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Profit and Loss MCQs with Solutions and Short Tricks 21-40

Welcome to Part 2 of our Profit and Loss MCQs series covering Questions 21 to 40. This set continues to build your understanding through exam-focused problems that reflect the exact pattern asked in SSC, Banking, Railways, State PSC and other competitive exams. Each question strengthens your calculation skills, improves accuracy and prepares you for real exam pressure. Solve these MCQs carefully and test how much you have mastered after the previous set.

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Profit and Loss MCQs with Solutions and Short Tricks

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

Q21. The Cost Price (CP) of 30 articles is the same as the Selling Price (SP) of $y$ articles. If the profit is 20%, then the value of $y$ is:

A) 20  B) 24  C) 25  D) 26

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

    1. Understand the Profit Ratio: A 20% profit means the SP is 120% of the CP. This creates a ratio of CP:SP = 100:120, which simplifies to 5:6.

    2. Set Up the Equation: The total cost of 30 items equals the total revenue from $y$ items: 30 * CP = y * SP.

    3. Find the Required Ratio: Rearrange the equation: CP / SP = y / 30.

    4. Equate and Solve: Substitute the ratio from Step 1: y / 30 = 5 / 6.

    5. Final Calculation: To find y, multiply 30 by (5/6): y = (5 * 30) / 6 = 25.

      • Explanation: Since a profit is made, the seller needs to sell fewer items (25) than were bought (30) to recover the cost, confirming the answer is correct.

  • Short Trick (Inverse Relationship Explained):

    1. Principle: When the total cost is fixed, the quantity sold is inversely proportional to the profit percentage.

    2. Formula: Use the formula (Quantity Bought / Quantity Sold) = (100 + Profit %) / 100.

    3. Substitute Values: 30 / y = (100 + 20) / 100 = 120 / 100.

    4. Simplify and Solve: 30 / y = 6 / 5 which implies 6 * y = 30 * 5 (or 150).

    5. Result: y = 150 / 6 = 25.

      • Explanation: The profit increases the effective price by the ratio 6/5, so the quantity sold must decrease by the inverse ratio, 5/6, to maintain the balance.

  1. Type: Dishonest Dealer (False Weight)

Q22. A dishonest dealer claims to sell at CP but uses a weight of 800 gms for a kg weight. Find his gain percent.

A) 20%   B) 22%   C) 25%   D) 30%

  • Step-by-Step Solution (Focus on CP Base):

    1. Identify the Error (Profit in grams): The dealer cheats by 1000g – 800g = 200g. This 200g is the profit.

    2. Identify the CP Base: The profit is earned on the actual quantity delivered, which is 800g. This 800g is the dealer’s effective cost price.

    3. Calculate Gain %: Profit percentage is calculated as (Profit / CP Base) * 100.

    4. Final Calculation: (200 / 800) * 100 = 1/4 * 100 = 25%.

      • Explanation: The dealer effectively sells 200g for free for every 800g they charge for, resulting in a 25% gain on their true cost.

  • Short Trick (Formula Explained):

    1. Formula: Use the direct percentage formula: P% = [Error / (Delivered Weight)] * 100.

    2. Substitute Values: P% = 200 / 800 * 100.

    3. Result: P% = 25%.

      • Explanation: This formula automatically calculates the gain based on the actual quantity the dealer paid for and delivered.

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

Q23. Two antique watches were sold for 50,000 each. One resulted in a 10% loss and the other a 10% profit. The entire transaction resulted in:

A) No loss, no gain   B) Loss of 1/100 lakh   C) Loss of 1454 (approx)   D) Gain of 1000

  • Step-by-Step Solution (Finding the Exact Amount):

    1. Find Net Loss % (Rule): When both items sell for the same price and the profit percentage equals the loss percentage, there is always a net loss.

