Class 7 Mathematics Ch 4 Mastery Guide: Profit & Loss, Discount, Property Tax, GST, Commission, VAT, Zakat, Ushr & Income Tax (FBISE)
Instructional Guide: Unit 04 Financial Arithmetic
- Define Cost Price (C.P.), Sale Price (S.P.), Profit, and Loss.
- Calculate Profit Percentage and Loss Percentage based on Cost Price ($\frac{\text{Profit}}{\text{C.P.}} \times 100$).
- Define Marked Price (M.P.) and Discount, calculating discount percentage always on Marked Price.
- Differentiate between Direct Taxes (levied on wealth/income, e.g., Property Tax, Income Tax) and Indirect Taxes (levied on expenditures, e.g., GST, VAT).
- Calculate Property Tax on residential/commercial properties, accounting for maintenance rebates.
- Compute General Sales Tax (GST) on invoices, utility bills (electricity and gas), and retail products.
- Define Commission for agents/brokers, calculating tiered and balance commission.
- Understand Value Added Tax (VAT) as a multi-stage tax: $\text{VAT} = \text{Output Tax} - \text{Input Tax}$.
- Define Zakat ($2.5\%$ or $\frac{1}{40}$) on savings, gold (Nisab $7.5\text{ tolas}$), and silver (Nisab $52.5\text{ tolas}$).
- Compute Ushr on agricultural produce: $10\%$ on rain/river irrigated land and $5\%$ on artificial irrigation (canals/tube-wells).
- Calculate Income Tax from annual salary and business income, applying standard tax rebates, teacher reductions, and deductions for Zakat and donations.
- Class 5 & 6 Percentages: Converting fractions to percentages and calculating $x\%$ of a given value ($P \times \frac{r}{100}$).
- Unitary Method: Finding the price of 1 item to determine the price of multiple items or back-calculating original values.
- Basic Algebra: Solving simple linear equations for an unknown original price ($1.17x = \text{Total}$ or $0.80x = \text{Sale Price}$).
- Discount Base Error: Students often calculate discount percentage on the Sale Price. Discount is ALWAYS calculated on the Marked Price (M.P.)!
- Profit/Loss Base Error: Profit and loss percentages are ALWAYS calculated on the Cost Price (C.P.), never on the Sale Price.
- Tax vs. Discount: A discount reduces the price ($\text{S.P.} = \text{M.P.} - \text{Discount}$), while a tax increases the final bill ($\text{Bill} = \text{Original} + \text{Tax}$).
- VAT Confusion: Retailers do not pay the full output tax to the government; they deduct the tax they already paid on purchase: $\text{VAT} = \text{Output Tax} - \text{Input Tax}$.
- Ushr Irrigation Rates: Natural water (rain, rivers, natural springs) $= 10\%$ Ushr; Artificial water (wells, pumps, tube-wells) $= 5\%$ Ushr.
- Income Tax Rebate vs. Tax Amount: A rebate of Rs. 400,000 means income up to Rs. 400,000 is taxed at $0\%$. Tax is calculated on $\text{Taxable Income} = \text{Total Income} - \text{Rebate} - \text{Exemptions}$.
Start this chapter by bringing real electricity bills, grocery receipts, and discount price tags into the classroom. Ask students: "Have you ever seen GST on your shopping bill? Where does that money go?" Connect this directly to the FBR hook: taxes fund national public services including schools, highways, hospitals, and national defense.
Emphasize the dual economic framework taught in Pakistani curriculum: commercial capitalism (profit, loss, discount, commercial taxes) balanced with Islamic social welfare (Zakat and Ushr) to eliminate poverty and maintain societal equilibrium.
Real-World Case Study: National Revenue & The Federal Board of Revenue (FBR)
The Engine of National Development: Why Do Governments Levy Taxes?
Every modern government requires substantial financial resources to maintain national security, construct infrastructure (highways, motorways, dams), and deliver free public schooling and healthcare. In Pakistan, the apex federal body responsible for formulating fiscal policies, collecting revenue, and auditing financial records is the Federal Board of Revenue (FBR), headquartered in Islamabad.
Taxation in Pakistan is divided into two broad categories:
• Direct Taxes: Taxes charged directly on individuals or corporations based on their wealth or earnings (e.g., Income Tax and Property Tax).
• Indirect Taxes: Taxes charged on expenditures, transactions, and consumer goods (e.g., General Sales Tax (GST), Value Added Tax (VAT), and Customs Duties). While everyone pays indirect taxes when purchasing goods, direct taxes ensure equitable contributions from high-income citizens.
Cost Price & Sale Price
Profit & Loss Percentages
Marked Price & Discounts
Property Tax (Residential/Shops)
General Sales Tax (GST @ 17%)
Utility Bills (Electricity & Gas)
Brokerage & Commissions
Tiered & Cash Commissions
VAT ($\text{Output} - \text{Input}$)
Zakat ($2.5\%$ on Gold/Silver/Cash)
Sahib-i-Nisab Criteria
Ushr ($10\%$ Rain / $5\%$ Canal)
Gross Annual Income
Rebates & Tax Exemptions
Teacher Reductions ($25\%-50\%$)
Section 1: Profit, Loss, and Percentage Analysis
Mastering commercial retail mechanics: Cost Price, Sale Price, Net Gains/Losses, and Relative Return.
1.1 Fundamental Definitions of Trading
Whenever business transactions take place, goods are bought and sold. To evaluate whether a trade was financially advantageous, we define two fundamental price points:
- Cost Price ($\text{C.P.}$): The actual price at which a merchant, dealer, or individual purchases an item. It also encompasses any transportation, repair, or overhead expenses required to prepare the item for sale.
- Sale Price ($\text{S.P.}$): The price at which the article is sold to the consumer or customer.
When an article is sold for more than its purchase cost ($\text{S.P.} > \text{C.P.}$), the transaction yields a profit: $$\text{Profit} = \text{S.P.} - \text{C.P.}$$ $$\text{Sale Price} = \text{C.P.} + \text{Profit}$$ $$\text{Cost Price} = \text{S.P.} - \text{Profit}$$
When an article is sold for less than its purchase cost ($\text{C.P.} > \text{S.P.}$), the seller suffers a loss: $$\text{Loss} = \text{C.P.} - \text{S.P.}$$ $$\text{Sale Price} = \text{C.P.} - \text{Loss}$$ $$\text{Cost Price} = \text{S.P.} + \text{Loss}$$
The Relative Benchmark: Why We Calculate Percentages on Cost Price
Suppose a merchant gains $\text{Rs. } 10$ by selling a pencil box, and another gains $\text{Rs. } 10$ by selling an expensive refrigerator. Even though the rupee profit is identical, the first merchant made a spectacular return on investment, while the second made an insignificant fraction of his investment. Therefore, profit or loss is always compared against the investment ($\text{Cost Price}$): $$\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\% = \frac{\text{S.P.} - \text{C.P.}}{\text{C.P.}} \times 100\%$$ $$\text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100\% = \frac{\text{C.P.} - \text{S.P.}}{\text{C.P.}} \times 100\%$$
Complete Step-by-Step Solutions: Exercise 4.1
11 Questions • 100% Solved
Find the profit or loss percentage in the following cases:
(i) $\text{C.P.} = \text{Rs. } 50, \quad \text{S.P.} = \text{Rs. } 70$
(ii) $\text{C.P.} = \text{Rs. } 1540, \quad \text{S.P.} = \text{Rs. } 1386$
(iii) $\text{C.P.} = \text{Rs. } 125, \quad \text{Profit} = \text{Rs. } 20$
(iv) $\text{C.P.} = \text{Rs. } 12.5, \quad \text{Loss} = \text{Rs. } 2.5$
Part (i): Since $\text{S.P.} > \text{C.P.}$, there is a profit.
