Question 1

True discount over double time: If the true discount on a bill of $110 due at the end of some time is $10, what is the true discount on the same amount due at the end of double that time (same rate, simple interest)?

Accepted Answer

Introduction / Context: True discount (TD) on a sum A for time fraction R = r * t (simple) is TD = A * R / (1 + R). Knowing TD for one time lets you solve for R, then compute TD at double time 2R. This avoids needing the actual rate r or time t separately. Given Data / Assumptions: A = $110 (face value). TD at time t is $10. Simple interest setting; same rate for double time. Concept / Approach: Let R = r * t. From TD = A * R / (1 + R) = 10, solve for R. Then for double time, use 2R in the same formula: TD(2t) = A * (2R) / (1 + 2R). Step-by-Step Solution: 10 = 110 * R / (1 + R) ⇒ 1/11 = R / (1 + R) ⇒ 1 + R = 11R ⇒ R = 0.1.Double time ⇒ 2R = 0.2.TD(2t) = 110 * 0.2 / (1 + 0.2) = 22 / 1.2 = $18.333… ≈ $18.33. Verification / Alternative check: Present worth at time t: PW = A − TD = 110 − 10 = 100; consistent with R = 0.1. At double time, TD drops below $22 due to the denominator (1 + 2R), giving ≈ $18.33. Why Other Options Are Wrong: $20 or $22 assume linear scaling; true discount is not linear with time. $21.81, $24.20 do not match the exact formula. Common Pitfalls: Treating TD like simple interest (proportional to time) instead of applying the TD formula with denominator 1 + R. Final Answer: $ 18.33

Question 2

Comparing single vs successive discounts: On a marked price, the difference between selling prices under a flat 30% discount and under two successive discounts of 20% and 10% is ₹72. Find the marked price.

Accepted Answer

Introduction / Context: Successive discounts multiply, not add. A flat 30% reduces price to 70% of MRP, whereas 20% followed by 10% reduces to 0.8 * 0.9 = 72% of MRP. Their difference times MRP equals the given rupee gap, allowing quick back-calculation of the MRP. Given Data / Assumptions: Single discount: 30% ⇒ SP1 = 0.70 * M. Successive discounts: 20% then 10% ⇒ SP2 = 0.8 * 0.9 * M = 0.72 * M. SP2 − SP1 = ₹72. Concept / Approach: Compute the difference factor: 0.72M − 0.70M = 0.02M. Set 0.02M = 72 and solve for M. This avoids any cost price involvement since only selling prices from M are compared. Step-by-Step Solution: 0.02M = 72 ⇒ M = 72 / 0.02 = ₹3600. Verification / Alternative check: SP1 = 0.70 * 3600 = ₹2520; SP2 = 0.72 * 3600 = ₹2592; difference = ₹72, as required. Why Other Options Are Wrong: ₹3000, ₹2500, ₹2400, ₹2800 do not produce a ₹72 gap under the specified discount schemes. Common Pitfalls: Adding discounts (20% + 10% = 30%) incorrectly; successive discounts multiply and are not simply additive. Final Answer: ₹ 3600

Question 3

Printed price vs cost price ratio: A book is sold at a 10% discount on its printed (marked) price, yet the shopkeeper earns a profit of 12% on cost. Find the ratio of the cost price to the printed price.

Accepted Answer

Introduction / Context: Relating cost, marked, and selling prices requires mapping discounts and profits as multiplicative factors. Here, discount is on the printed price, while profit is relative to cost. Express both with symbols and eliminate the selling price to directly get the ratio of cost to printed price. Given Data / Assumptions: Printed price = P. Discount = 10% ⇒ Selling price S = 0.9P. Profit = 12% on cost ⇒ S = 1.12C. Concept / Approach: Set 0.9P = 1.12C. Rearranging yields C : P = 0.9 : 1.12. Reduce the fraction to a clean ratio by multiplying numerator and denominator by 100 and then simplifying. Step-by-Step Solution: 0.9P = 1.12C ⇒ C/P = 0.9/1.12 = 90/112 = 45/56. Verification / Alternative check: If P = 56 units, S = 0.9 * 56 = 50.4; with C = 45, profit% = (50.4 − 45)/45 = 12%, consistent. Why Other Options Are Wrong: 8:11, 47:56, 3:4, 9:11 do not satisfy both the 10% discount and the 12% profit simultaneously. Common Pitfalls: Taking profit on printed price or discount on cost price; always apply each percentage to its proper base. Final Answer: 45 : 56

Question 4

Back-solving cost from marked price and outcome: An article is marked ₹50 and sold with a 20% discount. If the seller’s profit is 25%, find the cost price.

