Question

Bala bought a motorbike at Rs 49050 which included sales tax. The rate of sales tax was \(9 \%\). Find the listed price of the motorbike (in \(\mathrm{Rs}\) s). (1) 44000 (2) 45000 (3) 46000 (4) 47000

Short answer

Answer: (2) 45000 Rupees.

Step-by-step solution

Set up the equation

Let the listed price of the motorbike be x rupees. Sales tax is calculated as 9% of x, which is (9/100)x. So, the total price including sales tax is: x + (9/100)x = 49050.

Simplify the equation

Combine x and (9/100)x. Multiply every term by 100 to eliminate the fraction. 100x + 9x = 49050 * 100

Solve the equation for x

109x = 4905000 x = 4905000 / 109 x = 45000

Check the options

Bala bought the motorbike at Rs 45000 before sales tax. Comparing this with the given options, the correct answer is: (2) 45000 Rupees.

Key concepts

Percentages in Mathematics

Understanding percentages is fundamental to many areas of mathematics and real life, including the calculation of sales tax, interest rates, and discounts. A percentage represents a fraction of 100 and is typically denoted using the percent symbol (%). For instance, to express 9% in a mathematical equation, we'd write it as \(0.09\) or \(\frac{9}{100}\). When a price includes a percentage-based sales tax, we calculate the tax by multiplying the percentage by the original price (the price before tax).

For practical applications such as calculating sales tax, it is important to be familiar with converting percentages to decimals and fractions. This simplifies the multiplication process involved in finding the tax amount. To illustrate, if you have a 9% sales tax on an item, you would convert the 9% to a decimal (0.09) and multiply it by the item's price to find out how much tax you will be paying on top of the base price.

Algebraic Equation Solving

Algebraic equation solving is a critical skill in mathematics that involves finding the value of unknown variables. We often encounter this in real-world situations, such as determining the original price of an item before tax. In our example with Bala's motorbike, setting up the equation is the first step, where \(x\) represents the unknown original price. The sales tax issue can be translated into a simple algebraic equation, \(x + \frac{9}{100}x = 49050\), combining the original price and the tax to equal the total price paid.

Simplifying this equation and solving for \(x\) involves combining like terms and isolating the variable on one side of the equation. Understanding the distribution of numbers and the basic operations of addition, subtraction, multiplication, and division applied to both sides of the equation is essential to find the correct value for \(x\).

Mathematical Problem-Solving

Mathematical problem-solving encompasses a set of skills and strategies used to tackle a wide range of mathematical challenges. The problem-solving process often starts with understanding the problem, which includes identifying all the relevant information and what is being sought. Next, devising a plan to find the solution is crucial; this may involve choosing appropriate formulas or setting up equations.

In Bala's motorbike purchase, we identified that the total cost and sales tax rate were the relevant pieces of information. Our plan was to translate these into an algebraic equation that could be manipulated to find the original price before tax. Once the plan is executed and the solution is found, as in Step 3 where we calculate \(x\) to be 45000 rupees, it is always good practice to review the solution, checking that it makes sense and aligns with the problem's parameters, which can be seen in the final step where the calculated price is matched with the provided options.