Math Notes For Class 8 Chapter 2 Ex 2.2 Solved & Quiz
What are the Core Formulas and Definitions for this Exercise?
Financial Arithmetic plays a fundamental role in everyday commercial and governance activities. In this unit, we explore government levies such as direct taxes (Property Tax and Income Tax) and indirect taxes (General Sales Tax).
- Tax: A mandatory financial charge levied by the government on individuals, property, or transactions to fund public goods and services.
- Direct Tax: A tax levied directly on personal or corporate income and property. Examples include Property Tax and Income Tax.
- Indirect Tax: A tax imposed on goods and services collected by merchants from consumers at the point of purchase. An example is the General Sales Tax (GST).
- Taxable Income: The portion of annual income that exceeds the government-defined annual exemption limit ($E$) and is subject to income tax.
| Financial Concept | Standard Mathematical Formula |
|---|---|
| Property Tax | $$\text{Property Tax} = \text{Total Property Value} \times \frac{\text{Tax Rate}}{100}$$ |
| General Sales Tax (GST) | $$\text{GST Amount} = \text{Original Item Price} \times \frac{\text{GST Rate}}{100}$$ |
| Total Price (Including GST) | $$\text{Total Price} = \text{Original Price} + \text{GST Amount} = \text{Original Price} \times \left(1 + \frac{\text{GST Rate}}{100}\right)$$ |
| Original Price (Excluding GST) | $$\text{Original Price} = \frac{\text{Total Price (incl. GST)}}{1 + \frac{\text{GST Rate}}{100}}$$ |
| Taxable Income | $$\text{Taxable Income} = \text{Annual Gross Income} - \text{Exemption Limit}$$ |
| Income Tax Payable | $$\text{Income Tax} = \text{Taxable Income} \times \frac{\text{Tax Rate}}{100}$$ |
How to Solve All Exercise Questions Step-by-Step?
Question 1: Calculate the property tax on a residential plot valued at $\text{Rs. } 15,000,000$ if the applicable property tax rate is $2\%$.
Solution:
Given data:
Total Value of Property = $\text{Rs. } 15,000,000$
Rate of Property Tax = $2\%$
Using the formula for property tax:
$$\text{Property Tax} = \text{Value of Property} \times \frac{\text{Tax Rate}}{100}$$
$$\text{Property Tax} = 15,000,000 \times \frac{2}{100}$$
$$\text{Property Tax} = 150,000 \times 2 = 300,000$$
Answer: $$\text{Rs. } 300,000$$
Question 2: A homeowner pays $\text{Rs. } 45,000$ as annual property tax at a tax rate of $1.5\%$. Determine the total assessed value of the property.
Solution:
Given data:
Property Tax Paid = $\text{Rs. } 45,000$
Property Tax Rate = $1.5\% = \frac{1.5}{100} = 0.015$
Let the total value of the property be $V$.
Using the formula:
$$\text{Property Tax} = V \times \frac{\text{Tax Rate}}{100}$$
$$45,000 = V \times \frac{1.5}{100}$$
$$V = \frac{45,000 \times 100}{1.5}$$
$$V = \frac{4,500,000}{1.5} = 3,000,000$$
Answer: $$\text{Rs. } 3,000,000$$
Question 3 (Part i): Find the General Sales Tax (GST) amount and total price payable for a microwave oven costing $\text{Rs. } 12,500$ at a GST rate of $18\%$.
Solution:
Original Price = $\text{Rs. } 12,500$
GST Rate = $18\%$
$$\text{GST Amount} = 12,500 \times \frac{18}{100} = 125 \times 18 = 2,250$$
$$\text{Total Price} = \text{Original Price} + \text{GST Amount} = 12,500 + 2,250 = 14,750$$
Answer: $$\text{GST Amount} = \text{Rs. } 2,250, \quad \text{Total Price} = \text{Rs. } 14,750$$
Question 3 (Part ii): Find the General Sales Tax (GST) amount and total price payable for a smart television costing $\text{Rs. } 45,000$ at a GST rate of $18\%$.