Accepted Answer

Introduction / Context: This is a one-step back calculation. The marked price gives the selling price after discount; comparing that selling price to an assumed cost with the target profit leads directly to the cost price. Keep track of which percentage applies to which base quantity. Given Data / Assumptions: Marked price M = ₹50. Discount = 20% ⇒ Selling price S = 0.8 * 50 = ₹40. Profit = 25% on cost ⇒ S = 1.25 * C. Concept / Approach: With S known, divide by 1.25 to recover cost. This is simply reversing a percentage increase from cost to selling price. Step-by-Step Solution: S = ₹40.C = S / 1.25 = 40 / 1.25 = ₹32. Verification / Alternative check: Selling at ₹40 on a cost of ₹32 gives profit = 8, i.e., 8/32 = 25%, matching the condition. Why Other Options Are Wrong: ₹40, ₹35, ₹30, ₹28 do not yield a 25% profit when the selling price is ₹40. Common Pitfalls: Applying the 25% to the marked price instead of the cost; or miscomputing the discounted selling price. Final Answer: ₹ 32

Question 5

Cash sale after discount on marked-up goods: A seller marks goods 30% above cost and allows a 15% cash discount. What is his percentage profit on a cash sale?

Accepted Answer

Introduction / Context: Profit under successive mark-up and discount is multiplicative in factors: mark up by 30% (factor 1.30), then discount by 15% (factor 0.85). The net selling price relative to cost gives the overall profit percentage for the cash transaction. Given Data / Assumptions: Cost = C. Marked price M = 1.30C. Cash discount = 15% ⇒ Selling price S = 0.85M. Concept / Approach: Combine the multiplicative factors: S = 0.85 * 1.30 * C = 1.105C. Profit% = (S − C)/C * 100 = (1.105 − 1) * 100. Step-by-Step Solution: S = 0.85 * 1.30 * C = 1.105C.Profit% = 0.105 * 100 = 10.5%. Verification / Alternative check: With C = 100, M = 130, cash S = 110.5, profit = 10.5, i.e., 10.5%. Why Other Options Are Wrong: 15% ignores the discount; 9% or 8.5% understate the net factor; 12% overstates it. Common Pitfalls: Adding or subtracting percentages arithmetically; always multiply factors for successive mark-ups/discounts. Final Answer: 10.5%

Question 6

Marked price vs cost when sale at 3/4th MRP gives 25% gain: By selling an article at three-quarters of its marked price, a trader gains 25%. What is the ratio of the marked price to the cost price?

Accepted Answer

Introduction / Context: Relate selling price to both MRP and cost via given fractions and gain. With sale at 3/4 of marked price and a 25% profit on cost, equate these two expressions for the same selling price to connect M and C directly as a ratio. Given Data / Assumptions: Marked price = M. Selling price S = (3/4)M. Profit = 25% ⇒ S = 1.25C. Concept / Approach: Set (3/4)M = 1.25C ⇒ M/C = (1.25)/(0.75) = (5/4)/(3/4) = 5/3. Express as a clean ratio M : C = 5 : 3. Step-by-Step Solution: (3/4)M = 1.25C.M/C = 1.25 / 0.75 = 5/3.Therefore M : C = 5 : 3. Verification / Alternative check: Let C = 3, then M = 5, S = (3/4)*5 = 3.75; profit = 0.75 = 25% of 3. Why Other Options Are Wrong: 3:5, 3:4, 4:3, 6:5 contradict the relationship (3/4)M = 1.25C. Common Pitfalls: Mixing which percentage applies to M or to C; remember profit is on cost, discount is on marked price. Final Answer: 5 : 3

Question 7

From discount and loss to profit at MRP: A businessman sells at a 40% discount on MRP and incurs a 30% loss. If instead he sells at MRP (no discount), what will his profit percentage?

