used to describe proportions, ratios, and comparisons. In our context, sales tax rates are expressed as percentages.

When calculating the sales tax, you convert the percentage to a decimal to perform multiplication. For example, a tax rate of 8% becomes 0.08 in decimal form. This conversion is critical to correctly calculate the additional cost on top of the list price. Furthermore, understanding percentages allows students to move comfortably between fractions, decimals, and percentages, which is a valuable skill in various mathematical and real-life contexts.

Equation Solving

Solving an equation is like discovering a mystery value that makes a mathematical statement true. In the case of our exercise, solving the equation enables us to determine the original list price of the motorcycle before tax was applied.

Equations can be simple or complex, but the aim is to isolate the variable, which represents the unknown number, on one side of the equation. This often involves applying inverse operations. For the given problem, we added sales tax (expressed as a percentage of the list price) to the list price and set this sum equal to the total price paid. To find the list price, we then separated the variable by dividing both sides of the equation by the sum of 1 plus the tax rate expressed as a decimal. The skill of equation solving is crucial for not only sales tax calculations but for understanding broader mathematical concepts and applications.