Solution:
Original Price = $\text{Rs. } 45,000$
GST Rate = $18\%$
$$\text{GST Amount} = 45,000 \times \frac{18}{100} = 450 \times 18 = 8,100$$
$$\text{Total Price} = \text{Original Price} + \text{GST Amount} = 45,000 + 8,100 = 53,100$$
Answer: $$\text{GST Amount} = \text{Rs. } 8,100, \quad \text{Total Price} = \text{Rs. } 53,100$$
Question 4: The retail price of an inverter air conditioner including an $18\%$ General Sales Tax is $\text{Rs. } 141,600$. Find the original tax-exclusive price of the air conditioner.
Solution:
Total Price (including GST) = $\text{Rs. } 141,600$
GST Rate = $18\%$
Let the original price be $x$.
$$\text{Total Price} = x + \left(x \times \frac{18}{100}\right) = x \left(1 + 0.18\right) = 1.18x$$
$$1.18x = 141,600$$
$$x = \frac{141,600}{1.18} = 120,000$$
Answer: $$\text{Rs. } 120,000$$
Question 5: An employee earns a gross annual income of $\text{Rs. } 1,200,000$. The government grants an annual income tax exemption limit of $\text{Rs. } 600,000$. If the income tax rate is $2.5\%$ on the taxable amount, calculate the total income tax payable for the year.
Solution:
Gross Annual Income = $\text{Rs. } 1,200,000$
Exemption Limit = $\text{Rs. } 600,000$
Tax Rate = $2.5\%$
$$\text{Taxable Income} = \text{Gross Annual Income} - \text{Exemption Limit}$$
$$\text{Taxable Income} = 1,200,000 - 600,000 = 600,000$$
$$\text{Income Tax Payable} = \text{Taxable Income} \times \frac{2.5}{100}$$
$$\text{Income Tax Payable} = 600,000 \times 0.025 = 15,000$$
Answer: $$\text{Rs. } 15,000$$
Question 6 (Part i): Mr. Ahmed receives a monthly salary of $\text{Rs. } 150,000$. Calculate his annual gross income.
Solution:
Monthly Salary = $\text{Rs. } 150,000$
Number of months in a year = $12$
$$\text{Annual Gross Income} = 150,000 \times 12 = 1,800,000$$
Answer: $$\text{Rs. } 1,800,000$$
Question 6 (Part ii): Referring to Mr. Ahmed's income in Part (i), if the annual exemption limit is $\text{Rs. } 600,000$ and the income tax rate on taxable income is $5\%$, calculate his annual income tax and the monthly income tax deduction.
Solution:
Annual Gross Income = $\text{Rs. } 1,800,000$
Exemption Limit = $\text{Rs. } 600,000$
$$\text{Taxable Income} = 1,800,000 - 600,000 = 1,200,000$$
$$\text{Annual Income Tax} = 1,200,000 \times \frac{5}{100} = 12,000 \times 5 = 60,000$$
$$\text{Monthly Tax Deduction} = \frac{\text{Annual Income Tax}}{12} = \frac{60,000}{12} = 5,000$$
Answer: $$\text{Annual Tax} = \text{Rs. } 60,000, \quad \text{Monthly Deduction} = \text{Rs. } 5,000$$
Interactive Practice Quiz: Test Your Understanding (Clickable MCQs)
Q1: What is the property tax on a house worth $\text{Rs. } 5,000,000$ at a rate of $2\%$?
Q2: If General Sales Tax (GST) is $18\%$, what is the sales tax on an article marked at $\text{Rs. } 2,000$?
Q3: An individual earns $\text{Rs. } 800,000$ annually. If the exemption limit is $\text{Rs. } 600,000$, what is the taxable income?
Q4: If total price including $18\%$ GST is $\text{Rs. } 1,180$, what is the original price before GST?
Q5: Which of the following is classified as a Direct Tax?
Q6: A property tax of $\text{Rs. } 12,000$ is paid at a rate of $1\%$. What is the property's value?
Q7: If annual income tax payable is $\text{Rs. } 36,000$, what is the equal monthly tax deduction?
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