Accepted Answer

Introduction / Context: This problem links discounting and loss to infer the ratio of MRP to cost. Once that ratio is known, we can compute the profit if sold at MRP without any discount. It is a neat algebraic manipulation of multiplicative price factors. Given Data / Assumptions: With 40% discount: SP = 0.6M. This SP yields a 30% loss: SP = 0.7C. M is marked price, C is cost price. Concept / Approach: Equate 0.6M = 0.7C ⇒ M/C = 7/6. Selling at M implies SP = M. Profit% at M equals [(M − C)/C] * 100 = [(M/C) − 1] * 100. Step-by-Step Solution: From 0.6M = 0.7C, M/C = 7/6.Profit at MRP = (7/6 − 1) * 100 = (1/6) * 100 = 16 2/3%. Verification / Alternative check: Let C = 6, then M = 7. Discounted SP = 0.6 * 7 = 4.2; loss% = (6 − 4.2)/6 = 30%. At M, profit% = (7 − 6)/6 = 16 2/3%. Why Other Options Are Wrong: 10%, 20%, 16 1/3%, 25% are not consistent with M/C = 7/6. Common Pitfalls: Treating 40% discount and 30% loss as directly additive/subtractive; always convert to factors and solve. Final Answer: 16 2/3%

Question 8

Bringing the net price down with an extra discount: An article is listed at ₹1500. After a first discount of 20%, what additional single discount should be offered to bring the net price to ₹1104?

Accepted Answer

Introduction / Context: Successive discounts multiply. Apply the first discount to get the intermediate price, then solve for the single second discount that lands the net amount at the target. This is a direct reverse-percentage application on the already discounted price, not on the original MRP. Given Data / Assumptions: MRP M = ₹1500. First discount = 20% ⇒ price after first = 0.8M = ₹1200. Target net price = ₹1104. Concept / Approach: Let x be the additional discount rate on ₹1200. Then 1200 * (1 − x) = 1104. Solve for x and express as a percentage. Step-by-Step Solution: 1200 * (1 − x) = 1104 ⇒ 1 − x = 1104 / 1200 = 0.92.x = 0.08 = 8%. Verification / Alternative check: Net factor from MRP: 0.8 * 0.92 = 0.736; 1500 * 0.736 = ₹1104, confirming. Why Other Options Are Wrong: 10%, 12%, 15%, 6% do not reduce ₹1200 to ₹1104 exactly. Common Pitfalls: Applying the second discount to the original MRP instead of the already discounted base of ₹1200. Final Answer: 8 %

Question 9

Marked price from target profit after a given discount: An article costs ₹800. After allowing a 10% discount on the marked price, a gain of 12.5% is made. Find the marked price.

Accepted Answer

Introduction / Context: This is a forward price-setting problem. Starting from cost, impose the desired profit to get the required selling price. Then reverse the known discount to back out the marked price that will produce that selling price when discounted by the stated percentage. Given Data / Assumptions: Cost C = ₹800. Desired profit = 12.5% ⇒ Target SP = 1.125 * 800 = ₹900. Discount on marked price = 10% ⇒ SP = 0.9 * M. Concept / Approach: Since SP = 0.9M and SP must equal ₹900, solve for M = SP / 0.9. This ensures that, after discount, the realized SP corresponds to the target profit. Step-by-Step Solution: Target SP = 1.125 * 800 = ₹900.0.9M = 900 ⇒ M = 900 / 0.9 = ₹1000. Verification / Alternative check: With M = ₹1000, discount 10% ⇒ SP = ₹900; profit = ₹100 on ₹800 = 12.5%. Why Other Options Are Wrong: ₹1100, ₹1200, ₹1300, ₹900 do not map to a 12.5% profit after a 10% discount. Common Pitfalls: Applying discount to cost or applying profit to marked price. Keep the bases distinct. Final Answer: ₹ 1000

Question 10

Profit without discount vs with discount: The marked price of a radio is ₹480. With a 10% discount, the shopkeeper still gains 8%. If no discount were given, what would the profit percentage be?

Accepted Answer

Introduction / Context: First recover the cost price from the discounted sale that yields an 8% gain. Then compare the full MRP to that cost to compute the hypothetical profit with no discount. This keeps percentage bases consistent and avoids shortcuts that misapply percentages. Given Data / Assumptions: MRP M = ₹480. Discount = 10% ⇒ SP(discounted) = 0.9M = ₹432. Gain at discounted sale = 8% ⇒ C = 432 / 1.08. Concept / Approach: Compute cost from the actual sale, then compute profit% for a sale at M: Profit% = [(M − C)/C] * 100. Step-by-Step Solution: C = 432 / 1.08 = ₹400.No-discount sale → SP = M = ₹480.Profit% = (480 − 400)/400 * 100 = 80/400 * 100 = 20%. Verification / Alternative check: At discount: profit = 432 − 400 = 32 ⇒ 32/400 = 8%. At MRP: 80/400 = 20%, as found. Why Other Options Are Wrong: 18%, 18.5%, 20.5%, 22% do not match the exact computation with the verified cost. Common Pitfalls: Using 8% directly on the MRP or assuming linearity between discount and profit without referencing cost. Final Answer: 20 %

Question 11

Finding the second of two successive discounts: A TV with MRP ₹16000 is sold for ₹11400 after two successive discounts. If the first discount is 5%, find the rate of the second discount.

