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Profit and Loss MCQs with Solutions and Short Tricks 01 to 20

Profit and Loss is one of the most frequently asked topics in SSC CGL, SSC CHSL, Banking exams, CAT, CDS, Railways and all major competitive exams. Mastering this chapter helps improve both accuracy and speed in quantitative aptitude.
In this guide, you will get 20 important Profit and Loss MCQs with detailed solutions and short tricks to help you revise fast and understand concepts clearly. These questions are structured exactly like real exam patterns, making this set ideal for daily practice and revision.

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Profit and Loss MCQs with Solutions and Short Tricks

  1. Type: CP and SP relation (Quantity based)

Q1. The Cost Price of 20 articles is the same as the Selling Price of x articles. If the profit is 25%, then the value of x is:

A) 15

B) 16

C) 18

D) 25

  • Step-by-Step Solution:

    1. Convert Profit to Ratio: Profit of 25% is equivalent to the fraction 1/4.

    2. Determine CP:SP: A profit of 1 on a CP of 4 means the SP must be 5. Ratio CP:SP is 4:5.

    3. Set up the Equation: The problem states 20 * CP = x * SP.

    4. Find the Ratio (x/20): Rearrange the equation: CP/SP = x/20.

    5. Equate and Solve: Set the ratios equal: x/20 = 4/5 -> x = (4 * 20) / 5 = 16.

  • Short Trick (Inverse Relationship):

    1. Use the formula: (Quantity Bought / Quantity Sold) = (100 + P%) / 100.

    2. Substitute values: 20/x = 125/100 = 5/4.

    3. Solve: x = 16.

  1. Type: Dishonest Dealer (False Weight)

Q2. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight. Find his gain percent.

A) 4%

B) 4.16%

C) 5%

D) 3.75%

  • Step-by-Step Solution:

    1. Identify the Error: The dealer cheats by 1000g – 960g = 40g.

    2. Identify the CP Base: Profit is calculated on the actual weight delivered (960g).

    3. Calculate Profit %: (Profit / CP Base) * 100 = (40 / 960) * 100.

    4. Calculate: 1/24 * 100 = 4.16%.

  • Short Trick (Formula):

    1. Formula: P% = [Error / (Delivered Weight)] * 100.

    2. Substitute values: P% = 40 / 960 * 100 = 4.16%.

  1. Type: Same SP, Equal Profit/Loss %

Q3. Two items were sold for 1 lakh each. One resulted in a 20% loss and the other a 20% profit. The entire transaction resulted in:

A) No loss, no gain

B) Gain of 1/24 lakh

C) Loss of 1/12 lakh

D) Loss of 1/18 lakh

  • Step-by-Step Solution:

    1. Find Net Loss % (Rule): When SP is same and Profit% = Loss%, there is always a net loss.

    2. Calculate Net Loss %: Loss % = (x^2) / 100 = (20^2) / 100 = 4%.

    3. Determine Total CP: A 4% loss means the Total SP (2 Lakhs) is 96% of Total CP. Total CP = 2 / 0.96.

    4. Calculate Loss Amount: Loss = Total CP – Total SP = (2 / 0.96) – 2 = 0.08 / 0.96.

    5. Simplify: 8 / 96 = 1/12 lakh.

  • Short Trick (Loss Amount Formula):

    1. Formula: Loss Value = (2 * SP * x^2) / (100^2 – x^2) (where x = 20, SP=1).

    2. Substitute values: Loss = (2 * 1 * 400) / (10000 – 400) = 800 / 9600 = 1/12.

  1. Type: Relation between MP, CP, Discount, and Profit

Q4. A tradesman marks his goods such that after a 15% discount, he makes a 20% profit. What is the Marked Price of an article whose Cost Price is 170?

