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compulsory · CSS study notes

17. Profit, Loss and Business Mathematics

CSS GSA — Paper 7, Part-II, Section VI, Sub-topic 17 (Profit, Loss and Business Mathematics)

Past Paper Weightage

  • High in MPT/General Ability papers — profit/loss percentage and marked-price/discount problems recur regularly.

Key Definitions and Formulas

  • Cost Price (CP): the price at which an item is bought/produced
  • Selling Price (SP): the price at which an item is sold
  • Profit = SP − CP (when SP > CP); Loss = CP − SP (when CP > SP)
Profit %=ProfitCP×100Loss %=LossCP×100\text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 \qquad \text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100

always calculated as a percentage of the Cost Price, not the Selling Price (a very common exam trap)

  • Marked Price (MP): the labeled/listed price before any discount
Discount=MP−SPDiscount %=DiscountMP×100\text{Discount} = MP - SP \qquad \text{Discount \%} = \frac{\text{Discount}}{MP} \times 100

discount is always a percentage of the Marked Price

  • To find SP given CP and a profit %:
SP=CP×(1+Profit%100)SP = CP \times \left(1 + \frac{\text{Profit\%}}{100}\right)
  • To find SP given MP and a discount %:
SP=MP×(1−Discount%100)SP = MP \times \left(1 - \frac{\text{Discount\%}}{100}\right)

Worked Example 1 (Basic Profit %)

  • A shopkeeper buys a table for Rs. 2,000 and sells it for Rs. 2,400. Find his profit percentage.
    • Step 1: Find the profit amount: Profit = SP − CP = 2,400 − 2,000 = Rs. 400.
    • Step 2: Apply the profit % formula, using CP as the base: Profit % = (400 ÷ 2,000) × 100.
    • Step 3: Calculate: 400/2000 = 0.2, so 0.2 × 100 = 20% profit.

Worked Example 2 (Find SP from CP and Profit %)

  • A merchant wants a 15% profit on an item that cost him Rs. 800. Find the selling price.
    • Step 1: Use the formula SP = CP × (1 + Profit%/100).
    • Step 2: Plug in values: SP = 800 × (1 + 15/100) = 800 × 1.15.
    • Step 3: Calculate: 800 × 1.15 = Rs. 920.

Worked Example 3 (Marked Price and Discount)

  • An item is marked at Rs. 1,500 and sold after a 20% discount. Find the selling price and the discount amount.
    • Step 1: Use SP = MP × (1 − Discount%/100) = 1,500 × (1 − 20/100) = 1,500 × 0.80.
    • Step 2: Calculate SP: 1,500 × 0.80 = Rs. 1,200.
    • Step 3: Find the discount amount: Discount = MP − SP = 1,500 − 1,200 = Rs. 300 (and SP = Rs. 1,200).

Worked Example 4 (Successive Discounts — Common Trap)

  • A shop offers two successive discounts of 10% and 20% on an item marked at Rs. 2,000. Find the final selling price, and check whether this equals a single 30% discount.
    • Step 1: Apply the first discount: 2,000 × (1 − 10/100) = 2,000 × 0.90 = Rs. 1,800.
    • Step 2: Apply the second discount to the NEW price (not the original): 1,800 × (1 − 20/100) = 1,800 × 0.80 = Rs. 1,440.
    • Step 3: Compare to a flat 30% discount: 2,000 × 0.70 = Rs. 1,400. Since Rs. 1,440 ≠ Rs. 1,400, successive discounts do NOT simply add up — the actual combined discount here is only 28%, not 30%.

Worked Example 5 (Loss Scenario)

  • A trader bought a bicycle for Rs. 5,000 and had to sell it at a loss of 8%. Find the selling price.
    • Step 1: A loss means SP < CP, so use SP = CP × (1 − Loss%/100).
    • Step 2: Plug in: SP = 5,000 × (1 − 8/100) = 5,000 × 0.92.
    • Step 3: Calculate: 5,000 × 0.92 = Rs. 4,600.

MCQ Traps

  • Profit/Loss % is ALWAYS calculated on the Cost Price, never the Selling Price — the single most common error in this topic
  • Discount % is calculated on the Marked Price, not the Cost Price or Selling Price
  • Successive percentage discounts/increases do NOT simply add together — always apply them sequentially, one after another, on the running total

Self-Test Questions

  1. A shopkeeper buys pens at Rs. 10 each and sells them at Rs. 13 each. Find his profit percentage, showing each step.
  2. Find the selling price of an item costing Rs. 1,200 if the trader wants a 25% profit, showing the formula and calculation.
  3. An item marked at Rs. 3,000 is sold after two successive discounts of 15% and 10%. Find the final selling price, and compare it to a flat 25% discount to show why they differ.
  4. A dealer sells a fan for Rs. 1,150, incurring a loss of 8%. Find the cost price.

Past-Paper MCQs (FPSC)

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The FPSC MCQ papers you shared (2024 and 2025) had no direct profit-and-loss question.

Past-Paper Questions with Answers (FPSC)

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Every question below appeared in the FPSC papers you shared; the year and question number are in each title. Answers are worked out by me. Discount, tax and percentage-change versions are also in the Percentage chapter.

  • CSS 2025 Q6(b): Mr. Rasheed pays a deposit of Rs. 60,000 then 36 equal monthly payments. The total he pays is 127% of the basic price of Rs. 3,360,000. Find his monthly payment. (5)
    1. Total paid = 1.27 × 3,360,000 = Rs. 4,267,200
    2. After the deposit: 4,267,200 − 60,000 = 4,207,200
    3. Monthly payment = 4,207,200 ÷ 36 ≈ Rs. 116,866.67
  • CSS 2024 Q8(a): A man buys a car for Rs. 2,400,000, which includes one-fourth extra as profit. Find the original amount and the profit. (5)
    1. Original price x plus x/4 = 2,400,000 → (5/4)x = 2,400,000
    2. Original price = Rs. 1,920,000
    3. Profit = 2,400,000 − 1,920,000 = Rs. 480,000
    • If the question is read as 'profit is a quarter of Rs. 2,400,000', profit would be Rs. 600,000; state your reading
  • CSS 2023 Q8(a): An oven costing Rs. 36,800 is sold at an 8.5% gain. Selling price? (5)
    • SP = 36,800 × 1.085 = Rs. 39,928
  • CSS 2021 Q6(c): Marked food price Rs. 15,000; 10% discount, 10% service charge, 17% GST. Total payable? (5)
    • 15,000 → 13,500 → 14,850 → Rs. 17,374.50
  • CSS 2017 Q7(A): 5 kg of meat at Rs. 500/kg plus 6% consumption tax. (5)
    • 2,500 + 150 tax = Rs. 2,650
  • CSS 2025 Q6(a), 2025 Q7(a), 2025 Q7(b), 2022 Q8(c): Sale, marked-price, sales-tax and reverse-percentage problems (5 each)
    • Answered in full in the Percentage chapter
    • Quick answers: fridge price Rs. 27,200; marked price Rs. 97,500 (second discount route gives Rs. 80,730); sales tax Rs. 6,720; sweater's original price Rs. 200

CSS Exam Perspective

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  • Most repeated areas: selling price with gain, discount plus tax, instalment totals, reverse calculations
  • Tip: apply a discount first and tax after; for 'x% more than', multiply by (1 + x/100)