Accepted Answer

Introduction / Context: Successive discounts are multiplicative. Apply the first discount to get the intermediate price, then compute the second discount needed to reduce the intermediate price to the final selling price. Always apply the second discount to the already reduced base, not to the original MRP. Given Data / Assumptions: MRP M = ₹16000. First discount = 5% ⇒ Price after first = 0.95M = ₹15200. Final selling price S = ₹11400. Concept / Approach: Let y be the second discount rate. Then 15200 * (1 − y) = 11400. Solve for y and convert to a percentage. Step-by-Step Solution: 1 − y = 11400 / 15200 = 0.75.y = 0.25 = 25%. Verification / Alternative check: Net factor = 0.95 * 0.75 = 0.7125; 16000 * 0.7125 = ₹11400, consistent. Why Other Options Are Wrong: 15%, 20%, 30%, 10% do not bring ₹15200 down to ₹11400. Common Pitfalls: Subtracting percentages directly or applying the second discount to the original MRP rather than to the intermediate price. Final Answer: 25 %

Question 12

Listing above cost and allowing a cash discount: A trader lists articles 20% above cost and allows a discount of 10% at sale. What is his overall gain percentage?

Accepted Answer

Introduction / Context: Mark-up followed by discount produces a net selling price that is the product of the two factors. Compare this net selling price with cost to find the profit percentage. This is a staple computation for successive mark-ups/downs. Given Data / Assumptions: Cost = C. List price M = 1.20C. Discount = 10% ⇒ S = 0.90M. Concept / Approach: Net selling price S = 0.90 * 1.20 * C = 1.08C. Gain% = (S − C)/C * 100 = (1.08 − 1) * 100 = 8%. Step-by-Step Solution: S = 1.20C * 0.90 = 1.08C.Gain% = 0.08 * 100 = 8%. Verification / Alternative check: Assume C = 100 → M = 120 → S = 108 → profit = 8, i.e., 8%. Why Other Options Are Wrong: 5%, 6%, 10%, 12% do not match the exact factor product 1.08. Common Pitfalls: Adding 20% − 10% = 10% incorrectly; successive changes must be multiplied. Final Answer: 8 %

Question 13

Inferring marked price from profit change with discount tweak: A shirt is sold with a 7% discount. If the discount had been 9%, the shopkeeper’s profit would have been ₹15 less. What is the marked price of the shirt?

Accepted Answer

Introduction / Context: The change in profit from changing the discount rate by 2 percentage points equals 2% of the marked price, because cost stays fixed and selling price changes by 2% of MRP. Using the given rupee change in profit, you can solve for the marked price directly without needing cost or initial profit explicitly. Given Data / Assumptions: Discount1 = 7% ⇒ SP1 = 0.93M. Discount2 = 9% ⇒ SP2 = 0.91M. Profit difference = SP1 − SP2 = ₹15. Concept / Approach: Since cost is unchanged, the change in profit equals the change in selling price. Therefore, (0.93M − 0.91M) = 0.02M = ₹15. Solve for M directly. Step-by-Step Solution: 0.02M = 15 ⇒ M = 15 / 0.02 = ₹750. Verification / Alternative check: At M = 750, SP1 = 697.50, SP2 = 682.50; difference = ₹15, matching. The cost cancels in the difference, hence not required. Why Other Options Are Wrong: ₹720, ₹712.50, ₹600, ₹840 do not satisfy a ₹15 change when discount shifts by 2 percentage points. Common Pitfalls: Trying to compute cost or initial profit unnecessarily; focusing on the selling price change is faster and cleaner. Final Answer: ₹ 750

Question 14

Discount and marked price: A watch is sold with a 5% discount. If the shopkeeper instead gives a 6% discount, his profit decreases by ₹15. What is the marked price (list price) of the watch?