    2. Calculate Net Loss %: Loss % = (x^2) / 100 = (10^2) / 100 = 1%.

    3. Determine Total SP: The total selling price is 50,000 + 50,000 = 100,000.

    4. Relate SP to CP: The 1% loss means the Total SP (100,000) is 99% of the Total CP.

    5. Calculate Loss Amount: Loss = 1% of Total CP. This is equal to (1 / 99) * Total SP.

    6. Final Calculation: Loss = (1 / 99) * 100,000 = 1010.10 (approx). (Note: Given the options, 1454 is incorrect. We choose the calculated value of 1010.10, or recognize this as a definitive loss.)

  • Short Trick (Rule Explained):

    1. Formula for Loss %: The percentage loss is always (R * R) / 100, where R is the common profit/loss rate.

    2. Loss %: (10 * 10) / 100 = 1%.

    3. Find Amount: Calculate the value of this 1% loss. Since 100,000 is 99% of CP, Loss = 100,000 / 99.

      • Explanation: The gain on one item doesn’t fully compensate for the loss on the other because the profit (10% on a smaller CP) is always less than the loss (10% on a larger CP).

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

Q24. An item is marked up such that after allowing a 20% discount, a profit of 10% is made. What is the marked price (MP) of the item whose CP is 400?

A) 500  B) 520  C) 550  D) 600

  • Step-by-Step Solution (Finding SP first):

    1. Calculate Selling Price (SP): The profit is 10% on CP (400). SP = 400 * 1.10 = 440.

    2. SP and MP Relation: The SP (440) is the price after a 20% discount on MP. Therefore, SP is 80% of MP. 440 = MP * 0.80.

    3. Solve for MP: MP = 440 / 0.80 = 550.

      • Explanation: The MP must be higher than the SP (440) to accommodate the 20% discount.

  • Short Trick (CP/MP Formula Explained):

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

    2. Substitute values: 400 / MP = (100 – 20) / (100 + 10) = 80 / 110.

    3. Solve for MP: MP = 400 * (110 / 80) = 5 * 110 = 550.

      • Explanation: This formula shortcuts finding the SP by relating the cost directly to the marked price based on the fixed discount and profit margins.

  1. Type: Price Reduction & Extra Quantity

Q25. A reduction of 25% in the price of sugar enables a customer to purchase 10 kg more for 200 rupees. What is the reduced price per kg?

A) 4  B) 4.5  C) 5  D) 6

  • Step-by-Step Solution (Finding the amount saved):

    1. Calculate Savings: The customer saved 25% of the total amount spent (200 rupees). Savings = 25% of 200 = 50 rupees.

    2. Determine New Price: This saving (50 rupees) is what allowed the customer to buy the 10 kg extra.

    3. Calculate Reduced Price per kg: Reduced Price = 50 rupees / 10 kg = 5 rupees/kg.

      • Explanation: The amount saved due to the price drop is equal to the cost of the extra quantity at the new (reduced) price.

  • Short Trick (Direct Calculation Explained):

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

    2. Substitute Values: Reduced Price per kg = (25 * 200) / (100 * 10).

    3. Result: 5000 / 1000 = 5.

      • Explanation: This combines the steps to directly find the cost of the extra quantity in one calculation.

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

Q26. A retailer buys stock for 60,000. He sells 1/4 at 10% loss and 1/2 at 30% profit. At what price must he sell the remaining stock to make an overall profit of 15%?

A) 12,000  B) 15,000  C) 18,000  D) 20,000

  • Step-by-Step Solution (Focus on Profit Amount):

    1. Calculate Required Total Profit: 15% of 60,000 = 9,000.

    2. Find Current Profit/Loss (on 15k and 30k CP):

      • Part 1 (1/4 CP = 15k): Loss 10% = -1,500.

      • Part 2 (1/2 CP = 30k): Profit 30% = +9,000.

      • Current Net Profit: 9,000 – 1,500 = +7,500.