$$\text{Profit} = \text{S.P.} - \text{C.P.} = 70 - 50 = \text{Rs. } 20$$ $$\text{Profit \%} = \frac{\text{Profit}}{\text{C.P.}} \times 100 = \frac{20}{50} \times 100 = 20 \times 2 = 40\%$$
Part (ii): Since $\text{C.P.} > \text{S.P.}$, there is a loss.
$$\text{Loss} = \text{C.P.} - \text{S.P.} = 1540 - 1386 = \text{Rs. } 154$$ $$\text{Loss \%} = \frac{\text{Loss}}{\text{C.P.}} \times 100 = \frac{154}{1540} \times 100 = \frac{1}{10} \times 100 = 10\%$$
Part (iii): $\text{C.P.} = 125$, $\text{Profit} = 20$.
$$\text{Profit \%} = \frac{20}{125} \times 100 = \frac{4}{25} \times 100 = 4 \times 4 = 16\%$$
Part (iv): $\text{C.P.} = 12.5$, $\text{Loss} = 2.5$.
$$\text{Loss \%} = \frac{2.5}{12.5} \times 100 = \frac{25}{125} \times 100 = \frac{1}{5} \times 100 = 20\%$$ Final Answers: (i) 40% Profit | (ii) 10% Loss | (iii) 16% Profit | (iv) 20% Loss
A bag costing Rs. 50 is sold for Rs. 45. Find profit or loss percent.
$$\text{Cost Price (C.P.)} = \text{Rs. } 50, \quad \text{Sale Price (S.P.)} = \text{Rs. } 45$$ Since $\text{C.P.} > \text{S.P.}$, it is a loss: $$\text{Loss} = \text{C.P.} - \text{S.P.} = 50 - 45 = \text{Rs. } 5$$ $$\text{Loss \%} = \frac{\text{Loss}}{\text{C.P.}} \times 100 = \frac{5}{50} \times 100 = 10\%$$ Final Answer: 10% Loss
Sonia bought a computer for Rs. 15000 and sold it for Rs. 15900. Find profit or loss percent.
$$\text{C.P.} = \text{Rs. } 15000, \quad \text{S.P.} = \text{Rs. } 15900$$ Since $\text{S.P.} > \text{C.P.}$, Sonia made a profit: $$\text{Profit} = \text{S.P.} - \text{C.P.} = 15900 - 15000 = \text{Rs. } 900$$ $$\text{Profit \%} = \frac{900}{15000} \times 100 = \frac{900}{150} = 6\%$$ Final Answer: 6% Profit
There was a loss of Rs. 150 when an item was sold for Rs. 2350. Find C.P and loss percent.
$$\text{Sale Price (S.P.)} = \text{Rs. } 2350, \quad \text{Loss} = \text{Rs. } 150$$ $$\text{Cost Price (C.P.)} = \text{S.P.} + \text{Loss} = 2350 + 150 = \text{Rs. } 2500$$ $$\text{Loss \%} = \frac{\text{Loss}}{\text{C.P.}} \times 100 = \frac{150}{2500} \times 100 = \frac{150}{25} = 6\%$$ Final Answer: C.P = Rs. 2500, Loss = 6%
Farooq bought some wedding cards for Rs. 500. He sold them for Rs. 480. Find profit or loss percent.
$$\text{C.P.} = \text{Rs. } 500, \quad \text{S.P.} = \text{Rs. } 480$$ Since $\text{C.P.} > \text{S.P.}$, there is a loss: $$\text{Loss} = \text{C.P.} - \text{S.P.} = 500 - 480 = \text{Rs. } 20$$ $$\text{Loss \%} = \frac{20}{500} \times 100 = \frac{20}{5} = 4\%$$ Final Answer: 4% Loss
Hassan sold a fan for Rs. 2500 and had a loss of Rs. 500. Find C.P and loss percent.
$$\text{S.P.} = \text{Rs. } 2500, \quad \text{Loss} = \text{Rs. } 500$$ $$\text{C.P.} = \text{S.P.} + \text{Loss} = 2500 + 500 = \text{Rs. } 3000$$ $$\text{Loss \%} = \frac{500}{3000} \times 100 = \frac{50}{3} = 16\frac{2}{3}\% \approx 16.67\%$$ Final Answer: C.P = Rs. 3000, Loss = 16.67%
Nawaz father bought two plots for Rs. 1250000. He sold them for Rs. 1500000. Find profit percent.
$$\text{C.P.} = \text{Rs. } 1250000, \quad \text{S.P.} = \text{Rs. } 1500000$$ $$\text{Profit} = \text{S.P.} - \text{C.P.} = 1500000 - 1250000 = \text{Rs. } 250000$$ $$\text{Profit \%} = \frac{250000}{1250000} \times 100 = \frac{1}{5} \times 100 = 20\%$$ Final Answer: 20% Profit
Kanwal bought an iron for Rs. 1000 and got a profit of Rs. 200. Find profit percent and sale price.
$$\text{C.P.} = \text{Rs. } 1000, \quad \text{Profit} = \text{Rs. } 200$$ $$\text{Sale Price (S.P.)} = \text{C.P.} + \text{Profit} = 1000 + 200 = \text{Rs. } 1200$$ $$\text{Profit \%} = \frac{200}{1000} \times 100 = 20\%$$ Final Answer: Profit = 20%, S.P = Rs. 1200
Which profit is better?
(i) $\text{C.P.} = \text{Rs. } 20, \quad \text{S.P.} = \text{Rs. } 23$
(ii) $\text{C.P.} = \text{Rs. } 25, \quad \text{S.P.} = \text{Rs. } 28$
Transaction (i):
$$\text{Profit} = 23 - 20 = \text{Rs. } 3$$ $$\text{Profit \%} = \frac{3}{20} \times 100 = 3 \times 5 = 15\%$$ Transaction (ii):
$$\text{Profit} = 28 - 25 = \text{Rs. } 3$$ $$\text{Profit \%} = \frac{3}{25} \times 100 = 3 \times 4 = 12\%$$ Comparing both percentages: $15\% > 12\%$. Even though both generate an absolute profit of Rs. 3, transaction (i) yields a superior return on capital.
Final Answer: (i) 15%, (ii) 12%; Profit in part (i) is better
Find sale price if:
(i) $\text{C.P.} = \text{Rs. } 500, \quad \text{Profit} = 5\%$
(ii) $\text{C.P.} = \text{Rs. } 300, \quad \text{Loss} = 10\%$
Part (i):
$$\text{Profit amount} = 5\% \text{ of } 500 = \frac{5}{100} \times 500 = \text{Rs. } 25$$ $$\text{S.P.} = \text{C.P.} + \text{Profit} = 500 + 25 = \text{Rs. } 525$$ Direct Formula: $\text{S.P.} = \text{C.P.} \times \left(1 + \frac{\text{Profit \%}}{100}\right) = 500 \times 1.05 = \text{Rs. } 525$.
Part (ii):
$$\text{Loss amount} = 10\% \text{ of } 300 = \frac{10}{100} \times 300 = \text{Rs. } 30$$ $$\text{S.P.} = \text{C.P.} - \text{Loss} = 300 - 30 = \text{Rs. } 270$$ Direct Formula: $\text{S.P.} = \text{C.P.} \times \left(1 - \frac{\text{Loss \%}}{100}\right) = 300 \times 0.90 = \text{Rs. } 270$.
Final Answers: (i) Rs. 525 | (ii) Rs. 270
A motorcycle was bought for Rs. 48000 and was sold at a profit of 6%. Find its sale price.
$$\text{Cost Price (C.P.)} = \text{Rs. } 48000$$ $$\text{Profit Rate} = 6\%$$ $$\text{Profit amount} = \frac{6}{100} \times 48000 = 6 \times 480 = \text{Rs. } 2880$$ $$\text{Sale Price (S.P.)} = \text{C.P.} + \text{Profit} = 48000 + 2880 = \text{Rs. } 50880$$ Final Answer: Rs. 50880
Section 2: Marked Price, Discount Mechanics & Consumer Pricing
Understanding promotional pricing, list prices, and finding original values from discounted selling prices.
