Math Notes For Class 8 Chapter 2 Ex 2.1 Solved & Quiz
What are the Core Formulas and Definitions for this Exercise?
Financial Arithmetic in the Class 8 Mathematics curriculum deals with Islamic financial obligations such as Zakat and Ushr, alongside modern municipal and state taxation such as Property Tax and General Sales Tax (GST). Understanding these concepts is essential for both academic excellence and real-world financial literacy.
1. Zakat: An obligatory financial contribution in Islam levied on wealth (cash, gold, silver, commercial stock) held for one full lunar year above the threshold called Nisab. The standard rate of Zakat is fixed at $2.5\%$ ($\frac{1}{40}$).
2. Ushr: An agricultural tax paid on land produce. The rate of Ushr depends directly on the method of irrigation used:
- Naturally Irrigated (Rain-fed / Canal / River): Ushr rate is $10\%$ ($\frac{1}{10}$).
- Artificially Irrigated (Tube-well / Motor / Hand-pump): Ushr rate is $5\%$ ($\frac{1}{20}$).
3. Property Tax & Sales Tax: Municipal taxes levied on real estate value or goods/services purchased. Income tax is calculated on net income exceeding a legally defined exemption threshold.
| Financial Concept | Standard Rate / Percentage | Formula / Mathematical Expression |
|---|---|---|
| Zakat | $2.5\%$ or $0.025$ | $$\text{Zakat} = \text{Total Net Wealth} \times \frac{2.5}{100}$$ |
| Ushr (Rain-Fed / Natural) | $10\%$ or $0.10$ | $$\text{Ushr} = \text{Total Produce Value} \times \frac{10}{100}$$ |
| Ushr (Artificially Irrigated) | $5\%$ or $0.05$ | $$\text{Ushr} = \text{Total Produce Value} \times \frac{5}{100}$$ |
| Property Tax | Variable Tax Rate $R\%$ | $$\text{Tax} = \text{Taxable Value} \times \frac{R}{100}$$ |
| Sales Tax / GST | Standard GST Rate (e.g. $18\%$) | $$\text{GST Amount} = \text{Original Price} \times \frac{\text{GST Rate}}{100}$$ |
How to Solve All Exercise Questions Step-by-Step?
Question 1 (Part i): Calculate the amount payable as Zakat on an amount of $\text{Rs. } 1,200,000$ kept in a savings account for a full year.
Solution:
Given Total Amount = $\text{Rs. } 1,200,000$
Rate of Zakat = $2.5\% = \frac{2.5}{100}$
$$\text{Zakat Payable} = \text{Total Amount} \times \frac{2.5}{100}$$
$$\text{Zakat Payable} = 1,200,000 \times 0.025 = 30,000$$
Answer: $$\text{Rs. } 30,000$$
Question 1 (Part ii): Calculate the Zakat payable on gold and silver assets having a combined market value of $\text{Rs. } 3,500,000$.
Solution:
Given Combined Value = $\text{Rs. } 3,500,000$
Rate of Zakat = $2.5\% = \frac{2.5}{100}$
$$\text{Zakat Payable} = 3,500,000 \times \frac{2.5}{100}$$
$$\text{Zakat Payable} = 3,500,000 \times 0.025 = 87,500$$
Answer: $$\text{Rs. } 87,500$$
Question 2 (Part i): Find the amount of Ushr on a rain-fed (naturally irrigated) agricultural land produce worth $\text{Rs. } 650,000$.
Solution:
Given Crop Value = $\text{Rs. } 650,000$
Since the crop is rain-fed (naturally irrigated), Rate of Ushr = $10\% = \frac{10}{100}$
$$\text{Ushr Payable} = \text{Crop Value} \times \frac{10}{100}$$
$$\text{Ushr Payable} = 650,000 \times 0.10 = 65,000$$
Answer: $$\text{Rs. } 65,000$$
Question 2 (Part ii): Find the amount of Ushr on an artificially irrigated wheat crop worth $\text{Rs. } 840,000$.
Solution:
Given Crop Value = $\text{Rs. } 840,000$
Since the crop is artificially irrigated (via tube-well/motor), Rate of Ushr = $5\% = \frac{5}{100}$
$$\text{Ushr Payable} = \text{Crop Value} \times \frac{5}{100}$$
$$\text{Ushr Payable} = 840,000 \times 0.05 = 42,000$$
Answer: $$\text{Rs. } 42,000$$
Question 3 (Part i): A commercial plot is evaluated at $\text{Rs. } 15,000,000$. Calculate the annual property tax at a rate of $2\%$.
Solution:
Property Value = $\text{Rs. } 15,000,000$
Tax Rate = $2\% = \frac{2}{100}$
$$\text{Property Tax} = 15,000,000 \times \frac{2}{100}$$
$$\text{Property Tax} = 150,000 \times 2 = 300,000$$
Answer: $$\text{Rs. } 300,000$$
Question 3 (Part ii): Calculate the total invoice amount for items worth $\text{Rs. } 45,000$ when a General Sales Tax (GST) of $18\%$ is added.