A) 220

B) 200

C) 240

D) 260

  • Step-by-Step Solution (Basic Method):

    1. Calculate Selling Price (SP): Profit is 20% on CP. SP = 170 * 1.20 = 204.

    2. SP and MP Relation: SP (204) is the result of a 15% discount on MP. 204 = MP * (1 – 0.15).

    3. Solve for MP: MP = 204 / 0.85 = 240.

  • Short Trick (CP/MP Formula):

    1. Formula: CP/MP = (100 – Discount%) / (100 + Profit%).

    2. Substitute values: 170/MP = (100 – 15) / (100 + 20) = 85 / 120.

    3. Solve for MP: MP = 170 * (120/85) = 240.

  1. Type: Price Reduction & Extra Quantity

Q5. A reduction of 20% in the price of bananas enables a customer to purchase 6 more for 80 rupees. What is the reduced price per dozen?

A) 32

B) 35

C) 36

D) 40

  • Step-by-Step Solution:

    1. Calculate Savings: The 20% drop saves 20% of 80 = 16 rupees.

    2. Determine New Price: This saving (16 rupees) buys 6 extra bananas. Reduced price of 6 bananas is 16 rupees.

    3. Calculate Reduced Price per Dozen (12): 12 bananas = 2 * 16 = 32 rupees.

  • Short Trick (Direct Calculation):

    1. Formula: Reduced Price per unit = (Drop% * Total Amount) / (100 * Extra Quantity).

    2. Reduced Price per banana = (20 * 80) / (100 * 6) = 16/6 rupees.

    3. Reduced Price per Dozen = (16/6) * 12 = 32.

  1. Type: Goods sold in fractions (Weighted Average)

Q6. A man buys land for 3,60,000. He sells 1/3 at 20% loss and 2/5 at 25% gain. At what price must he sell the remaining so as to make an overall profit of 10%?

A) 1,00,000

B) 1,15,000

C) 1,20,000

D) 1,25,000

  • Step-by-Step Solution:

    1. Calculate Required Total Profit: 10% of 360k = 36,000.

    2. Calculate Loss/Gain so far:

      • Part 1 (120k): Loss 20% = -24,000.

      • Part 2 (144k): Profit 25% = +36,000.

      • Current Net Profit: +12,000.

    3. Required Profit on Remaining Part: Need 36,000 – 12,000 = 24,000 more.

    4. Calculate Remaining CP: 360k – 120k – 144k = 96,000.

    5. Calculate Required SP for Remaining Part: 96,000 + 24,000 = 1,20,000.

  • Short Trick (Percentage Calculation):

    1. Remaining part: 1 – 1/3 – 2/5 = 4/15.

    2. Formula: (1/3 * -20) + (2/5 * 25) + (4/15 * x) = 10 (Total Profit).

    3. Solve for x: -6.66 + 10 + 4/15 x = 10 -> x = 25%.

    4. SP of Remaining Part: 96,000 * 1.25 = 1,20,000.

  1. Type: Profit Calculated on Selling Price

Q7. If a man estimates his loss as 20% of the selling price, then his actual loss percent is:

A) 20%

B) 25%

C) 16.66%

D) 15%

  • Step-by-Step Solution (Assuming Values):

    1. Assume SP: Let SP = 100.

    2. Calculate Loss: Loss is 20% of SP, so Loss = 20.

    3. Calculate CP: CP = SP + Loss = 100 + 20 = 120.

    4. Calculate Actual Loss % (on CP): (Loss / CP) * 100 = (20 / 120) * 100.

    5. Simplify: 1/6 * 100 = 16.66%.

  • Short Trick (Fraction Conversion):

    1. Given Fraction: 20% = 1/5 (1 is Loss, 5 is SP).

    2. Actual CP Base: CP = 5 + 1 = 6.

    3. Actual Loss %: 1/6 * 100 = 16.66%.

  1. Type: Successive Discounts

Q8. A single discount equivalent to a discount series of 30%, 20%, and 10% is:

A) 50%

B) 49.6%

C) 50.4%

D) 51%

  • Step-by-Step Solution (Step-by-Step Discount):

    1. Assume MP: Let MP = 100.

    2. After 30% Discount: 100 * 0.70 = 70.

    3. After 20% Discount (on 70): 70 * 0.80 = 56.

    4. After 10% Discount (on 56): 56 * 0.90 = 50.4 (Final SP).

    5. Calculate Equivalent Discount: 100 – 50.4 = 49.6%.

  • Short Trick (A + B – AB/100):

    1. Combine 30% and 20%: 30 + 20 – (30 * 20 / 100) = 50 – 6 = 44%.

    2. Combine 44% and 10%: 44 + 10 – (44 * 10 / 100) = 54 – 4.4 = 49.6%.

  1. Type: Cross Quantity Price (Lemon Type)

Q9. A boy buys oranges at 9 for 16 rupees and sells them at 11 for 20 rupees. What is his gain or loss percent?