2.1 What is Marked Price and Discount?
When shopping in stores, super markets, or garment outlets, every article features a printed tag or label indicating its initial retail price.
- Marked Price ($\text{M.P.}$): Also referred to as the List Price or Catalog Price, it is the initial price displayed or printed on the product.
- Discount: A price concession, reduction, or rebate granted by the seller on the marked price to stimulate sales or clear stock.
- Sale Price ($\text{S.P.}$): The actual cash amount paid by the customer after subtracting the discount from the marked price.
$$\text{Discount} = \text{Marked Price (M.P.)} - \text{Sale Price (S.P.)}$$ $$\text{Sale Price (S.P.)} = \text{Marked Price (M.P.)} - \text{Discount} = \text{M.P.} \times \left(1 - \frac{\text{Discount \%}}{100}\right)$$ $$\text{Discount Percentage} = \frac{\text{Discount}}{\text{Marked Price (M.P.)}} \times 100\%$$
Golden Rule: Discount percentage is ALWAYS calculated on the Marked Price ($\text{M.P.}$), NEVER on the Sale Price or Cost Price!
Reverse Calculation: Finding Marked Price When Sale Price is Known
If an item is sold for $\text{Rs. } S$ after a discount of $d\%$, the sale price represents $(100 - d)\%$ of the marked price: $$\text{M.P.} = \frac{\text{S.P.}}{1 - \frac{d}{100}} = \frac{\text{S.P.} \times 100}{100 - d}$$ Example: A bicycle sold for $\text{Rs. } 12,000$ at a $20\%$ discount has: $$\text{M.P.} = \frac{12000 \times 100}{100 - 20} = \frac{12000 \times 100}{80} = 150 \times 100 = \text{Rs. } 15,000$$
Complete Step-by-Step Solutions: Exercise 4.2
10 Questions • 100% Solved
Complete the following table:
(i) $\text{M.P.} = \text{Rs. } 80, \quad \text{S.P.} = \text{Rs. } 70$
(ii) $\text{M.P.} = \text{Rs. } 100, \quad \text{Discount} = \text{Rs. } 20$
(iii) $\text{M.P.} = \text{Rs. } 400, \quad \text{Discount \%} = 25\%$
(iv) $\text{S.P.} = \text{Rs. } 180, \quad \text{Discount} = \text{Rs. } 20$
Part (i):
$$\text{Discount} = \text{M.P.} - \text{S.P.} = 80 - 70 = \text{Rs. } 10$$ $$\text{Discount \%} = \frac{10}{80} \times 100 = \frac{1}{8} \times 100 = 12.5\%$$
Part (ii):
$$\text{S.P.} = \text{M.P.} - \text{Discount} = 100 - 20 = \text{Rs. } 80$$ $$\text{Discount \%} = \frac{20}{100} \times 100 = 20\%$$
Part (iii):
$$\text{Discount} = 25\% \text{ of } 400 = \frac{25}{100} \times 400 = \text{Rs. } 100$$ $$\text{S.P.} = \text{M.P.} - \text{Discount} = 400 - 100 = \text{Rs. } 300$$
Part (iv):
$$\text{M.P.} = \text{S.P.} + \text{Discount} = 180 + 20 = \text{Rs. } 200$$ $$\text{Discount \%} = \frac{20}{200} \times 100 = 10\%$$ Final Answers: (i) Rs. 10, 12.5% | (ii) Rs. 80, 20% | (iii) Rs. 100, Rs. 300 | (iv) Rs. 200, 10%
Which is better discount?
(i) Discount of Rs. 12 on M.P. of Rs. 100.
(ii) Discount of Rs. 110 on M.P. of Rs. 1000.
Option (i):
$$\text{Discount \%} = \frac{12}{100} \times 100 = 12\%$$ Option (ii):
$$\text{Discount \%} = \frac{110}{1000} \times 100 = 11\%$$ Comparing rates: $12\% > 11\%$. Therefore, a discount of $12\%$ in part (i) saves the consumer a larger percentage of the price.
Final Answer: (i) 12%, (ii) 11%; Discount in part (i) is better
The marked price of a fan is Rs. 1400. Find its sale price if discount is 10%.
$$\text{Marked Price (M.P.)} = \text{Rs. } 1400$$ $$\text{Discount Rate} = 10\%$$ $$\text{Discount amount} = \frac{10}{100} \times 1400 = \text{Rs. } 140$$ $$\text{Sale Price (S.P.)} = \text{M.P.} - \text{Discount} = 1400 - 140 = \text{Rs. } 1260$$ Academic Note on Textbook Key: The textbook answer key prints $\text{Rs. } 1540$, which arose from accidentally adding $10\%$ as tax ($1400 + 140 = 1540$) instead of subtracting discount. The mathematically correct sale price after a $10\%$ discount is $\text{Rs. } 1260$.
Final Answer: Rs. 1260 (Standard) | Rs. 1540 (Textbook key typographical add)
The marked price of an item is Rs. 320. It is sold for Rs. 300. Find discount percent.
$$\text{M.P.} = \text{Rs. } 320, \quad \text{S.P.} = \text{Rs. } 300$$ $$\text{Discount} = \text{M.P.} - \text{S.P.} = 320 - 300 = \text{Rs. } 20$$ $$\text{Discount \%} = \frac{20}{320} \times 100 = \frac{1}{16} \times 100 = \frac{25}{4} = 6.25\%$$ Final Answer: 6.25%
A bicycle is sold for Rs. 3500 having marked price Rs. 3600. Find discount percent.
$$\text{M.P.} = \text{Rs. } 3600, \quad \text{S.P.} = \text{Rs. } 3500$$ $$\text{Discount} = \text{M.P.} - \text{S.P.} = 3600 - 3500 = \text{Rs. } 100$$ $$\text{Discount \%} = \frac{100}{3600} \times 100 = \frac{100}{36} = \frac{25}{9} = 2\frac{7}{9}\% \approx 2.78\%$$ Final Answer: 2.78%
An item is sold for Rs. 1800 at a discount of Rs. 200. Find its marked price and discount percent.
$$\text{S.P.} = \text{Rs. } 1800, \quad \text{Discount} = \text{Rs. } 200$$ $$\text{Marked Price (M.P.)} = \text{S.P.} + \text{Discount} = 1800 + 200 = \text{Rs. } 2000$$ $$\text{Discount \%} = \frac{200}{2000} \times 100 = 10\%$$ Final Answer: M.P = Rs. 2000, Discount = 10%
Find marked price of a bag at a discount of 12% having sale price Rs. 132.
Let the marked price be $x$.
$$\text{Sale Price} = x \times (100\% - 12\%) = x \times 88\% = \frac{88}{100} x$$ $$\frac{88}{100} x = 132 \implies x = \frac{132 \times 100}{88}$$ Divide numerator and denominator by 44: $$x = \frac{3 \times 100}{2} = 3 \times 50 = \text{Rs. } 150$$ Final Answer: Rs. 150
A shopkeeper sells an article having marked price Rs. 160. Find its sale price if the discount is:
(i) $8\%$
(ii) $10\%$
Part (i): At $8\%$ discount:
$$\text{Discount} = \frac{8}{100} \times 160 = \text{Rs. } 12.80$$ $$\text{S.P.} = 160 - 12.80 = \text{Rs. } 147.20$$ Part (ii): At $10\%$ discount:
$$\text{Discount} = \frac{10}{100} \times 160 = \text{Rs. } 16$$ $$\text{S.P.} = 160 - 16 = \text{Rs. } 144$$ Final Answers: (i) Rs. 147.2 | (ii) Rs. 144
A toy car is sold for Rs. 4600 at the discount of 8%. What is marked price of toy car?
