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Category: Maths

  • Profit / Loss questions

    Profit and Loss Questions & Answers

    100 Questions & Answers: Profit and Loss

    Key Formulas and Concepts:
    • Profit (P) = Selling Price (SP) – Cost Price (CP)
    • Loss (L) = Cost Price (CP) − Selling Price (SP)
    • Profit % = (Profit / Cost Price) × 100
    • Loss % = (Loss / Cost Price) × 100
    • Selling Price (SP) = Cost Price × [(100 + Profit%) / 100] (for profit)
    • Cost Price (CP) = Selling Price × [100 / (100 + Profit%)] (for profit)
    • Discount = Marked Price (MP) − Selling Price (SP)

    Basic Questions & Answers (1–30)

    1. Q: What is profit?
      A: The amount earned when the selling price is greater than the cost price.
    2. Q: What is loss?
      A: The amount lost when the cost price is greater than the selling price.
    3. Q: Define cost price.
      A: The price at which an article is purchased.
    4. Q: Define selling price.
      A: The price at which an article is sold.
    5. Q: A shopkeeper buys a pen for ₹10 and sells it for ₹15. Find the profit.
      A: Profit = ₹15 − ₹10 = ₹5.
    6. Q: What is the profit percent in question 5?
      A: Profit % = (5/10) × 100 = 50%.
    7. Q: If CP = ₹50, SP = ₹40. What is the loss?
      A: Loss = ₹50 − ₹40 = ₹10.
    8. Q: Loss percent in question 7?
      A: (10/50) × 100 = 20%.
    9. Q: If cost price and selling price are equal, what is the result?
      A: Neither profit nor loss.
    10. Q: If an item is bought for ₹200 and sold for ₹250, find profit%?
      A: Profit = ₹50; Profit% = (50/200) × 100 = 25%.
    11. Q: Article bought at ₹300, sold at loss of ₹60. Find SP.
      A: SP = ₹300 − ₹60 = ₹240.
    12. Q: If selling price is ₹120 and profit is ₹20, what was cost price?
      A: CP = ₹120 − ₹20 = ₹100.
    13. Q: Find the loss % if CP is ₹80, SP is ₹68.
      A: Loss = ₹12; Loss% = (12/80) × 100 = 15%.
    14. Q: If profit% is 10% and CP is ₹2,000, what is SP?
      A: SP = 2,000 × (110/100) = ₹2,200.
    15. Q: If loss% is 25% and CP is ₹400, what is SP?
      A: SP = 400 × (75/100) = ₹300.
    16. Q: If SP = ₹480 and loss% = 20%, find CP.
      A: CP = 480 × 100/80 = ₹600.
    17. Q: If SP = ₹1,000 and profit% = 25%, find CP.
      A: CP = 1000 × 100/125 = ₹800.
    18. Q: CP = ₹350, profit% = 15%. Find SP.
      A: SP = 350 × 115/100 = ₹402.50.
    19. Q: Item sold for ₹75, loss = ₹25. Find CP.
      A: CP = 75 + 25 = ₹100.
    20. Q: Item bought for ₹180, sold at profit of 20%. SP?
      A: SP = 180 × 120/100 = ₹216.
    21. Q: If CP = ₹1, SP = ₹0.85, loss%?
      A: Loss% = ((1−0.85)/1)×100 = 15%.
    22. Q: SP is 125% of CP, profit%?
      A: 25%.
    23. Q: CP is ₹60, sold at loss of 10%. SP?
      A: ₹60 × 0.9 = ₹54.
    24. Q: SP is ₹90, profit = ₹10. CP?
      A: ₹80.
    25. Q: CP = ₹300. To get 20% profit, SP?
      A: ₹300 × 1.2 = ₹360.
    26. Q: CP = ₹200, SP = ₹150, loss%?
      A: 25%.
    27. Q: Item bought and sold at same price. What’s profit/loss %?
      A: 0%.
    28. Q: CP = ₹50, SP = ₹65, profit%?
      A: (15/50) × 100 = 30%.
    29. Q: SP = ₹140, loss = ₹10, find CP.
      A: ₹150.
    30. Q: Article sold at ₹900, profit is 20%. CP?
      A: 900 × 100/120 = ₹750.