A) Gain 2.27%

B) Loss 2.27%

C) Gain 3.5%

D) Loss 3.5%

  • Step-by-Step Solution (Equating Quantity):

    1. Find LCM of Quantities (9 and 11): LCM is 99.

    2. Calculate CP of 99 items: 11 * 16 = 176.

    3. Calculate SP of 99 items: 9 * 20 = 180.

    4. Calculate Profit %: (Profit / CP) * 100 = (4 / 176) * 100.

    5. Simplify: 1/44 * 100 = 2.27%.

  • Short Trick (Cross Multiplication):

    1. CP is the cross-product that starts from the selling quantity: 11 * 16 = 176.

    2. SP is the cross-product that starts from the buying quantity: 9 * 20 = 180.

    3. Profit %: (180 – 176) / 176 * 100 = 2.27%.

  1. Type: Numerical Value of CP = Profit %

Q10. The selling price of an article is 144. If the percentage of profit is numerically equal to the cost price, then the cost price is:

A) 72

B) 80

C) 90

D) 100

  • Step-by-Step Solution (Using Equation):

    1. Define Variables: Let CP = x. Then Profit% = x.

    2. Formulate SP Equation: SP = x + (x * x/100) = 144.

    3. Quadratic Equation: x^2 + 100x – 14400 = 0.

    4. Solve: (x + 180)(x – 80) = 0. Since CP must be positive, x = 80.

  • Short Trick (Factor 10 Rule):

    1. Find two factors of SP (144) that have a difference of 10.

    2. Factors: 18 and 8.

    3. Multiply the smaller factor by 10: 8 * 10 = 80.

  1. Type: Variable Quantity, Fixed Amount

Q11. By selling 32 oranges for 1 rupee, a man loses 40%. How many for a rupee did he sell to earn 20%?

A) 16

B) 15

C) 20

D) 22

  • Step-by-Step Solution (Ratio of Percentage):

    1. Initial Condition: 1 Rupee is 60% of the CP (due to 40% loss).

    2. Target Condition: 1 Rupee must be 120% of the CP (to earn 20%).

    3. Ratio of Percentage: 120% / 60% = 2.

    4. Quantity Relationship (Inverse): If the price per unit doubles (to reach the target % from the initial %), the quantity sold for the same amount must be halved.

    5. New Quantity: 32 / 2 = 16.

  • Short Trick (Inverse Formula):

    1. Formula: N1 * (100 – R1) = N2 * (100 + R2).

    2. Substitute values: 32 * (100 – 40) = N2 * (100 + 20).

    3. 32 * 60 = N2 * 120.

    4. N2 = 16.

  1. Type: Buy X Get Y Free

Q12. A shopkeeper gives 3 items free on the purchase of 5 items. Find the discount percentage.

A) 33.33%

B) 60%

C) 37.5%

D) 40%

  • Step-by-Step Solution:

    1. Calculate Total Items: 5 (paid) + 3 (free) = 8 items.

    2. Determine Discount: The discount is equivalent to the cost of the 3 free items.

    3. Calculate Discount %: (Discount Items / Total Items) * 100 = (3 / 8) * 100.

    4. Calculate: 37.5%.

  • Short Trick (Direct Formula):

    1. Formula: Discount % = [Free / Total] * 100.

    2. Discount % = 3 / (5 + 3) * 100 = 37.5%.

  1. Type: Difference in SP changes Profit nature

Q13. An article was sold at a loss of 5%. If it were sold for 150 more, the seller would have gained 10%. The cost price of the article is:

A) 800

B) 1000

C) 1200

D) 1500

  • Step-by-Step Solution:

    1. Calculate Percentage Difference: The jump is from -5% to +10%. Total difference is 15%.

    2. Equate Value and Percentage: The 15% difference corresponds to 150 rupees.

    3. Solve for CP (100%): 15% = 150 -> 1% = 10 -> 100% = 1000.

  • Short Trick (Sum of Percentages):

    1. If the change crosses from Loss to Gain, add the percentages: 5% + 10% = 15%.

    2. 15% = 150 -> CP = 1000.