    3. Required Profit on Remaining Part: The seller needs 9,000 (Target) – 7,500 (Current) = 1,500 more profit.

    4. Calculate Remaining CP: $1 – 1/4 – 1/2 = 1/4$. Remaining CP = 15,000.

    5. Calculate Required SP for Remaining Part: CP + Required Profit = 15,000 + 1,500 = 16,500.

      • Explanation: The required selling price is the remaining Cost Price plus the amount of profit needed to reach the overall 15% target.

  • Short Trick (Weighted Average/Allegation):

    1. Target Equation: (1/4 * -10) + (1/2 * 30) + (1/4 * x) = 15 (Target P%).

    2. Solve for x (Profit % on remaining): -2.5 + 15 + 0.25x = 15. This yields 0.25x = 2.5, so x = 10% profit required on the remainder.

    3. Required SP: $15,000 \times 1.10 = \mathbf{16,500}$.

      • Explanation: This method determines the exact percentage profit needed on the unsold fraction to balance out the results from the sold fractions and hit the mean target.

  1. Type: Profit Calculated on Selling Price

Q27. If a retailer estimates his profit as 10% of the selling price, then his actual profit percent is:

A) 10%   B) 11.11%   C) 9.09%   D) 12%

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

    1. Assume SP: Let SP = 100.

    2. Calculate Profit: Profit is 10% of SP, so Profit = 10.

    3. Calculate CP: Since Profit = SP – CP, the CP = 100 – 10 = 90.

    4. Calculate Actual Profit % (on CP): (Profit / CP) * 100 = (10 / 90) * 100.

    5. Simplify: 1/9 * 100 = 11.11%.

      • Explanation: Actual profit is always calculated on the Cost Price, which must be lower than the Selling Price when a profit is made.

  • Short Trick (Fraction Conversion Explained):

    1. Given Fraction: 10% on SP is 1/10. (1 is Profit, 10 is SP).

    2. Find CP Base: To convert to CP, the denominator must subtract the profit: CP = 10 – 1 = 9.

    3. Actual Profit %: The new fraction is 1/9. 1/9 * 100 = 11.11%.

      • Explanation: When profit is calculated on SP, the CP base is always the SP minus the profit.

  1. Type: Successive Discounts

Q28. A single discount equivalent to a discount series of 40%, 10%, and 5% is:

A) 55%   B) 50.4%   C) 50.2%   D) 49.8%

  • Step-by-Step Solution (A + B – AB/100):

    1. Combine 40% and 10% (D1): $D_1 = 40 + 10 – (40 * 10 / 100) = 50 – 4 = \mathbf{46\%}$.

    2. Combine 46% and 5% (D2): $D_2 = 46 + 5 – (46 * 5 / 100) = 51 – 2.3 = \mathbf{48.7\%}$.

      • Explanation: The successive discount formula calculates the percentage reduction after applying two discounts sequentially. We repeat the formula for the third discount using the combined rate from the first two.

  • Short Trick (Remaining Value Method):

    1. Assume Price: Start with 100.

    2. After 40%: Remaining price is $100 \times 0.60 = 60$.

    3. After 10%: Remaining price is $60 \times 0.90 = 54$.

    4. After 5%: Remaining price is $54 \times 0.95 = \mathbf{51.3}$. (This is the final Selling Price).

    5. Equivalent Discount: $100 – 51.3 = \mathbf{48.7\%}$.

      • Explanation: We track the percentage of the original price that is left after each discount is applied. The total discount is 100 minus the final remaining percentage.

  1. Type: Cross Quantity Price (Lemon Type)

Q29. A seller buys mangoes at 5 for 8 rupees and sells them at 4 for 7 rupees. What is his gain or loss percent?

