Practice Questions

Identify the base price on which a discount is calculated.

What does the abbreviation GST stand for in the context of taxes?

Explain the difference between Marked Price and Sale Price.

Justify why compound interest always yields a higher return than simple interest for the same principal, rate, and a time period greater than one year.

State the formula to calculate the amount (A) when interest is compounded annually.

A school has 1200 students and 50 teachers. Calculate the ratio of the number of teachers to the number of students.

Write the formula with substituted values to calculate the Amount (A) for a Principal (P) of ₹10,000 at a Rate (R) of 8% per annum for a time (n) of 2 years, compounded annually. Do not solve the expression.

Recall the formula for calculating Simple Interest (SI) and explain what each variable (P, R, T) represents.

The price of a toy car is ₹500. If the GST is 12%, calculate the amount of GST on the toy.

Define the term 'Discount'.

A student was asked to find the original price of a bicycle sold for ₹4,250, including 6.25% VAT. The student calculated: "VAT = 6.25% of ₹4,250 = ₹265.625. Original Price = ₹4,250 - ₹265.625 = ₹3,984.375." Critique the student's method, explain the error, and calculate the correct original price.

Explain what a ratio represents.

Describe the process of converting the ratio $a:b$ into a percentage.

The marked price of a book is ₹350. If a discount of 15% is offered, calculate the discount amount.

Explain how Sales Tax or GST is calculated and added to a bill.

List three real-world situations where the compound interest formula can be applied, other than calculating interest on money.

Describe how to find the total bill amount if the cost of an item and the sales tax percentage are known.

The population of a town was 50,000 in 2020. If it increases at a rate of 4% per annum, calculate the estimated population of the town at the end of 2022.

Summarize the key difference between how Simple Interest and Compound Interest are calculated over multiple years.

Summarize the step-by-step method for calculating compound interest for a period of 2 years without using the direct formula. Use an example with a principal of ₹1000 and a rate of 10% per annum.

A shopkeeper sold 45 kg of rice from a 75 kg sack. Calculate the percentage of rice that is left.

In an election, candidate A received 45% of the total votes. Candidate B received 35% of the total votes. The remaining 12,000 votes went to candidate C. Analyze the given information to find the total number of votes cast.

A washing machine is sold for ₹19,550 after a discount of ₹3,450. Calculate the marked price and the discount percentage.

A shopkeeper marks his goods 40% above the cost price of ₹10,000. He then allows a discount of 25% on the marked price. Calculate the final selling price of the goods and determine his profit or loss percentage.

Calculate the difference between the compound interest and simple interest on a sum of ₹15,000 for 2 years at a rate of 6% per annum.

A new car is purchased for ₹4,50,000. Its value depreciates at a rate of 10% per annum. Analyze the depreciation to find the value of the car after 3 years.

Critique the statement: "Applying a 20% discount and then adding a 20% sales tax on an item results in the original price." Justify your conclusion.

Evaluate which is a better offer for a customer on an item: (A) a single discount of 40% or (B) two successive discounts of 20% and 25%? Justify your evaluation.

A shopkeeper marks an item 50% above its cost price and then offers a 50% discount on the marked price. Critique this strategy and determine the percentage profit or loss.

A shopkeeper offers two discount schemes on a television marked at ₹25,000. Scheme A: A flat 28% discount. Scheme B: Two successive discounts of 15% and 15%. Evaluate which scheme is more beneficial for the customer and justify by calculating the difference in the selling price.

An investor has ₹60,000 to invest for 2 years. Bank A offers 7% per annum simple interest. Bank B offers 6.8% per annum compounded annually. Propose the better investment plan for maximizing returns and justify your proposal with calculations.

Create a complex bill for a customer at a hardware store. The bill should include:

• 20 meters of wire at ₹45 per meter.
• 5 light bulbs, where the marked price is ₹120 per bulb but a 10% discount is applied.
• 1 toolbox for ₹800. A GST of 12% is added to the total bill amount. The customer then pays using a coupon that gives a flat ₹150 off the final amount. Calculate the net amount paid by the customer.

Create a word problem where the population of a town is given after two years of change. The population first increased by 20% and then decreased by 15%. The final population is 51,000. The problem should ask for the initial population. Solve the problem you have created.

The marked price of a refrigerator is ₹30,000. A shopkeeper offers a 10% discount on it. On the discounted price, a GST of 18% is charged. Calculate the final amount a customer has to pay for the refrigerator.

Meera bought a microwave for ₹8,960, which includes 12% GST. Analyze the bill to calculate the original price of the microwave before the GST was added.

Anjali borrows ₹25,000 from a bank for 3 years at an interest rate of 10% per annum, compounded annually. Calculate the total amount she has to repay at the end of 3 years. Also, calculate the compound interest she paid.

A car travels 90 km in 2 hours, and a train travels 120 km in 3 hours. Analyze their speeds to find the ratio of the speed of the car to the speed of the train.

Design a pricing strategy for a furniture store that buys a sofa set for ₹40,000. The store has overhead expenses of 10% of the cost price. The owner needs to set a marked price such that they can offer a 15% discount to customers and still make an overall profit of 20%. Formulate the steps and calculate the required marked price.

Formulate and derive a simplified formula for the difference between the Compound Interest (CI) and Simple Interest (SI) on a principal amount $P$ for 2 years at an annual interest rate of $R\%$.

Formulate a general expression for the final value of a quantity $P$ after it is first increased by $x\%$ and then decreased by $y\%$.

Describe two different methods to find the total number of students in a class if it is known that 40% of the students are girls and the number of girls is 20.

The population of a district was 800,000. Propose a method to calculate its population after 3 years given the following annual changes: a decrease of 2% in the first year, an increase of 5% in the second year, and an increase of 4% in the third year. Justify why the standard compound interest formula $A = P(1 + R/100)^n$ is not suitable for this problem and show the correct calculation.

The value of a machine depreciates by 10% each year. Justify whether the total depreciation over 3 years is 30% of the original value. If not, calculate the actual total percentage depreciation.

Two friends, Anjali and Bimal, each invest ₹50,000 for 3 years.

• Anjali invests in a scheme offering 8% per annum simple interest.
• Bimal invests in a scheme offering 7.5% per annum compounded annually. Evaluate whose investment will yield more returns after 3 years. Critique the common assumption that the type of interest (simple vs. compound) is less important than the rate.

Explain the concept of depreciation. How is the formula for calculating the depreciated value related to the compound interest formula?