  1. Type: Markup and Discount on CP

Q14. The CP is 800. After allowing a discount of 10%, a gain of 12.5% was made. Then the marked price is:

A) 1000

B) 1100

C) 1200

D) 1300

  • Step-by-Step Solution (Basic Method):

    1. Calculate SP: Profit is 12.5% (or 1/8) of CP. SP = 800 + 100 = 900.

    2. SP and MP Relation: SP (900) is the result of a 10% discount on MP. 900 = MP * 0.90.

    3. Solve for MP: MP = 900 / 0.90 = 1000.

  • Short Trick (CP/MP Formula):

    1. Formula: CP/MP = (100 – Discount%) / (100 + Profit%).

    2. Substitute values: 800/MP = (100 – 10) / (100 + 12.5) = 90 / 112.5.

    3. Solve: MP = 800 * (112.5 / 90) = 1000.

  1. Type: Total P/L on unequal CP but same SP

Q15. Ranjit sells two items at 480 each. On one he gains 20% and on the other he loses 20%. What is the net profit or loss amount (in rupees)?

A) Loss of 40

B) Loss of 20

C) No profit No loss

D) Gain of 20

  • Step-by-Step Solution (Finding Individual CP):

    1. Item 1 (20% Gain): 480 = 120% of CP1 -> CP1 = 400.

    2. Item 2 (20% Loss): 480 = 80% of CP2 -> CP2 = 600.

    3. Total CP and SP: Total CP = 1000. Total SP = 960.

    4. Net Result: Loss = 1000 – 960 = 40.

  • Short Trick (Loss % based on Total SP):

    1. Net Loss % (Since SP is same): (x^2) / 100 = 4%.

    2. Total SP (960) is 96% of Total CP.

    3. Loss Amount (4%) = (4 / 96) * Total SP = (4 / 96) * 960 = 40.

  1. Type: Allegation in P/L

Q16. A man has 50 kg of rice. He sells a part at 10% profit and the rest at 5% loss. He gains 7% on the whole. What is the quantity sold at 10% gain?

A) 40kg

B) 30kg

C) 35kg

D) 25kg

  • Step-by-Step Solution (Using Allegation Rule):

    1. Set up Allegation: Profit Rate 1: +10%; Profit Rate 2: -5%; Mean Rate: +7%.

    2. Find the Ratio Difference: (7 – (-5)) : (10 – 7) = 12 : 3 or 4 : 1.

    3. Determine Quantity: The quantity sold at 10% gain (Q1) corresponds to the ‘4’ parts.

    4. Calculate Quantity: 4/5 * 50 kg = 40 kg.

  • Short Trick (Direct Equation):

    1. Let x be the quantity at 10% profit. 10x – 5(50 – x) = 7(50).

    2. 15x = 600 -> x = 40 kg.

  1. Type: Cheating while Buying and Selling (Weight)

Q17. A dealer cheats 20% in weight while buying as well as selling. Find his profit %.

A) 40%

B) 44%

C) 50%

D) 21%

  • Step-by-Step Solution (Based on 1000g reference):

    1. Profit from Buying: Receives 1200g (paid for 1000g).

    2. Loss from Selling: Delivers 800g (charged for 1000g).

    3. Total Gain: 1200g – 800g = 400g.

    4. Profit %: (Total Gain / Qty Sold) * 100 = (400 / 800) * 100 = 50%.

  • Short Trick (Multiplier):

    1. Total Profit Factor: (1200/1000) * (1000/800) = 1.5.

    2. Profit: (1.5 – 1) * 100 = 50%.

  1. Type: Chain Selling (A to B to C)

Q18. A sells a cycle to B at 10% profit. B sells to C at 20% profit. If C pays 264, what did A pay for it?