Since the discount is $8\%$, the sale price is $(100 - 8)\% = 92\%$ of marked price.
$$0.92 \times \text{M.P.} = 4600$$ $$\text{M.P.} = \frac{4600}{0.92} = \frac{4600 \times 100}{92} = 50 \times 100 = \text{Rs. } 5000$$ Final Answer: Rs. 5000
A shopkeeper offers a discount of 20% on the cell phone. Find the marked price of cell phone if its sale price is Rs. 7200.
At $20\%$ discount, the sale price represents $(100 - 20)\% = 80\%$ of the marked price.
$$0.80 \times \text{M.P.} = 7200$$ $$\text{M.P.} = \frac{7200}{0.80} = \frac{7200 \times 10}{8} = 900 \times 10 = \text{Rs. } 9000$$ Final Answer: Rs. 9000
Property Tax, General Sales Tax (GST) & Public Revenue
Taxes are compulsory financial contributions imposed by the government on individuals, businesses, and property owners. The word tax originates from the Latin word taxo (meaning “I estimate” or “I assess”). Tax revenue enables the state to construct highways, maintain public hospitals, fund national education systems, and guarantee civilian security.
1. Property Tax (Provincial Direct Tax)
A tax levied annually by provincial excise and taxation departments on immovable real estate including residential houses, commercial plazas, shops, and plots.
- Financial year runs from 1st July to 30th June of the next calendar year.
- Rates differ between residential and commercial zones, and for on-road vs. off-road locations.
2. General Sales Tax (GST — Indirect Tax)
An indirect consumption tax paid by the ultimate consumer at the point of purchase of manufactured goods and utility services (electricity, gas, telecommunications).
- Standard GST rate in Pakistan is 17% (can range between 0% and 25% depending on sector).
- If price inclusive of GST is known: $\text{Original Price} = \frac{\text{Sale Price}}{1 + \frac{r}{100}}$.
Direct Taxes are paid directly by individuals on personal income or real estate wealth (e.g., Property Tax, Income Tax). Indirect Taxes are levied on goods and services and collected through intermediaries (e.g., GST, Customs Duties). In Pakistan, approximately 70% of state revenue is generated through indirect taxes because only 16% to 20% of the population directly files tax returns.
Exercise 4.3 — Complete Step-by-Step Textbook Solutions
Find the property tax @ 3% on a shop worth Rs. 475000. Also find the net amount including property tax.
Worth of shop $= \text{Rs. } 475,000$
Rate of property tax $= 3\%$
$$\text{Property Tax} = 475000 \times \frac{3}{100} = 4750 \times 3 = \text{Rs. } 14,250$$ $$\text{Net Amount Paid} = \text{Worth} + \text{Property Tax} = 475000 + 14250 = \text{Rs. } 489,250$$ Final Answer: Property Tax = Rs. 14,250; Net Amount = Rs. 489,250
Value of a shopping centre is Rs. 5600000. Find the property tax paid by the owner @ 3.5% if there is a rebate of Rs. 50000 in tax for maintenance.
Value of shopping centre $= \text{Rs. } 5,600,000$
Rate of property tax $= 3.5\% = \frac{35}{1000}$
$$\text{Gross Tax} = 5600000 \times \frac{3.5}{100} = 56000 \times 3.5 = \text{Rs. } 196,000$$ $$\text{Rebate for maintenance} = \text{Rs. } 50,000$$ $$\text{Net Tax Paid} = \text{Gross Tax} - \text{Rebate} = 196000 - 50000 = \text{Rs. } 146,000$$ Final Answer: Rs. 146,000
Ammara paid property tax Rs. 35000 @ 2.5% for a house. Calculate the value of the property.
Let the value of the house be $V$.
$$\text{Tax} = 2.5\% \times V = 35000$$ $$\frac{2.5}{100} \times V = 35000 \implies \frac{1}{40} \times V = 35000$$ $$V = 35000 \times 40 = \text{Rs. } 1,400,000$$ Final Answer: Rs. 1,400,000
Tariq paid property tax Rs. 10800 for a property worth Rs. 180000. What is the rate of property tax?
$$\text{Rate of Property Tax} = \left(\frac{\text{Property Tax}}{\text{Property Worth}}\right) \times 100\%$$ $$\text{Rate} = \left(\frac{10800}{180000}\right) \times 100\% = \frac{108}{18} = 6\%$$ Final Answer: 6%
Factory price of a bicycle is Rs. 10000. Calculate general sales tax @ 16% and sales price of bicycle.
Factory Price $= \text{Rs. } 10,000$
Rate of GST $= 16\%$
$$\text{GST} = 10000 \times \frac{16}{100} = \text{Rs. } 1,600$$ $$\text{Sales Price} = \text{Factory Price} + \text{GST} = 10000 + 1600 = \text{Rs. } 11,600$$ Final Answer: GST = Rs. 1,600; Sales Price = Rs. 11,600
The sale price of a table is Rs. 9360 including sales tax @ 17%. Find the original price of table.
Let original price be $x$.
Sale price includes $17\%$ sales tax, so $\text{Sale Price} = 1.17x$.
$$1.17x = 9360 \implies x = \frac{9360}{1.17} = \frac{936000}{117}$$ Dividing $936$ by $117$: $117 \times 8 = 936$.
$$x = 8 \times 1000 = \text{Rs. } 8,000$$ Final Answer: Rs. 8,000
Rustam runs 5 shopping centres worth Rs. 50000000. Last month he paid a property tax of Rs. 1000000 in total.
(i) Find the rate of property tax.
(ii) Find the property tax of each shopping centre at the same rate.
(i) Rate of Property Tax:
$$\text{Rate} = \left(\frac{1000000}{50000000}\right) \times 100\% = \frac{1}{50} \times 100\% = 2\%$$ (ii) Property Tax on each shopping centre:
Since all 5 centres total Rs. 1,000,000 at an equal rate:
$$\text{Tax per centre} = \frac{\text{Total Tax}}{5} = \frac{1000000}{5} = \text{Rs. } 200,000$$ Verification: Worth of each centre $= 50,000,000 / 5 = \text{Rs. } 10,000,000$. $2\% \text{ of } 10,000,000 = \text{Rs. } 200,000$.
Final Answer: (i) 2% (ii) Rs. 200,000
General sales tax @ 17% written on an electricity bill is Rs. 170. Calculate the total electricity bill.
Let electricity charges before GST be $C$.
$$\text{GST} = 17\% \times C = 170$$ $$\frac{17}{100} \times C = 170 \implies C = \frac{170 \times 100}{17} = \text{Rs. } 1,000$$ $$\text{Total Electricity Bill} = \text{Charges} + \text{GST} = 1000 + 170 = \text{Rs. } 1,170$$ Final Answer: Rs. 1,170
Original (factory) price of a motor car is Rs. 800000. Amount of GST is Rs. 95000. Find the rate of GST.
$$\text{Rate of GST} = \left(\frac{\text{GST}}{\text{Original Price}}\right) \times 100\%$$ $$\text{Rate} = \left(\frac{95000}{800000}\right) \times 100\% = \frac{95}{8}\% = 11.875\%$$ Final Answer: 11.875%
Asma bought the following items from a super store:
(i) 10 litres cooking oil @ Rs. 250 per litre.
(ii) 5 kg sugar @ Rs. 80 per kg.
(iii) 2 bottles of tomato ketchup @ Rs. 120 per bottle.
Calculate GST @ 17% on each item paid by her. Also find net GST paid by her.
(i) Cooking Oil: Cost $= 10 \times 250 = \text{Rs. } 2500$.
$$\text{GST} = 2500 \times \frac{17}{100} = 25 \times 17 = \text{Rs. } 425$$ (ii) Sugar: Cost $= 5 \times 80 = \text{Rs. } 400$.
$$\text{GST} = 400 \times \frac{17}{100} = 4 \times 17 = \text{Rs. } 68$$ (iii) Tomato Ketchup: Cost $= 2 \times 120 = \text{Rs. } 240$.
$$\text{GST} = 240 \times \frac{17}{100} = \frac{4080}{100} = \text{Rs. } 40.80$$ Net GST Paid:
$$\text{Net GST} = 425 + 68 + 40.80 = \text{Rs. } 533.80$$ Final Answer: (i) Rs. 425 (ii) Rs. 68 (iii) Rs. 40.80; Net GST = Rs. 533.80
Commercial Intermediation: Commission & Value Added Tax (VAT)
Modern distribution networks rely on specialized intermediaries (brokers, distributors, commission agents) and multi-stage indirect tax mechanisms (VAT). Understanding these calculations is central to corporate finance and wholesale commerce.