Solution:
Original Price = $\text{Rs. } 45,000$
GST Rate = $18\%$
$$\text{GST Amount} = 45,000 \times \frac{18}{100} = 450 \times 18 = 8,100$$
$$\text{Total Invoice Amount} = \text{Original Price} + \text{GST Amount}$$
$$\text{Total Invoice Amount} = 45,000 + 8,100 = 53,100$$
Answer: $$\text{Rs. } 53,100$$
Question 4: A business person has cash in bank worth $\text{Rs. } 850,000$, gold jewelry worth $\text{Rs. } 1,150,000$, and silver worth $\text{Rs. } 200,000$. He also owes a short-term business debt of $\text{Rs. } 200,000$. Calculate his net Zakat liability.
Solution:
Step 1: Calculate Gross Wealth:
$$\text{Gross Wealth} = 850,000 + 1,150,000 + 200,000 = 2,200,000$$
Step 2: Subtract Liabilities/Debts:
$$\text{Net Taxable Wealth} = \text{Gross Wealth} - \text{Liabilities}$$
$$\text{Net Taxable Wealth} = 2,200,000 - 200,000 = 2,000,000$$
Step 3: Calculate Zakat at $2.5\%$:
$$\text{Zakat Payable} = 2,000,000 \times \frac{2.5}{100} = 2,000,000 \times 0.025 = 50,000$$
Answer: $$\text{Rs. } 50,000$$
Question 5: A farmer harvested two different crops in one year: Crop A (rain-fed produce) valued at $\text{Rs. } 920,000$, and Crop B (artificially irrigated produce) valued at $\text{Rs. } 1,400,000$. Calculate the total combined Ushr payable on both crops.
Solution:
Step 1: Calculate Ushr on Crop A (Rain-fed at $10\%$):
$$\text{Ushr}_A = 920,000 \times \frac{10}{100} = 92,000$$
Step 2: Calculate Ushr on Crop B (Artificially Irrigated at $5\%$):
$$\text{Ushr}_B = 1,400,000 \times \frac{5}{100} = 70,000$$
Step 3: Calculate Total Ushr:
$$\text{Total Ushr} = \text{Ushr}_A + \text{Ushr}_B = 92,000 + 70,000 = 162,000$$
Answer: $$\text{Rs. } 162,000$$
Question 6: An employee earns a total annual gross income of $\text{Rs. } 1,800,000$. If the official tax-exempt income threshold is $\text{Rs. } 600,000$ and the income tax rate on taxable income above this threshold is $12.5\%$, calculate his annual income tax payable.
Solution:
Gross Annual Income = $\text{Rs. } 1,800,000$
Exemption Limit = $\text{Rs. } 600,000$
$$\text{Taxable Income} = \text{Gross Income} - \text{Exemption Limit}$$
$$\text{Taxable Income} = 1,800,000 - 600,000 = 1,200,000$$
Tax Rate = $12.5\% = 0.125$
$$\text{Income Tax Payable} = 1,200,000 \times \frac{12.5}{100}$$
$$\text{Income Tax Payable} = 1,200,000 \times 0.125 = 150,000$$
Answer: $$\text{Rs. } 150,000$$
Interactive Practice Quiz: Test Your Understanding (Clickable MCQs)
Q1: What is the standard rate of Zakat on net wealth held for one lunar year?
Q2: What is the rate of Ushr applied to crops grown using natural rain-fed water sources?
Q3: If a farmer produces wheat worth $\text{Rs. } 500,000$ using tube-well irrigation, how much Ushr must be paid?
Q4: How much Zakat is payable on cash savings of $\text{Rs. } 400,000$?
Q5: On a purchase worth $\text{Rs. } 10,000$, a $18\%$ General Sales Tax (GST) is charged. What is the total bill amount?
Q6: If annual income is $\text{Rs. } 1,000,000$ and the tax-exempt threshold is $\text{Rs. } 600,000$, what is the taxable income?
Q7: What is the Property Tax on a house valued at $\text{Rs. } 8,000,000$ if the property tax rate is $1.5\%$?
Q8: Which factor determines whether Ushr rate is $5\%$ or $10\%$?
Frequently Asked Questions: What are Common Student Errors in this Exercise?
Q1: Why do students confuse the Ushr rate between $5\%$ and $10\%$ in board examinations?
Ans: Students often forget to read the source of irrigation specified in the question statement. If the crop is watered naturally by rain, river, or natural streams, the rate is strictly $10\%$. If artificial pumps, tube-wells, or paid water delivery are used, the rate is halved to $5\%$ to account for the farmer's operational expenses. Always underline the irrigation method before selecting the formula.
Q2: How do short-term debts affect the calculation of Zakat?
Ans: Zakat is calculated on net wealth, not total gross assets. Outstanding debts that must be paid back immediately should be subtracted from total cash and asset values prior to multiplying by $2.5\%$. Skipping debt subtraction leads to an incorrect over-calculation of Zakat.
Q3: What is the most common mistake when calculating Income Tax on gross salary?
Ans: The most frequent error is applying the tax percentage directly to the gross income rather than subtracting the basic tax exemption threshold first. Income tax applies strictly to the amount that exceeds the exemption limit ($\text{Taxable Income} = \text{Gross Salary} - \text{Exemption Limit}$).
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