A) 200

B) 220

C) 225

D) 240

  • Step-by-Step Solution (Forward Calculation):

    1. Define A’s CP: Let A’s CP be A.

    2. Set up Equation: A * 1.10 * 1.20 = 264.

    3. Simplify: A * 1.32 = 264.

    4. Solve for A: A = 264 / 1.32 = 200.

  • Short Trick (Reverse Multiplier):

    1. Formula: A’s CP = C’s Price * (100 / 120) * (100 / 110).

    2. Calculate: 264 * (5/6) * (10/11) = 200.

  1. Type: Change in SP / CP variables

Q19. If the selling price is tripled and cost price is doubled, the profit would become 65%. What is the present profit %?

A) 10%

B) 15%

C) 20%

D) 25%

  • Step-by-Step Solution (Algebraic):

    1. Define Variables: Let CP = C and SP = S.

    2. New Condition: New CP = 2C. New SP = 3S. New Profit = 0.65 * 2C = 1.3C.

    3. Formulate Equation: New SP = New CP + New Profit -> 3S = 2C + 1.3C = 3.3C.

    4. Simplify: S = 1.1C.

    5. Original Profit %: (S – C) / C * 100 = (1.1C – C) / C * 100 = 0.1 * 100 = 10%.

  • Short Trick (Substitution/Testing Options):

    1. Test Option A (10%): Let CP = 100, then SP = 110.

    2. Calculate New P/L: New CP = 200. New SP = 330.

    3. New Profit %: (330 – 200) / 200 * 100 = 65%. (Matches).

  1. Type: Pure Ratio based P/L

Q20. The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.

A) 37.5%

B) 42.5%

C) 50%

D) 35%

  • Step-by-Step Solution:

    1. Assume MP: Let MP = 100.

    2. Determine CP: CP = 64% of 100 = 64.

    3. Determine SP: Discount is 12% on MP. SP = 100 – 12 = 88.

    4. Calculate Profit % (on CP): (Profit / CP) * 100 = (88 – 64) / 64 * 100.

    5. Simplify: 24 / 64 * 100 = 3/8 * 100 = 37.5%.

  • Short Trick (MP/CP Formula):

    1. Formula: MP * (100 – D%) = CP * (100 + P%).

    2. Substitute values: 100 * (100 – 12) = 64 * (100 + P).

    3. 8800 = 64 * (100 + P).

    4. 137.5 = 100 + P -> P = 37.5%.

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✔ Conclusion

These 20 Profit and Loss MCQs cover all major concepts like CP and SP relations, discount, mark price, successive profit and loss, cheating cases and weighted scenarios. Regular practice of such questions helps strengthen quantitative aptitude for SSC, Banking, CAT, CDS and all government exams.
For more chapters and MCQ series, continue with the next part Profit and Loss MCQs with Solutions and Short Tricks 21 to 40.

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FAQs – Profit and Loss Questions

1. What is the best way to learn Profit and Loss for competitive exams?

The fastest way is to understand CP, SP, profit percent and discount relations using short formulas. After learning concepts, solve MCQs with step-by-step solutions to build speed. Practice previous year questions for SSC, Banking and CAT to improve accuracy.

2. Why are Profit and Loss questions important in SSC and Banking exams?

Profit and Loss questions test percentage concepts, logical reasoning and basic arithmetic. These questions are asked frequently since they are easy to solve with the right shortcuts and help examiners judge calculation ability.

3. How many Profit and Loss questions come in SSC CGL and Banking exams?

In SSC CGL Tier 1, one to two questions commonly appear. In Banking exams like SBI PO and IBPS Clerk, one or two questions may appear as part of the arithmetic section or data interpretation sets.

4. What formulas should I memorize for Profit and Loss?

You should remember CP–SP–Profit relations, discount formula, successive profit and loss formula, false weight gain calculation and markup–discount relation. These formulas help solve questions faster during exams.

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