1. Commercial Commission
A service fee paid as a fixed percentage on the written or sale price of an article given by manufacturers or clients to agents, brokers, or dealers.
- Real Estate Commission: Agents frequently collect agreed commission percentages from both the buyer and seller.
- Tiered Commission: Higher rates may apply to sales beyond specific milestone thresholds.
2. Value Added Tax (VAT)
A multi-stage consumption tax levied at each stage of the supply chain where incremental value is added, avoiding the cascading “tax-on-tax” problem.
- Equivalently: $\text{VAT} = (\text{Selling Price} - \text{Purchase Price}) \times \text{Tax Rate}$.
- Whereas standard retail sales tax is collected only at the final point of purchase, VAT is gathered progressively across production, wholesale, and retail tiers.
Exercise 4.4 — Complete Step-by-Step Textbook Solutions
A publisher gives a commission of 20% on books. Find commission if a book seller buys books having sum of written price as Rs. 2350.
Written Price $= \text{Rs. } 2350$
Commission Rate $= 20\%$
$$\text{Commission} = 2350 \times \frac{20}{100} = 235 \times 2 = \text{Rs. } 470$$ Final Answer: Rs. 470
A factory gives 12% commission on the written price of an article to a broker. Find amount paid by the broker to the factory if written price of article is Rs. 4900.
Written Price $= \text{Rs. } 4900$
Commission Rate $= 12\%$
$$\text{Commission} = 4900 \times \frac{12}{100} = 49 \times 12 = \text{Rs. } 588$$ $$\text{Amount Paid to Factory} = 4900 - 588 = \text{Rs. } 4,312$$ Alternative Method: $\text{Broker pays } (100 - 12)\% = 88\%$: $4900 \times 0.88 = \text{Rs. } 4,312$.
Final Answer: Rs. 4,312
A manufacturer gives 10% commission on his product and an additional commission of 5% on balance on cash payment. Find the commission of the shopkeeper if price of product is Rs. 26780. What does shopkeeper pay?
Price of product $= \text{Rs. } 26,780$
$$\text{First Commission (10\%)} = 26780 \times \frac{10}{100} = \text{Rs. } 2,678$$ $$\text{Balance Amount} = 26780 - 2678 = \text{Rs. } 24,102$$ $$\text{Additional Commission (5\% on balance)} = 24102 \times \frac{5}{100} = \frac{120510}{100} = \text{Rs. } 1,205.10$$ $$\text{Total Commission} = 2678 + 1205.10 = \text{Rs. } 3,883.10$$ $$\text{Amount Shopkeeper Pays} = \text{Balance} - \text{Additional Commission} = 24102 - 1205.10 = \text{Rs. } 22,896.90$$ Final Answer: Commission = Rs. 3,883.10; Amount Paid = Rs. 22,896.90
A factory owner allows 12% commission at the sale of Rs. 12000 and an additional commission of 15% beyond the sale of Rs. 12000. An agent sold articles for Rs. 27000. Find commission of agent.
Total sales $= \text{Rs. } 27,000$
Base sales limit $= \text{Rs. } 12,000$
$$\text{Commission on first Rs. 12,000 (12\%)} = 12000 \times \frac{12}{100} = \text{Rs. } 1,440$$ $$\text{Sales exceeding Rs. 12,000} = 27000 - 12000 = \text{Rs. } 15,000$$ $$\text{Commission on excess (15\%)} = 15000 \times \frac{15}{100} = 150 \times 15 = \text{Rs. } 2,250$$ $$\text{Total Commission} = 1440 + 2250 = \text{Rs. } 3,690$$ Final Answer: Rs. 3,690
An agent sold goods for Rs. 50000 and got a commission of Rs. 3000. Find the percentage of commission.
$$\text{Percentage of Commission} = \left(\frac{\text{Commission}}{\text{Total Sales}}\right) \times 100\%$$ $$\text{Percentage} = \left(\frac{3000}{50000}\right) \times 100\% = \frac{30}{5}\% = 6\%$$ Final Answer: 6%
A property dealer sold a house for Rs. 2550000 and charged a commission of 2% from both parties. What did the dealer and seller get? What did the buyer pay?
Note on Textbook Typo: In the official answer key, the numbers given correspond to a house price of Rs. 255,000 (one zero less):
Commission from each party $= 255000 \times 2\% = \text{Rs. } 5,100$
Dealer got (from both parties) $= 5100 \times 2 = \mathbf{\text{Rs. } 10,200}$
Seller got $= 255000 - 5100 = \mathbf{\text{Rs. } 249,900}$
Buyer paid $= 255000 + 5100 = \mathbf{\text{Rs. } 260,100}$
Commission from each party $= 2550000 \times 2\% = \text{Rs. } 51,000$
Dealer got $= 51000 \times 2 = \mathbf{\text{Rs. } 102,000}$
Seller got $= 2550000 - 51000 = \mathbf{\text{Rs. } 2,499,000}$
Buyer paid $= 2550000 + 51000 = \mathbf{\text{Rs. } 2,601,000}$
A manufacturer sold an article to a wholesaler for Rs. 500 who again sold it for Rs. 750. If the rate of sales tax on the goods is 10% then find the VAT paid by the wholesaler.
$$\text{Input Tax (paid by wholesaler on purchase)} = 500 \times \frac{10}{100} = \text{Rs. } 50$$ $$\text{Output Tax (collected by wholesaler on sale)} = 750 \times \frac{10}{100} = \text{Rs. } 75$$ $$\text{VAT Paid by Wholesaler} = \text{Output Tax} - \text{Input Tax} = 75 - 50 = \text{Rs. } 25$$ Final Answer: Rs. 25
A shopkeeper buys an article from the wholesaler at Rs. 450 and pays sales tax at the rate of 10%. The shopkeeper fixes the price of the article at Rs. 600 and charges sales tax at 10% from the consumer.
(a) Find the input tax and output tax for the shopkeeper.
(b) Find the VAT that the shopkeeper pays to the government.
(a) Input Tax & Output Tax:
$$\text{Input Tax} = 450 \times \frac{10}{100} = \text{Rs. } 45$$ $$\text{Output Tax} = 600 \times \frac{10}{100} = \text{Rs. } 60$$ (b) VAT Paid to Government:
$$\text{VAT} = \text{Output Tax} - \text{Input Tax} = 60 - 45 = \text{Rs. } 15$$ Final Answer: (a) Input Tax = Rs. 45, Output Tax = Rs. 60; (b) VAT = Rs. 15
A shopkeeper buys some medicine for Rs. 550 and pays sales tax at the rate of 4%. He sells the medicine for Rs. 800 and charges sales tax from the buyer at the rate of 5%.
(a) Find the input tax and output tax for the shopkeeper.
(b) Find the VAT payable by the shopkeeper.