    Intermediate Questions & Answers (31–70)

    1. Q: If CP = ₹120, loss% = 10%, SP?
      A: ₹108.
    2. Q: Marked price = ₹200, discount = 10%, SP?
      A: ₹180.
    3. Q: A pen bought for ₹80, sold for ₹104. Profit%?
      A: 30%.
    4. Q: SP is ₹540, loss% is 10%. CP?
      A: 540 × 100/90 = ₹600.
    5. Q: CP is ₹1,000. Find SP for 5% loss.
      A: ₹950.
    6. Q: Article bought for ₹40, sold to gain 20%. SP?
      A: ₹48.
    7. Q: SP = ₹75, loss = ₹15. CP?
      A: ₹90.
    8. Q: A loss of 25%, SP = ₹300. CP?
      A: 300 × 100/75 = ₹400.
    9. Q: Marked price = ₹250, discount 20%. SP?
      A: ₹200.
    10. Q: SP is 90% of CP. What is loss%?
      A: 10%.
    11. Q: CP = ₹600, profit = ₹180. Find SP.
      A: ₹780.
    12. Q: SP = ₹1,100, profit = ₹200. CP?
      A: ₹900.
    13. Q: A man buys for ₹200, spends ₹20 on transport, sells for ₹270. Find profit%.
      A: Net CP = ₹220; Profit = ₹50; Profit% ≈ 22.73%.
    14. Q: Profit% = 20%, CP = ₹150. SP?
      A: ₹180.
    15. Q: Loss% = 20%, SP = ₹480. CP?
      A: ₹600.
    16. Q: If the CP is increased by 20% and SP increased by 20%, what happens to profit%?
      A: Profit% remains unchanged.
    17. Q: CP = ₹250, profit = 10%, SP?
      A: ₹275.
    18. Q: CP = ₹125, profit = ₹25. SP?
      A: ₹150.
    19. Q: SP = ₹900, profit% = 50%. CP?
      A: 900/1.5 = ₹600.
    20. Q: SP = ₹88, loss% = 20%. CP?
      A: 88/0.8 = ₹110.
    21. Q: Profit = 25% of CP. If CP = ₹200, find SP.
      A: ₹250.
    22. Q: Loss = 12% on CP of ₹700. SP?
      A: ₹616.
    23. Q: Marked price = ₹120, discount = 5%, SP?
      A: ₹114.
    24. Q: If SP is 125% of CP, what is profit%?
      A: 25%.
    25. Q: CP = ₹80, sold at 125% of CP. SP?
      A: ₹100.
    26. Q: Loss = ₹20, CP = ₹100. SP?
      A: ₹80.
    27. Q: Profit = 10%, CP = ₹90. SP?
      A: ₹99.
    28. Q: Loss = 16.67%, CP = ₹60. SP?
      A: ₹50.
    29. Q: SP = ₹270, CP = ₹300. Loss%?
      A: 10%.
    30. Q: SP = ₹550, profit = ₹50. CP?
      A: ₹500.
    31. Q: A man bought an item for ₹200, sold for ₹220. Find profit%.
      A: 10%.
    32. Q: SP = ₹75, CP = ₹60. Profit%?
      A: 25%.
    33. Q: Loss = ₹18, SP = ₹162. CP?
      A: ₹180.
    34. Q: CP = ₹250. Sold at 10% loss. SP?
      A: ₹225.
    35. Q: Profit = ₹40, CP = ₹200. Profit%?
      A: 20%.
    36. Q: Loss = ₹45, CP = ₹300. Find loss%.
      A: 15%.
    37. Q: SP = ₹180, CP = ₹225. Profit/Loss?
      A: Loss, Loss% = 20%.
    38. Q: CP = ₹1,000, profit% = 5%. SP?
      A: ₹1,050.
    39. Q: A person made 10% profit on ₹500. Find profit.
      A: ₹50.
    40. Q: Loss is 14%, CP = ₹350. SP?
      A: ₹301.

