Question

Amrit Raj bought a Nokia mobile for Rs 5040 which includes \(10 \%\) discount on the market price and \(12 \%\) sales tax on the remaining price. Find the marked price of the mobile phone. (1) \(\mathrm{Rs} 4672\) (2) \(\operatorname{Rs} 5124\) (3) \(\mathrm{Rs} 5000\) (4) Rs 4830

Short answer

Answer: The original market price of the Nokia mobile phone was Rs 5000.

Step-by-step solution

Find the price before sales tax

To find the price before the sales tax, we need to know that the 12% sales tax was applied to the discounted price, not the original market price. Since Amrit Raj paid Rs 5040 after the sales tax, we can represent this as: Discounted price + 12% sales tax = Rs 5040 Let P_d represent the discounted price. Then the equation can be written as: P_d + (12% of P_d) = Rs 5040 We will now solve for P_d: P_d (1 + 0.12) = Rs 5040 P_d (1.12) = Rs 5040 Now, divide by 1.12 to find the discounted price: P_d = Rs 5040 / 1.12 = Rs 4500

Find the original market price

Now that we have found the discounted price (P_d = Rs 4500), we can find the original market price. Since Amrit Raj received a 10% discount on the market price, we can represent this as: Market price - 10% discount = Rs 4500 Let P_m represent the original market price. Then the equation can be written as: P_m - (10% of P_m) = Rs 4500 We will now solve for P_m: P_m (1 - 0.10) = Rs 4500 P_m (0.90) = Rs 4500 Now, divide by 0.90 to find the original market price: P_m = Rs 4500 / 0.90 = Rs 5000 So, the original market price of the Nokia mobile phone is Rs 5000, which corresponds to option (3).

Key concepts

Market Price Calculation

Calculating the market price of a product involves determining the original price before any discounts or taxes are applied. In this case, Amrit Raj's Nokia mobile purchase at Rs 5040 included both a discount and a sales tax. To discover the original market price, we need to backtrack to understand how each deduction and addition influences the final cost.

Firstly, we needed to find out what the discounted price was before adding the sales tax. This process involves reversing the 12% sales tax calculation. By considering the price after tax (Rs 5040), we can work backwards to discover the discounted price. Once we know the discounted price, finding the original market price becomes a process of reversing the discount back from this reduced price.

Understanding market price calculation aids buyers and sellers in setting reasonable selling prices and keeping track of discounts and taxes to avoid misunderstanding actual costs. Thus, it ensures knowledgeable financial decisions during transactions. This form of calculation is vital for anyone aiming to better comprehend their expenses and savings during purchase activities.

Percentage Problems

Percentage problems are commonplace in day-to-day mathematics; they pop up in financial calculations, sales, and discounts very often. In scenarios like this, we see the utility in computing both discount percentages and tax percentages independently to determine the actual total amount paid.

Consider the sale of the Nokia mobile: we first figure out the effect of a 12% sales tax on its discounted price. By establishing the equation:

• Discounted Price + 12% Sales Tax = Total Cost

we determine how much tax was added to the price, and thus find out what the base (discounted) price was before tax.

Subsequently, we deal with finding the initial market price from the discounted price by employing a similar percentage problem. Here, understanding that a 10% discount means the customer ultimately pays 90% of the initial planned price allows us to solve:

• Market Price – 10% Discount = Discounted Price

This reveals the original value before any deductions.

By learning how to tackle percentage problems, students can expertly handle many real-world tasks involving finance, shopping, and budgeting with increased confidence and accuracy.

Step-by-Step Problem Solving

Step-by-step problem solving is critical when approaching mathematical scenarios, particularly when they're compounded with multiple calculations like discounts and taxes. This technique involves breaking down calculations into smaller, manageable parts rather than attempting to process everything at once.

In the original exercise problem, we utilized step-by-step problem solving by first separating the problem into finding the discounted price before sales tax. It prevents confusion and ensures each section of the problem, especially complex ones, is clearly understood before proceeding. Once the discounted price is realized, the next step makes use of this to ascertain the initial market price.

To apply step-by-step methods effectively, always:

• Identify each part of the problem and its requirements.
• Tackle one section at a time, allowing for thorough initial understanding.
• Employ calculations independently before combining results to get a comprehensive answer.

Such refined problem solving not only clarifies computations but also builds a structured approach to problem-solving applicable to other complex tasks encountered in academia and daily life.