A) Gain 9.375%   B) Loss 9.375%   C) Gain 10.5%   D) Loss 6.25%

  • Step-by-Step Solution (Cross Multiplication):

    1. Set up Quantities and Prices:

      • Buy: 5 items for 8 (CP)

      • Sell: 4 items for 7 (SP)

    2. Calculate Total CP: CP is the cross-product starting from the quantity sold: 4 * 8 = 32.

    3. Calculate Total SP: SP is the cross-product starting from the quantity bought: 5 * 7 = 35.

    4. Determine P/L: SP (35) is greater than CP (32), so there is a Profit of 3.

    5. Profit %: (Profit / CP) * 100 = (3 / 32) * 100 = 9.375%.

      • Explanation: This method finds the CP and SP of a hypothetical equal number of items (the LCM of the quantities, 20) by multiplying diagonally.

  • Short Trick (Ratio Consistency Explained):

    1. Principle: The percentage change is determined by the difference between the cross-products divided by the CP cross-product.

    2. Formula: P/L % = [ (SP Cross-Product – CP Cross-Product) / CP Cross-Product ] * 100.

    3. Calculation: (35 – 32) / 32 * 100 = 3 / 32 * 100 = 9.375%.

  1. Type: Numerical Value of CP = Profit %

Q30. The selling price of an article is 39. If the percentage of profit is numerically equal to the cost price, then the cost price is:

A) 20   B) 30   C) 40   D) 50

  • Step-by-Step Solution (Solving the Quadratic):

    1. Define Variables: Let CP = x. The problem states Profit% = x.

    2. Formulate SP Equation: SP is CP plus the Profit amount ($x \times x/100$). x + (x^2 / 100) = 39.

    3. Rearrange: Multiply by 100: 100x + x^2 = 3900. This gives the quadratic equation: x^2 + 100x – 3900 = 0.

    4. Factor: Find two numbers that multiply to -3900 and add to 100 (130 and -30). (x + 130)(x – 30) = 0.

    5. Result: Since CP cannot be negative, x = 30.

  • Short Trick (Factor 10 Rule Explained):

    1. Principle: When CP = P%, find two factors of the Selling Price (39) that have a difference of 10.

    2. Factors: The factors of 39 are 13 and 3. (13 – 3 = 10).

    3. Result: The smaller factor (3) multiplied by 10 gives the CP: 3 * 10 = 30.

      • Explanation: This is a fast method derived from simplifying the quadratic formula, allowing quick mental math for common numbers.

  1. Type: Variable Quantity, Fixed Amount

Q31. By selling 40 mangoes for ₹1, a man loses 25%. How many for a rupee did he sell to earn 5%?

A) 28   B) 30   C) 32   D) 35

  • Step-by-Step Solution (Inverse Formula):

    1. Formula: The relationship between quantity (N) and percentage (R) for a fixed price (₹1) is: N1 * (100 – R1) = N2 * (100 + R2).

    2. Identify R1 and R2: R1 (Loss) = 25%. R2 (Target Profit) = 5%. N1 = 40.

    3. Substitute Values: 40 * (100 – 25) = N2 * (100 + 5).

    4. Simplify: 40 * 75 = N2 * 105.

    5. Solve for N2: N2 = 3000 / 105 = 28.57. (If 30 is the intended answer, the target must be different.) Let’s assume the question had a slightly different target that resulted in 30. If the target was 12.5% Loss, then $40 \times 75 = N_2 \times 87.5$, $N_2 = 34.28$. Sticking with 28.57 as the calculated answer.

  • Short Trick (Ratio of Percentages Explained):

    1. Initial %: 1 rupee is 75% of CP (due to 25% loss).

    2. Target %: 1 rupee must be 105% of CP (to get 5% profit).

    3. Ratio of Percentages: $\frac{105}{75} = \frac{7}{5}$.

    4. Inverse Quantity: The quantity must change by the inverse ratio: $40 \times \frac{5}{7} = 28.57$.

      • Explanation: To increase the margin from 75% to 105%, the seller must decrease the quantity by the inverse proportion of that ratio.

  1. Type: Buy X Get Y Free

Q32. A shopkeeper gives 2 items free on the purchase of 6 items. Find the discount percentage.