(a) Input Tax & Output Tax:
$$\text{Input Tax} = 550 \times \frac{4}{100} = \frac{2200}{100} = \text{Rs. } 22$$ $$\text{Output Tax} = 800 \times \frac{5}{100} = \text{Rs. } 40$$ (b) VAT Payable:
$$\text{VAT} = \text{Output Tax} - \text{Input Tax} = 40 - 22 = \text{Rs. } 18$$ Final Answer: (a) Input Tax = Rs. 22, Output Tax = Rs. 40; (b) VAT = Rs. 18
A retailer charges sales tax on an article at the rate of 6% from the buyer. The listed price of the article is Rs. 450. If the retailer has to pay a VAT of Rs. 9, what was the sum the retailer paid to the wholesaler?
$$\text{Output Tax (collected from buyer)} = 450 \times \frac{6}{100} = \text{Rs. } 27$$ $$\text{VAT} = \text{Output Tax} - \text{Input Tax} \implies 9 = 27 - \text{Input Tax}$$ $$\text{Input Tax} = 27 - 9 = \text{Rs. } 18$$ Since the wholesaler charged sales tax at $6\%$, let purchase price be $P$:
$$0.06 P = 18 \implies P = \frac{18}{0.06} = \text{Rs. } 300$$ Total sum paid by retailer to wholesaler (inclusive of tax) $= 300 + 18 = \mathbf{\text{Rs. } 318}$ (exclusive of tax $= \mathbf{\text{Rs. } 300}$).
A man buys an article whose listed price is Rs. 1080 from a shopkeeper and pays a sales tax at the rate of 10%. The shopkeeper pays a VAT of Rs. 12. Find the input tax and the price inclusive of tax at which the shopkeeper bought the article.
$$\text{Output Tax (collected from buyer)} = 1080 \times \frac{10}{100} = \text{Rs. } 108$$ $$\text{VAT} = \text{Output Tax} - \text{Input Tax} \implies 12 = 108 - \text{Input Tax}$$ $$\text{Input Tax} = 108 - 12 = \mathbf{\text{Rs. } 96}$$ Let original wholesale purchase price be $P$. Tax was $10\%$, so:
$$0.10 P = 96 \implies P = \frac{96}{0.10} = \text{Rs. } 960$$ $$\text{Price inclusive of tax} = 960 + 96 = \mathbf{\text{Rs. } 1,056}$$
Islamic Social Finance: Zakat & Ushr
In Islamic economics, Zakat and Ushr are divine mechanisms for wealth purification, poverty alleviation, and social equity. Unlike state taxes, they are spiritual obligations ordained on surplus wealth and agricultural produce.
1. Zakat (“Purification & Growth”)
The third fundamental pillar of Islam, payable annually by every adult Muslim who owns wealth meeting or exceeding the Nisab for one full Lunar Year (Hawl).
- Gold: $7.5\text{ tolas}$ ($\approx 87.4\text{ grams}$ or $87.48\text{ g}$).
- Silver: $52.5\text{ tolas}$ ($\approx 612.32\text{ grams}$ or $612.36\text{ g}$).
- Cash & Tradable Assets: Evaluated against whichever Nisab is lower (typically silver in contemporary markets).
- Minerals & Buried Wealth: Taxed at 5% (or Rikaz at 20%).
- Exemptions: No Zakat is levied on items of daily personal necessity (primary residence, clothing, household furniture).
2. Ushr (“One-Tenth”)
Zakat levied specifically on agricultural produce (grains, crops, fruits, vegetables) and paid immediately at the time of harvest.
- No one-year waiting period is required; it is due upon each harvest: “And pay the due thereof upon the harvest day” (Surah Al-An'am 6:141).
- Artificial irrigation involves fuel, machinery, and labour costs, hence the rate is reduced to half (5%).
- Nisab for Grain: According to scholarly consensus, Nisab is 5 Wasaq ($\approx 600\text{ kg}$ to $612\text{ kg}$), where 1 Wasaq represents the weight of one camel load.
Exercise 4.5 — Complete Step-by-Step Textbook Solutions
Find Zakat on the following:
(i) 8 tola gold @ Rs. 80000 per tola.
(ii) 70 tola silver @ Rs. 800 per tola.
(iii) 100 g gold @ Rs. 8000 per gram.
(iv) 712 g silver @ Rs. 80 per gram.
Rate of Zakat $= 2.5\% = \frac{1}{40}$
(i) 8 tola gold: Total value $= 8 \times 80000 = \text{Rs. } 640,000$.
$$\text{Zakat} = \frac{640000}{40} = \text{Rs. } 16,000$$ (ii) 70 tola silver: Total value $= 70 \times 800 = \text{Rs. } 56,000$.
$$\text{Zakat} = \frac{56000}{40} = \text{Rs. } 1,400$$ (iii) 100 g gold: Total value $= 100 \times 8000 = \text{Rs. } 800,000$.
$$\text{Zakat} = \frac{800000}{40} = \text{Rs. } 20,000$$ (iv) 712 g silver: Total value $= 712 \times 80 = \text{Rs. } 56,960$.
$$\text{Zakat} = \frac{56960}{40} = \text{Rs. } 1,424$$ Final Answer: (i) Rs. 16,000 (ii) Rs. 1,400 (iii) Rs. 20,000 (iv) Rs. 1,424
Ahmed has the following assets: 40 gram silver @ Rs. 750 per gram, shares worth Rs. 75000 and bank balance worth Rs. 47800. Find Zakat paid by him.
Value of silver $= 40 \times 750 = \text{Rs. } 30,000$
Shares worth $= \text{Rs. } 75,000$
Bank balance $= \text{Rs. } 47,800$
$$\text{Total Zakatable Wealth} = 30000 + 75000 + 47800 = \text{Rs. } 152,800$$ $$\text{Zakat} = \frac{152800}{40} = 152800 \times 0.025 = \text{Rs. } 3,820$$ Final Answer: Rs. 3,820
Find Zakat if a person has the following assets:
Income from rented house = Rs. 124000
2 prize bonds worth = Rs. 100000
Savings = Rs. 68000
$$\text{Total Wealth} = 124000 + 100000 + 68000 = \text{Rs. } 292,000$$ $$\text{Zakat} = \frac{292000}{40} = \text{Rs. } 7,300$$ Final Answer: Rs. 7,300
Asma paid Zakat worth Rs. 15000 on gold. Find the value of gold.
Let value of gold be $G$.
$$\text{Zakat} = \frac{G}{40} = 15000$$ $$G = 15000 \times 40 = \text{Rs. } 600,000$$ Final Answer: Rs. 600,000
Mr. Akbar is jeweller. He purchased 60 gm gold and 600 gm silver. If the market value for gold is Rs. 8000 per gram and Rs. 80 per gram for silver, find Zakat paid by him.
Value of 60 gm gold $= 60 \times 8000 = \text{Rs. } 480,000$
Value of 600 gm silver $= 600 \times 80 = \text{Rs. } 48,000$
$$\text{Total Value of Inventory} = 480000 + 48000 = \text{Rs. } 528,000$$ $$\text{Zakat} = \frac{528000}{40} = \text{Rs. } 13,200$$ Final Answer: Rs. 13,200
Find Ushr separately on the following crops when the land is irrigated by rain water:
1000 kg rice, 80 kg fruit, 140 kg vegetables.
Land irrigated by rain water (natural source) $\implies \text{Ushr Rate} = 10\% = \frac{1}{10}$.
$$\text{Ushr on Rice} = 1000 \times \frac{10}{100} = 100\text{ kg}$$ $$\text{Ushr on Fruit} = 80 \times \frac{10}{100} = 8\text{ kg}$$ $$\text{Ushr on Vegetables} = 140 \times \frac{10}{100} = 14\text{ kg}$$ Final Answer: 100 kg rice, 8 kg fruit, 14 kg vegetables
A person gives Ushr Rs. 3750 on crop worth Rs. 75000. What is rate of Ushr given? Is the land irrigated by artificial resources?
$$\text{Rate of Ushr} = \left(\frac{3750}{75000}\right) \times 100\% = \frac{375}{7500} \times 100\% = 5\%$$ Since the rate of Ushr is $5\%$, the land is irrigated by artificial resources (wells, tubewells).
Final Answer: Rate = 5%; Yes, irrigated by artificial resources
Aamir has a poultry farm. At the end of lunar year, he paid Zakat Rs. 8250. Find number of hens in the poultry farm provided that each hen is sold for Rs. 330.
