Profit, Loss and Discount

“Profit, Loss, and Discount are essential in commerce-related questions, often asked in SSC, RRB, Banking, and Defence exams.”

1. Basic Concepts and Formulas

  • Profit = Selling Price (SP) – Cost Price (CP)
  • Loss = CP – SP
  • Profit% = (Profit / CP) × 100
  • Loss% = (Loss / CP) × 100
  • SP = CP × (100 + Profit%) / 100
  • SP = CP × (100 – Loss%) / 100
  • CP = SP × 100 / (100 + Profit%)
  • Marked Price (MP) – Discount = SP
  • Discount% = (Discount / MP) × 100

2. Type-Wise Questions

  • Type 1: Direct Profit Calculation
    Example: CP = ₹500, SP = ₹600 ⇒ Profit = ₹100 ⇒ Profit% = 20%
  • Type 2: Loss Based Question
    Example: CP = ₹300, SP = ₹240 ⇒ Loss = ₹60 ⇒ Loss% = 20%
  • Type 3: Find SP when CP and Profit% Given
    Example: CP = ₹400, Profit% = 25% ⇒ SP = 400 × (125/100) = ₹500
  • Type 4: Find CP when SP and Loss% Given
    Example: SP = ₹720, Loss% = 10% ⇒ CP = 720 × 100 / 90 = ₹800
  • Type 5: Find Marked Price with Profit & Discount
    Example: CP = ₹800, Profit = 20%, Discount = 10% ⇒ MP = (SP × 100) / (100 – Discount%) = ₹1000
  • Type 6: Successive Discounts
    Formula: a + b – ab/100
    Example: Discounts of 20% and 10% ⇒ Net Discount = 20 + 10 – (20×10)/100 = 28%
  • Type 7: Equal SP – Which Transaction Gave Profit?
    Example: Item 1 sold at 20% profit, Item 2 at 20% loss, both at same SP. Overall result?
    Solution: Always results in a loss ⇒ Loss% = (Common %)^2 / 100 = (20×20)/100 = 4% loss
  • Type 8: Overall % Profit/Loss
    Example: CP = ₹1000, Profit = ₹200 ⇒ Profit% = (200/1000) × 100 = 20%
  • Type 9: Two Articles Sold at Same Price, One Profit One Loss
    Example: 20% profit and 20% loss on equal SP ⇒ Always a loss of 4%
  • Type 10: When % Gain = % Loss
    Result: Always a loss
    Formula: Loss% = (Common Gain or Loss%)² / 100

3. Previous Year Exam Questions

  • (SSC CGL 2022): CP = ₹500, Marked Price = ₹700, Discount = 10%. Find Profit%
    Solution: SP = 700 – 10% of 700 = ₹630 ⇒ Profit = 130 ⇒ Profit% = 26%
  • (RRB NTPC 2020): Marked Price = ₹1500, Discount = 20%, CP = ₹1100. Find profit %
    Solution: SP = 1500 – 20% of 1500 = ₹1200 ⇒ Profit = 100 ⇒ Profit% = 9.09%
  • (SSC CHSL 2019): SP = ₹960, Loss% = 20%. Find CP
    Solution: CP = 960 × 100 / 80 = ₹1200
  • (HSSC 2021): Trader makes 10% profit on SP. Find profit % on CP.
    Solution: Profit% on CP = 10/90 × 100 = 11.11%
  • (SSC MTS 2018): Successive discounts of 30% and 10% on ₹2000
    Solution: Net discount = 30 + 10 – (30×10)/100 = 37% ⇒ Final price = ₹1260

4. Tips to Remember

  • When discount & profit both are involved, use SP = MP – Discount and back-calculate.
  • If % gain = % loss, it’s always a net loss (use formula).
  • Marked Price = CP × (100 + Profit%) / (100 – Discount%)
  • Practice reverse calculations to find missing values efficiently in exams.
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