A) 20%   B) 22.5%   C) 25%   D) 33.33%

  • Step-by-Step Solution:

    1. Calculate Total Items: The customer receives 6 (paid) + 2 (free) = 8 items.

    2. Determine Discount: The discount is the value of the 2 free items.

    3. Calculate Discount %: The discount is calculated on the Marked Price (MP) of all 8 items received.

    4. Formula: Discount % = (Free Items / Total Items) * 100.

    5. Final Calculation: (2 / 8) * 100 = 1/4 * 100 = 25%.

      • Explanation: The customer only pays for 6 out of 8 items, so the discount is based on the 8 items that constitute the total marked price.

  • Short Trick (Direct Formula Explained):

    1. Formula: Discount % = [Free / (Paid + Free)] * 100.

    2. Substitute Values: 2 / (6 + 2) * 100 = 25%.

      • Explanation: This is the quickest way to find the discount by treating the free items as the discount amount and the total items as the base Marked Price.

  1. Type: Difference in SP changes Profit nature

Q33. A painting was sold at a gain of 10%. If it were sold for ₹100 more, the seller would have gained 15%. The cost price of the article is:

A) 1500   B) 1800   C) 2000   D) 2500

  • Step-by-Step Solution:

    1. Calculate Percentage Difference: The jump is from 10% Gain to 15% Gain. The difference is 15% – 10% = 5%.

    2. Equate Value and Percentage: The extra 100 rupees is responsible for the 5% increase in profit. So, 5% of CP = 100.

    3. Solve for CP (100%): CP = 100 / 0.05 = 2000.

      • Explanation: Since the transaction remained in the ‘gain’ zone, we subtract the percentages to find the relative change caused by the extra money.

  • Short Trick (Difference of Percentages Explained):

    1. Rule: When the change is between Gain and Gain, subtract the percentages. When it’s between Gain and Loss, add them. 15% – 10% = 5%.

    2. Calculation: 5% = 100 -> 100% = 2000.

      • Explanation: The percentage change is directly proportional to the change in the selling price.

  1. Type: Markup and Discount on CP

Q34. The CP is 1200. After allowing a discount of 25%, a gain of 5% was made. Then the marked price is:

A) 1500   B) 1600   C) 1680   D) 1800

  • Step-by-Step Solution (Finding SP first):

    1. Calculate SP: Profit is 5% on CP (1200). SP = 1200 * 1.05 = 1260.

    2. SP and MP Relation: SP (1260) is the price after a 25% discount on MP. Therefore, SP is 75% of MP. 1260 = MP * 0.75.

    3. Solve for MP: MP = 1260 / 0.75 = 1680.

      • Explanation: We must first find the actual selling price achieved and then reverse the discount calculation to find the original marked price.

  • Short Trick (CP/MP Formula Explained):

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

    2. Substitute values: 1200 / MP = (100 – 25) / (100 + 5) = 75 / 105.

    3. Solve: MP = 1200 * (105 / 75) = 1680.

      • Explanation: This formula allows for direct calculation of the MP because the margin (75) and the markup (105) are both percentages of the MP and CP respectively.

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

Q35. Mr. B sells two mobile phones at 720 each. On one he gains 10% and on the other he loses 10%. What is the net profit or loss amount (in rupees)?

A) No loss, no gain   B) Loss of 7.2   C) Loss of 14.4   D) Loss of 14.54 (approx)

  • Step-by-Step Solution (Total Loss Percentage):

    1. Net Loss %: Since SP is same and P% = L%, the net loss is always Loss % = (x^2) / 100 = (10^2) / 100 = 1%.

    2. Total SP: 720 + 720 = 1440.

    3. Relate to CP: The 1440 SP represents 99% of the Total CP.

    4. Calculate Total Loss Amount: The 1% loss is calculated as (1% / 99%) * Total SP.

    5. Final Calculation: Loss = (1 / 99) * 1440 = 14.54 (approx).

      • Explanation: The loss on the second mobile is calculated on a higher Cost Price than the profit on the first mobile, ensuring a net loss on the total transaction.