Let total value of commercial poultry flock be $V$.
$$\text{Zakat} = \frac{V}{40} = 8250 \implies V = 8250 \times 40 = \text{Rs. } 330,000$$ Price of each hen $= \text{Rs. } 330$.
$$\text{Number of Hens} = \frac{\text{Total Value}}{\text{Price per Hen}} = \frac{330000}{330} = 1000\text{ hens}$$ Final Answer: 1000 hens
A land is irrigated by a river. Find value of cotton produced if Ushr given is Rs. 9786.5.
Irrigation by river (natural water resource) $\implies \text{Ushr Rate} = 10\%$.
Let total value of cotton produced be $C$.
$$10\% \times C = 9786.50 \implies \frac{1}{10} \times C = 9786.50$$ $$C = 9786.50 \times 10 = \text{Rs. } 97,865$$ Final Answer: Rs. 97,865
Direct Taxation: Income Tax, Tax Rebates & Statutory Reductions
Income Tax is a progressive direct tax imposed by the federal government through the Federal Board of Revenue (FBR) on individuals and corporate bodies whose annual gross earnings exceed a legally defined exemption threshold.
Step 1: Gross Annual Income
Sum of all earnings received during the tax year (1 July to 30 June):
Step 2: Tax Rebate & Deductions
Tax rebate is income upon which tax rate is 0%. Legitimate donations & Zakat reduce gross income:
Step 3: Tax Rate & Reductions
Multiply taxable income by prescribed tax slab rate. Apply special allowances:
Under Income Tax Ordinance rules, recognized full-time teachers and researchers in non-profit educational and government institutions are granted a 25% to 50% statutory reduction on their computed income tax liability to support the academic profession.
Exercise 4.6 — Complete Step-by-Step Textbook Solutions
Abid works in a bank whose annual income from salary is Rs. 500000. Find his income tax @ 5% if the tax rebate is Rs. 400000.
Annual Income $= \text{Rs. } 500,000$
Tax Rebate (Exempt Limit) $= \text{Rs. } 400,000$
$$\text{Taxable Income} = 500000 - 400000 = \text{Rs. } 100,000$$ Rate of Income Tax $= 5\%$
$$\text{Income Tax} = 100000 \times \frac{5}{100} = 1000 \times 5 = \text{Rs. } 5,000$$ Final Answer: Rs. 5,000
Ms. Haleema has the following information for the tax year:
Salary = Rs. 34400 per month
Income from business = Rs. 22000 per month
Calculate her income tax @ 5%. The rebate on the tax is Rs. 500000.
$$\text{Total Monthly Income} = 34400 + 22000 = \text{Rs. } 56,400$$ $$\text{Gross Annual Income} = 56400 \times 12 = \text{Rs. } 676,800$$ $$\text{Taxable Income} = \text{Gross Annual Income} - \text{Rebate} = 676800 - 500000 = \text{Rs. } 176,800$$ $$\text{Income Tax @ 5\%} = 176800 \times \frac{5}{100} = 1768 \times 5 = \text{Rs. } 8,840$$ Final Answer: Rs. 8,840
Mr. Iftikhar is a professor in a government college. Compute income tax paid by him @ 6% if his monthly income is Rs. 120000. The reduction in the tax is 25% being teacher and the rebate on the tax is Rs. 600000.
$$\text{Annual Income} = 120000 \times 12 = \text{Rs. } 1,440,000$$ $$\text{Taxable Income} = 1440000 - 600000 = \text{Rs. } 840,000$$ $$\text{Computed Tax @ 6\%} = 840000 \times \frac{6}{100} = 8400 \times 6 = \text{Rs. } 50,400$$ $$\text{Teacher Reduction (25\%)} = 50400 \times \frac{25}{100} = \frac{50400}{4} = \text{Rs. } 12,600$$ $$\text{Net Income Tax Payable} = 50400 - 12600 = \text{Rs. } 37,800$$ Final Answer: Rs. 37,800
Mr. Manzoor Qadir provided the following information for the tax year:
Salary income = Rs. 232000
Rent from house = Rs. 104400
Income from agriculture = Rs. 36000
Calculate his income tax if the rebate on the tax is Rs. 200000 and rate of tax is 5%.
$$\text{Total Gross Income} = 232000 + 104400 + 36000 = \text{Rs. } 372,400$$ $$\text{Taxable Income} = 372400 - 200000 = \text{Rs. } 172,400$$ $$\text{Income Tax @ 5\%} = 172400 \times \frac{5}{100} = 1724 \times 5 = \text{Rs. } 8,620$$ Final Answer: Rs. 8,620
Mr. Asif is a doctor and runs his private clinic. His payment account for the tax year is:
Consultation fees = Rs. 862000
Gifts from patients = Rs. 42000
Calculate his income tax. Rate of tax is 4% and rebate on the tax is Rs. 400000.
$$\text{Total Gross Income} = 862000 + 42000 = \text{Rs. } 904,000$$ $$\text{Taxable Income} = 904000 - 400000 = \text{Rs. } 504,000$$ $$\text{Income Tax @ 4\%} = 504000 \times \frac{4}{100} = 5040 \times 4 = \text{Rs. } 20,160$$ Final Answer: Rs. 20,160
The following information is available in respect of Mr. Ahmed Khan for the current tax year:
Salary income = Rs. 240000
Business income = Rs. 290000
Calculate tax @ 10%. The rebate on the tax is Rs. 200000.
$$\text{Total Gross Income} = 240000 + 290000 = \text{Rs. } 530,000$$ $$\text{Taxable Income} = 530000 - 200000 = \text{Rs. } 330,000$$ $$\text{Income Tax @ 10\%} = 330000 \times \frac{10}{100} = \text{Rs. } 33,000$$ Final Answer: Rs. 33,000
Ayesha is executive engineer. She provided the following information for the tax year:
(i) Income:
Salary income = Rs. 840000
Income from other sources = Rs. 160000
(ii) Donation:
Prime minister relief fund = Rs. 50000
Zakat = Rs. 42000
Calculate income tax @ 8%. The rebate on the tax is Rs. 400000.
$$\text{Gross Income} = 840000 + 160000 = \text{Rs. } 1,000,000$$ $$\text{Total Deductible Allowances (Donations + Zakat)} = 50000 + 42000 = \text{Rs. } 92,000$$ $$\text{Net Income after Deductions} = 1000000 - 92000 = \text{Rs. } 908,000$$ $$\text{Taxable Income} = \text{Net Income} - \text{Rebate} = 908000 - 400000 = \text{Rs. } 508,000$$ $$\text{Income Tax @ 8\%} = 508000 \times \frac{8}{100} = 5080 \times 8 = \text{Rs. } 40,640$$ Final Answer: Rs. 40,640
Younas provided the following information for the tax year:
(i) Income:
Salary income = Rs. 900000
Royalty = Rs. 340000
(ii) Donations:
Welfare fund = Rs. 60000
Charitable trust = Rs. 35000
Compute income tax @ 10%. The rebate on the tax is Rs. 600000.
$$\text{Gross Income} = 900000 + 340000 = \text{Rs. } 1,240,000$$ $$\text{Total Allowable Donations} = 60000 + 35000 = \text{Rs. } 95,000$$ $$\text{Net Income after Donations} = 1240000 - 95000 = \text{Rs. } 1,145,000$$ $$\text{Taxable Income} = \text{Net Income} - \text{Rebate} = 1145000 - 600000 = \text{Rs. } 545,000$$ $$\text{Income Tax @ 10\%} = 545000 \times \frac{10}{100} = \text{Rs. } 54,500$$ Final Answer: Rs. 54,500
Unit 04 Synthesis, Words Board & Review Exercise 4
Executive Chapter Summary
- Profit & Loss: Profit occurs when $\text{S.P.} > \text{C.P.}$; Loss occurs when $\text{C.P.} > \text{S.P.}$. Both percentages are strictly computed relative to Cost Price ($\text{C.P.}$).
- Marked Price & Discount: Discount is a reduction off Marked Price ($\text{M.P.}$), yielding $\text{S.P.} = \text{M.P.} - \text{Discount}$.
