Question

Giri bought an auto for Rs 89880 which included a sales tax of \(\mathrm{Rs} 5880 .\) Find the rate of the sales tax. (1) \(5 \%\) (2) \(8 \%\) (3) \(9 \%\) (4) \(7 \%\)

Short answer

Answer: The sales tax rate is 7%.

Step-by-step solution

Determine the original cost of the auto

To find the original cost of the auto before tax, subtract the sales tax amount from the total cost. In this case, the total cost is Rs 89880, and the sales tax is Rs 5880. So, the original cost of the auto is: Original Cost = Total Cost - Sales Tax Original Cost = Rs 89880 - Rs 5880 Original Cost = Rs 84000

Calculate the sales tax rate

Now, we will divide the sales tax amount by the original cost of the auto and multiply the result by 100 to get the sales tax rate as a percentage: Sales Tax Rate = (Sales Tax / Original Cost) × 100 Sales Tax Rate = (Rs 5880 / Rs 84000) × 100 Sales Tax Rate = 0.07 × 100 Sales Tax Rate = 7 So, the correct answer is: (4) 7%

Key concepts

Percentage Calculation

Percentage calculation is a fundamental concept in mathematics that allows us to express a number as a part of 100. This concept is especially useful in various real-life situations, including calculating discounts, determining interest rates, and analyzing data. In this exercise, understanding how to calculate percentages is crucial to finding the sales tax rate.

When we calculate the percentage, we essentially want to know how much a particular value represents in relation to a whole. For example, when we calculated the sales tax rate, we wanted to know what fraction of the original auto cost the sales tax represented. This fraction is then converted into a percentage by multiplying by 100.

Here are the steps to perform a percentage calculation:

• Identify the part value and the whole value.
• Divide the part value by the whole value to get the decimal.
• Multiply the decimal by 100 to convert it to a percentage.

By following these steps, you can successfully solve percentage problems like the sales tax calculation shown in the exercise.

Cost Analysis

Cost analysis involves evaluating and understanding the individual components that contribute to the total cost of an item or service. It's a key skill for both consumers and businesses, as it helps in budgeting and financial planning.

In the context of this exercise, cost analysis comes into play when determining the original price of the auto before sales tax was added. By understanding that the total cost included both the base price of the auto and the sales tax, we can calculate the original cost and then analyze it further.

Here is how the cost evaluation process worked in the exercise:

• Start with the total cost, which is made up of the base cost and additional fees like taxes.
• Subtract any additional fees (e.g., sales tax) from the total cost to find the base cost.

This skill is valuable not only in tax calculations but also in many areas where cost breakdowns are necessary, such as project budgeting, financial accounting, and everyday purchases.

Mathematical Problem Solving

Mathematical problem-solving is a critical-thinking process that involves breaking down complex questions into manageable steps, allowing us to find clear, accurate solutions. The exercise we're discussing showcases this process effectively.

Problem-solving can be approached by understanding each element involved, like identifying what is given, determining what needs solving, and developing a plan to find the solution. In the sales tax exercise, the steps were as follows:

• First, find the original price of the auto by subtracting the sales tax from the total cost.
• Next, calculate the percentage that the sales tax represents of the original price.
• Conclude by multiplying the result by 100 to find the sales tax rate in percentage form.

These problem-solving steps can be applied to many scenarios beyond just sales tax calculations. Whether solving equations, analyzing statistical data, or financial planning, developing systematic problem-solving skills is essential for academic and real-world success.