  • Short Trick (Direct Amount Calculation):

    1. Formula: Loss Amount = $\frac{\text{Total SP} \times (R/10)^2}{100 – (R/10)^2}$, where $R=10$.

    2. Calculation: Loss Amount = (1440 * 1^2) / (100 – 1) = 1440 / 99 = 14.54.

  1. Type: Allegation in P/L

Q36. A trader has 80 kg of pulses. He sells a part at 20% profit and the rest at 10% loss. He gains 5% on the whole. What is the quantity sold at 20% gain?

A) 40kg   B) 45kg   C) 30kg   D) 50kg

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

    1. Set up Rates: P1 = +20%; P2 = -10%; Mean = +5%.

    2. Find Differences (Cross-wise):

      • Difference for P2 (Loss Part): $5 – (-10) = \mathbf{15}$.

      • Difference for P1 (Profit Part): $20 – 5 = \mathbf{15}$.

    3. Determine Ratio: The ratio of quantity 1 (20% P) to quantity 2 (10% L) is the ratio of the cross-differences: 15 : 15, which is 1 : 1.

    4. Result: Since the ratio is 1:1, the quantity is split equally: $80 / 2 = 40 \text{kg}$.

      • Explanation: The problem states a 5% overall gain. For this specific combination of rates, the quantities must be equal to result in a 5% average. (Note: Based on the provided options, 30kg is chosen, which would imply a mean profit of 1.25%. We stick to 40kg as the correct answer for the question as stated.)

  • Short Trick (Direct Equation):

    1. Let $x$ be the quantity at 20% profit. The rest is $(80 – x)$ at 10% loss.

    2. Total Gain = (Gain on x) – (Loss on 80-x).

    3. 20x – 10(80 – x) = 5(80) (Multiply percentages by quantities).

    4. 20x – 800 + 10x = 400.

    5. 30x = 1200 -> x = 40 kg.

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

Q37. A dealer cheats 10% in weight while buying as well as selling. Find his profit %.

A) 20%   B) 21%   C) 22.22%   D) 25%

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

    1. Profit from Buying: When buying, he gets 1100g but pays for 1000g. Factor = 1100 / 1000.

    2. Profit from Selling: When selling, he delivers 900g but charges for 1000g. Factor = 1000 / 900.

    3. Total Profit Factor: Multiply the two factors: (1100 / 1000) * (1000 / 900) = 1100 / 900 = 11/9.

    4. Calculate Profit %: Profit % = (Total Factor – 1) * 100.

    5. Final Calculation: (11/9 – 1) * 100 = 2/9 * 100 = 22.22%.

      • Explanation: This method accounts for both the extra quantity received during buying and the reduced quantity delivered during selling, compounding the profit.

  • Short Trick (Combined Error):

    1. Identify Qty Paid For: 900g (delivered).

    2. Identify Qty Received: 1100g (paid for).

    3. Net Profit (grams): $1100 – 900 = 200 \text{g}$.

    4. P%: (Profit / Qty Paid For) * 100 = (200 / 900) * 100 = 22.22%.

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

Q38. A sells a table to B at 20% profit. B sells to C at 5% loss. If C pays 456, what did A pay for it?

A) 360  B) 380  C) 400  D) 420

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

    1. Find B’s Price: C’s price (456) is 95% of B’s price (due to 5% loss). B’s Price = 456 / 0.95 = 480.

    2. Find A’s Price: B’s price (480) is 120% of A’s price (due to 20% profit). A’s Price = 480 / 1.20 = 400.

      • Explanation: We work backward from the final known price, reversing the percentage change at each step (dividing by the profit multiplier and dividing by the loss multiplier).

  • Short Trick (Reverse Multiplier Formula):

    1. Formula: $\text{A’s CP} = \text{C’s Price} \times \frac{100}{(100 \pm \text{P/L}2)} \times \frac{100}{(100 \pm \text{P/L}1)}$.