    Advanced/Word Problem Questions (71–100)

    1. Q: Bought 5 items for ₹200, sold at ₹50 each. Profit%?
      A: Sold for ₹250; profit = ₹50; profit% = 25%.
    2. Q: Bought a car for ₹2,00,000, sold for ₹2,20,000, expenses ₹10,000. Profit%?
      A: Net CP = ₹2,10,000; profit = ₹10,000; profit% ≈ 4.76%.
    3. Q: A sold a bike for ₹8,000 at a profit of 25%. Find CP.
      A: CP = 8,000/1.25 = ₹6,400.
    4. Q: Sold 80 pens at ₹10 each, profit of ₹160. Find CP of one pen.
      A: Total SP = ₹800, profit = ₹160, CP = (800–160)/80 = ₹8.
    5. Q: If profit% = 0, then SP equals?
      A: SP = CP.
    6. Q: SP is 112% of CP. Find profit%.
      A: 12%.
    7. Q: SP = ₹850, CP = ₹1,000. Find loss%.
      A: 15%.
    8. Q: A watch bought at ₹500, sold at loss of 10%. SP?
      A: ₹450.
    9. Q: Item sold at ₹600, incurred a loss of ₹120. CP?
      A: ₹720.
    10. Q: Sold at a profit of ₹60, CP is ₹540. Find SP.
      A: ₹600.
    11. Q: Item purchased at ₹2,400, sold at 20% profit. SP?
      A: ₹2,880.
    12. Q: SP = ₹70, profit = ₹20. Find CP.
      A: ₹50.
    13. Q: CP = ₹2,500, loss percent = 20%. SP?
      A: ₹2,000.
    14. Q: Marked price = ₹900, discount = 10%, SP?
      A: ₹810.
    15. Q: Sold at 10% profit, CP = ₹250. SP?
      A: ₹275.
    16. Q: Loss = ₹30, CP = ₹200. Loss%?
      A: 15%.
    17. Q: Marked price = ₹800, discount = ₹160. SP?
      A: ₹640.
    18. Q: SP is 40% more than CP. Find profit%.
      A: 40%.
    19. Q: SP is 30% less than CP. Loss%?
      A: 30%.
    20. Q: CP = ₹120, profit = 25%. SP?
      A: ₹150.
    21. Q: Loss of 5% on ₹600, SP?
      A: ₹570.
    22. Q: Sold a pen at 80% of CP, incurring a 20% loss. Find CP if SP = ₹80.
      A: CP = 80/0.8 = ₹100.
    23. Q: Selling price is double the cost price. Profit%?
      A: 100%.
    24. Q: Bought at ₹400, sold at a loss of 25%. SP?
      A: ₹300.
    25. Q: Marked price = ₹2,000. Discount = 10%. Find SP.
      A: ₹1,800.
    26. Q: After 20% discount on marked price, item sold at ₹160. Marked price?
      A: ₹160/0.8 = ₹200.
    27. Q: Loss = 33.33%, CP = ₹60, SP?
      A: ₹40.
    28. Q: SP = ₹120, CP = ₹80. Profit%?
      A: 50%.
    29. Q: If profit% and loss% on two articles is equal and SPs are same, net result?
      A: Always a loss.
    30. Q: A sold for ₹600 at profit of 20%; B sold for ₹720 at loss of 10%. Find net profit/loss% if CPs added and SPs added.
      A: CP(A) = 600/1.2 = 500, CP(B) = 720/0.9 = 800. Total CP = 1,300. Total SP = 1,320. Net Profit = 20, Profit% ≈ 1.54%.

    End of set — Practice more for mastery!

  • Mind Maths – Series 2

    Mind Math Quiz – Set 2

    Mind Math Quiz – Set 2

  • Mind Maths – Series 1

    Mind Math Quiz

    Mind Math Quiz

  • Aptitude – Major Topics

    Major Topics in Aptitude

    Major Topics in Aptitude

    • 1. Number System – Types of numbers, divisibility, factors, LCM, HCF
    • 2. Percentage – Percent values, profit & loss, discount
    • 3. Ratio and Proportion – Ratios, proportions, mixtures and alligation
    • 4. Time and Work – Efficiency, work equations, pipes and cisterns
    • 5. Time, Speed and Distance – Speed, trains, boats and streams
    • 6. Profit, Loss, and Discount – CP, SP, profit/loss %, successive discount
    • 7. Simple and Compound Interest – SI and CI formulas and difference
    • 8. Averages – Average concepts, missing values, weighted average
    • 9. Problems on Ages – Age equations and comparisons
    • 10. Algebra – Linear, quadratic equations, simplifications
    • 11. Geometry and Mensuration – Shapes, area, perimeter, volume
    • 12. Data Interpretation – Tables, charts, pie diagrams
    • 13. Permutation and Combination – Arrangements, selections
    • 14. Probability – Basics, card, dice, and coin problems