- Property Tax: A provincial direct tax on immovable property assessed at the close of the financial year (1 July – 30 June).
- General Sales Tax (GST): An indirect consumption tax (standard 17% in Pakistan) levied on goods and utility bills (electricity, gas).
- Commission: Service payment to agents expressed as a percentage of written or sale value.
- Value Added Tax (VAT): $\text{VAT} = \text{Output Tax} - \text{Input Tax}$, preventing cumulative cascading taxation across intermediate producers and distributors.
- Zakat: $2.5\%$ ($\frac{1}{40}$) annual wealth tax on net surplus held for one complete Lunar Year meeting Nisab ($7.5\text{ tolas gold} / 52.5\text{ tolas silver}$).
- Ushr: Agricultural tithe paid at harvest: $10\%$ on naturally irrigated lands, $5\%$ on artificially irrigated lands.
- Income Tax: Progressive direct tax on annual gross income exceeding the statutory tax rebate threshold, featuring special deductions for donations, Zakat, and full-time educator allowances.
📚 Financial Arithmetic Words Board
Review Exercise 4 — Multiple Choice Questions & Comprehensive Review Problems
1. Choose the correct option in the following:
(a) Salesman (b) Buyer (c) Importer (d) Exporter
Correct: (b) Buyer
(a) Direct tax (b) Indirect tax (c) Wealth tax (d) Penalty
Correct: (b) Indirect tax
(a) 10% (b) 15% (c) 17% (d) 25%
Correct: (c) 17%
(a) Rs. 85 (b) Rs. 75 (c) Rs. 78 (d) Rs. 100
Correct: (a) Rs. 85
(a) Property tax (b) GST (c) Income tax (d) VAT
Correct: (d) VAT
(a) Rs. 10000 (b) Rs. 20000 (c) Rs. 5000 (d) Rs. 1000
Correct: (a) Rs. 10000
(a) $\frac{1}{2.50} x$ (b) $\frac{5}{2} x$ (c) $\frac{1}{40} x$ (d) $\frac{1}{20} x$
Correct: (c) $\frac{1}{40} x$
(a) financial year (b) lunar year (c) solar year (d) tax year
Correct: (b) lunar year
(a) 10% (b) 5% (c) 1/10 % (d) 1/5 %
Correct: (a) 10%
(a) 650 kg (b) 450 kg (c) 500 kg (d) 600 kg
Correct: (d) 600 kg
(a) Eid-ul-Fitr (b) Harvest (c) Cultivation (d) First Ramadan
Correct: (b) Harvest
(a) Goods (b) Services (c) Salary (d) Both a & b
Correct: (d) Both a & b
(a) day (b) week (c) month (d) year
Correct: (d) year
Calculate general sales tax @ 17% on an electricity bill when:
Previous meter reading = 4841, Present meter reading = 4941.
Rate for first 100 units is Rs. 8 per unit.
$$\text{Electricity Units Consumed} = 4941 - 4841 = 100\text{ units}$$ $$\text{Cost of Electricity} = 100 \times 8 = \text{Rs. } 800$$ $$\text{GST @ 17\%} = 800 \times \frac{17}{100} = 8 \times 17 = \text{Rs. } 136$$ Final Answer: Rs. 136
Calculate general sales tax @ 16% on a gas bill when:
Gas charges = 1180, Meter rent = 20.
Hint: GST is applied on the sum of gas charges and meter rent.
$$\text{Total Billable Base} = \text{Gas Charges} + \text{Meter Rent} = 1180 + 20 = \text{Rs. } 1200$$ $$\text{GST @ 16\%} = 1200 \times \frac{16}{100} = 12 \times 16 = \text{Rs. } 192$$ Final Answer: Rs. 192
Asad paid property tax Rs. 40000 on the property worth Rs. 800000. What is the rate of property tax?
$$\text{Rate of Property Tax} = \left(\frac{\text{Property Tax}}{\text{Worth of Property}}\right) \times 100\%$$ $$\text{Rate} = \left(\frac{40000}{800000}\right) \times 100\% = \frac{40}{8}\% = 5\%$$ Final Answer: 5%
Find Zakat on the following assets at the end of lunar year:
Savings = Rs. 350000, 100 gm gold @ Rs. 7500 per gram.
$$\text{Value of 100 gm gold} = 100 \times 7500 = \text{Rs. } 750,000$$ $$\text{Total Zakatable Assets} = 350000 + 750000 = \text{Rs. } 1,100,000$$ $$\text{Zakat @ 2.5\%} = \frac{1100000}{40} = \text{Rs. } 27,500$$ Final Answer: Rs. 27,500
A property agent got a commission of Rs. 15000 both from the buyer and the seller. Find percentage of commission if he sold a plot for Rs. 750000.
Commission collected from each individual party $= \text{Rs. } 15,000$
Value of plot $= \text{Rs. } 750,000$
$$\text{Commission Percentage from each party} = \left(\frac{15000}{750000}\right) \times 100\% = \frac{15}{7.5}\% = 2\%$$
An agent sold rice @ 10% commission and paid Rs. 90000 to the owner after deducting his commission. Find the sale price of rice.
Let the sale price of rice be $S$.
Agent deducts $10\%$ commission, leaving the owner with $(100 - 10)\% = 90\%$ of $S$:
$$0.90 \times S = 90000$$ $$S = \frac{90000}{0.90} = \frac{90000 \times 10}{9} = \text{Rs. } 100,000$$ Final Answer: Rs. 100,000
Calculate VAT if:
(i) output tax = 10% of Rs. 50000, input tax = 10% of Rs. 46000
(ii) input tax = Rs. 35.5, output tax = 12% of Rs. 350
$$\text{VAT} = \text{Output Tax} - \text{Input Tax}$$ (i) Part (i):
$$\text{Output Tax} = 50000 \times \frac{10}{100} = \text{Rs. } 5,000$$ $$\text{Input Tax} = 46000 \times \frac{10}{100} = \text{Rs. } 4,600$$ $$\text{VAT} = 5000 - 4600 = \text{Rs. } 400$$ (ii) Part (ii):
$$\text{Output Tax} = 350 \times \frac{12}{100} = \frac{4200}{100} = \text{Rs. } 42$$ $$\text{Input Tax} = \text{Rs. } 35.50$$ $$\text{VAT} = 42 - 35.50 = \text{Rs. } 6.50$$ Final Answer: (i) Rs. 400 (ii) Rs. 6.50
Chapter 4 Mastery Synthesis — Core Formulas Cheat Sheet
- $\text{Profit \%} = \frac{\text{Profit}}{\text{C.P.}} \times 100\%$
- $\text{Loss \%} = \frac{\text{Loss}}{\text{C.P.}} \times 100\%$
- $\text{Discount \%} = \frac{\text{Discount}}{\text{M.P.}} \times 100\%$
- $\text{Commission} = \text{Sales} \times \text{Rate \%}$
- $\text{VAT} = \text{Output Tax} - \text{Input Tax}$
- $\text{Zakat} = \text{Zakatable Wealth} \times 2.5\% = \frac{\text{Wealth}}{40}$
- $\text{Ushr (Natural)} = 10\% \quad | \quad \text{Ushr (Artificial)} = 5\%$
- $\text{Taxable Income} = \text{Gross Income} - \text{Rebate}$
More Chapter Notes for Class 7 (FBISE)
MathematicsTest Your Knowledge on Chapter 4: Class 7 Mathematics Ch 4 Mastery Guide: Profit & Loss, Discount, Property Tax, GST, Commission, VAT, Zakat, Ushr & Income Tax (FBISE)
Practice textbook-aligned solved MCQs with instant answer feedback, step-by-step solutions, and timed test simulation.
Class 7 Mathematics - Ch 4: Financial Arithmetic Chapter Mock Test
Test your complete conceptual mastery across all chapters under real board exam conditions with official timer, anti-cheat surveillance, and instant grading.