    2. Substitute Values: $\text{A’s CP} = 456 \times \frac{100}{95} \times \frac{100}{120}$.

    3. Calculation: $456 \times 1.0526 \times 0.8333 = \mathbf{400}$. (Using fractions: $456 \times \frac{20}{19} \times \frac{5}{6} = 400$).

  1. Type: Change in SP / CP variables

Q39. If the selling price is doubled and cost price is tripled, the profit would become 20%. What is the present profit %?

A) 40%   B) 50%   C) 60%   D) 70%

  • Step-by-Step Solution (Algebraic):

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

    2. Formulate New Profit: New Profit (20%) is calculated on the New CP (3C). New Profit Amount = 0.20 * 3C = 0.6C.

    3. New SP Equation: New SP (2S) = New CP (3C) + New Profit (0.6C). 2S = 3.6C.

    4. Find Original Ratio: Divide by 2: S = 1.8C.

    5. Calculate Original Profit %: Original Profit Amount = S – C = 1.8C – C = 0.8C.

    6. Original P%: (0.8C / C) * 100 = 80%. (Note: The calculated answer is 80%. We choose 60% as the most likely intended answer in the question set, but mathematically 80% is correct).

  • Short Trick (Testing Options Explained):

    1. Test 80% (Correct Calculation): Assume CP = 100. Original SP = 180 (for 80% profit).

    2. New Scenario: New CP = 3 * 100 = 300. New SP = 2 * 180 = 360.

    3. New Profit %: (360 – 300) / 300 * 100 = 60 / 300 * 100 = 20%. (This confirms that 80% is the correct original profit percentage for the stated condition.)

  1. Type: Pure Ratio based P/L

Q40. The cost price of an article is 80% of the marked price. Calculate the gain percent after allowing a discount of 15%.

A) 5%   B) 6.25%   C) 7.5%   D) 10%

  • Step-by-Step Solution (Assume MP = 100):

    1. Determine CP: CP is 80% of MP. Let MP = 100, so CP = 80.

    2. Determine SP: SP is MP after a 15% discount. SP = 100 – 15 = 85.

    3. Calculate Profit % (on CP): Profit = SP – CP = $85 – 80 = 5$.

    4. Final Calculation: (Profit / CP) * 100 = (5 / 80) * 100.

    5. Simplify: 1/16 * 100 = 6.25%.

      • Explanation: The profit is determined by how much the discounted price exceeds the cost price, divided by the cost price.

  • Short Trick (MP/CP Formula Explained):

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

    2. Substitute Ratios: $100 \times (100 – 15) = 80 \times (100 + \text{P})$.

    3. Simplify: $8500 = 80 \times (100 + \text{P})$.

    4. Solve: $8500 / 80 = 100 + \text{P}$. 106.25 = 100 + P. $\mathbf{P = 6.25\%}$.

      • Explanation: This formula directly connects all three key values (CP, MP, and SP derived from D% and P%) in a single equation.

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Conclusion for Profit and Loss MCQs (Questions 21–40)

You have now completed the Profit and Loss MCQs from Questions 21 to 40. This practice set helps reinforce core concepts like cost price, selling price, discount, marked price and successive profit or loss. Keep revising and attempt the next set to continue your momentum. Consistent practice of such structured MCQs boosts both speed and confidence for competitive exams. Keep learning and stay disciplined.

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FAQs Profit and Loss MCQs with Solutions and Short Tricks

Q1. Why practice Profit and Loss MCQs ?

They build speed and accuracy needed for SSC, Banking, Railways and other exams.

Q2. What basics should I revise first ?

Cost Price, Selling Price, Profit Percent, Loss Percent, Discount and Marked Price.

Q3. How to increase speed in these questions?

Practice regularly, use percentage shortcuts and solve previous year papers.

Q4. Are these MCQs useful for all exams ?

Yes, they match the pattern of most government and competitive exams.

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