  • Basic branches of Maths

  • Profit / Loss formulas

    Profit and Loss Formulas

    📘 Profit and Loss Formulas

    Concept Formula
    Cost Price (CP)The price at which an item is purchased
    Selling Price (SP)The price at which an item is sold
    Profit (Gain)Profit = SP – CP
    LossLoss = CP – SP
    Profit %(Profit / CP) × 100
    Loss %(Loss / CP) × 100
    SP (given Profit %)SP = CP × (100 + Profit%) / 100
    SP (given Loss %)SP = CP × (100 – Loss%) / 100
    CP (given Profit %)CP = SP × 100 / (100 + Profit%)
    CP (given Loss %)CP = SP × 100 / (100 – Loss%)
    DiscountDiscount = MP – SP
    Discount %(Discount / MP) × 100
    SP with DiscountSP = MP × (100 – Discount%) / 100

    ✅ Examples

    Profit: CP = ₹100, SP = ₹120 → Profit = ₹20
    Profit %: Profit % = (20 / 100) × 100 = 20%
    Loss: CP = ₹150, SP = ₹130 → Loss = ₹20
    Loss %: (20 / 150) × 100 = 13.33%
    SP (Profit 10%): CP = ₹200 → SP = 200 × 110 / 100 = ₹220
    SP (Loss 20%): CP = ₹500 → SP = 500 × 80 / 100 = ₹400
    CP (Profit 10%): SP = ₹220 → CP = 220 × 100 / 110 = ₹200
    CP (Loss 20%): SP = ₹400 → CP = 400 × 100 / 80 = ₹500
    Discount: MP = ₹1000, SP = ₹800 → Discount = ₹200
    Discount %: (200 / 1000) × 100 = 20%

  • A number divisible by 12

    Divisibility by 12

    Divisibility Rule for 12

    ✅ Shortcut: A number is divisible by 12 if it is divisible by both 3 and 4.

    How to Check:

    • ✔️ Check if the sum of digits is divisible by 3.
    • ✔️ Check if the last two digits form a number divisible by 4.
    • ✔️ If both are true, the number is divisible by 12.

    Examples:

    Number Sum of Digits Last 2 Digits Div by 3? Div by 4? Div by 12?
    144 9 44 ✅ ✅ ✅ Yes
    60 6 60 ✅ ✅ ✅ Yes
    66 12 66 ✅ ❌ ❌ No
    48 12 48 ✅ ✅ ✅ Yes
    120 3 20 ✅ ❌ ❌ No

  • A number divisible by 11

    Divisibility by 11

    Divisibility Rule for 11

    ✅ Shortcut: Find the alternating sum of the digits. If the result is divisible by 11 (or equals 0), then the number is divisible by 11.

    Steps:

    • Take the digits of the number.
    • Alternately add and subtract them.
    • If the result is divisible by 11 or is 0, it’s divisible by 11.

    Examples:

    Number Alternating Sum Result Divisible by 11?
    2728 2 − 7 + 2 − 8 -11 ✅ Yes
    121 1 − 2 + 1 0 ✅ Yes
    1234 1 − 2 + 3 − 4 -2 ❌ No
    462 4 − 6 + 2 0 ✅ Yes
    713 7 − 1 + 3 9 ❌ No

  • A number divisible by 10

    Divisibility by 10

    Divisibility Rule for 10

    ✅ Shortcut: If a number ends in 0, it is divisible by 10.

    Examples:

    Number Last Digit Divisible by 10? Reason
    120 0 ✅ Yes Ends in 0
    3050 0 ✅ Yes Ends in 0
    67 7 ❌ No Does not end in 0
    890 0 ✅ Yes Ends in 0
    743 3 ❌ No Does not end in 0

  • A number divisible by 9

    Divisibility by 9

    Divisibility Rule for 9

    ✅ Shortcut: Add all the digits of the number. If the total is divisible by 9, then the whole number is divisible by 9.

    Examples:

    Number Sum of Digits Divisible by 9? Reason
    729 7 + 2 + 9 = 18 ✅ Yes 18 ÷ 9 = 2
    123 1 + 2 + 3 = 6 ❌ No 6 ÷ 9 = 0.666
    9999 9 + 9 + 9 + 9 = 36 ✅ Yes 36 ÷ 9 = 4
    2527 2 + 5 + 2 + 7 = 16 ❌ No 16 ÷ 9 = 1.77
    8019 8 + 0 + 1 + 9 = 18 ✅ Yes 18 ÷ 9 = 2