Accepted Answer

Introduction / Context:This problem tests the link between discount percentage and selling price. A 1% extra discount reduces the selling price by exactly 1% of the marked price, which directly shows up as a reduction in profit (since cost price is unchanged). Given Data / Assumptions: Discount changes from 5% to 6%. Profit decreases by ₹15 when discount increases by 1%. Marked price = MP, cost price = CP (constant). Concept / Approach:With MP fixed, selling price SP = MP*(1 − discount). If discount rises by 1%, SP falls by 0.01*MP. Because CP is constant, the decrease in profit equals the decrease in SP, which equals 0.01*MP. Hence 0.01*MP is directly the given ₹15 drop. Step-by-Step Solution: Drop in profit = ₹15 Drop in SP due to extra 1% discount = 0.01 * MP So, 0.01 * MP = 15 ⇒ MP = 15 / 0.01 = ₹1500 Verification / Alternative check:If MP = 1500, SP at 5% is 1500*0.95 = 1425; SP at 6% is 1500*0.94 = 1410; difference = ₹15, matching the statement. Why Other Options Are Wrong:Values like ₹1250, ₹1400, ₹750, ₹1600 would not make a 1% of MP equal ₹15; their 1% differs from ₹15. Common Pitfalls:Confusing profit percent with discount percent; here only the SP change matters since CP is unchanged. Final Answer:₹ 1500

Question 15

Discount with profit: After allowing a 16% discount, a shopkeeper still makes a 5% gain. By what percentage is the marked price above the cost price?

Accepted Answer

Introduction / Context:The question connects discount on marked price (MP) with gain on cost price (CP). Converting both to a single equation allows solving for MP/CP and hence the percentage markup over cost. Given Data / Assumptions: Discount = 16% on MP ⇒ SP = 0.84 * MP. Gain = 5% on CP ⇒ SP = 1.05 * CP. Concept / Approach:Equate the two expressions for SP to relate MP and CP, then convert the ratio to a percentage increase of MP over CP: (MP − CP)/CP * 100%. Step-by-Step Solution: 0.84 * MP = 1.05 * CP MP / CP = 1.05 / 0.84 = 1.25 Hence MP is 25% more than CP. Verification / Alternative check:Assume CP = 100; then SP = 105. Since SP = 0.84*MP, MP = 105/0.84 = 125 = 25% above 100. Why Other Options Are Wrong:15%, 18%, 21% do not satisfy 0.84*MP = 1.05*CP. Only 25% yields equality. Common Pitfalls:Adding or subtracting percentages directly rather than forming and equating the correct expressions. Final Answer:25%

Question 16

Marked price, discount, free gift and profit: An article is marked at ₹60 and sold at a 15% discount. The shopkeeper also gives a free gift worth ₹3. If he still makes a 20% profit on the article, what is the cost price of the article (excluding the…

Accepted Answer

Introduction / Context:This problem integrates a percentage discount with an additional fixed cost (a free gift) and asks for the original cost price (CP) of the article. The key is to treat the gift as the shopkeeper’s extra cost while profit percent is computed on the article’s CP. Given Data / Assumptions: Marked price = ₹60, discount = 15% ⇒ SP from the article = 60 * 0.85 = ₹51. Gift cost to shopkeeper = ₹3 (extra cost incurred). Net profit on the article = 20% of CP. Concept / Approach:Profit = Selling proceeds − total cost. Total cost here is CP of article + ₹3 (gift). Set this profit equal to 0.20*CP and solve for CP. Step-by-Step Solution: SP (from article) = 51 Total cost = CP + 3 Profit = 51 − (CP + 3) = 0.20 * CP 48 − CP = 0.20CP ⇒ 48 = 1.20CP ⇒ CP = 48 / 1.20 = 40 Verification / Alternative check:If CP = 40, profit = 20% of 40 = 8. Net: SP − (CP + gift) = 51 − (40 + 3) = 8, consistent. Why Other Options Are Wrong:Other values do not simultaneously satisfy both the discount-derived SP and the required 20% profit after including the gift cost. Common Pitfalls:Ignoring the gift cost in total cost or mistakenly computing profit percent on (CP + gift) rather than on CP of the article. Final Answer:₹ 40

Question 17

Required markup with a fixed discount: A tradesman allows a 15% discount on the marked price. By what percentage above the cost price must he mark the goods to gain 19% after giving this discount?

Accepted Answer

Introduction / Context:We need to determine the markup (MP over CP) when discount is known and desired profit is fixed. The selling price is controlled by both MP and discount, while profit compares SP to CP. Given Data / Assumptions: Discount = 15% ⇒ SP = 0.85 * MP. Desired profit = 19% ⇒ SP = 1.19 * CP. Concept / Approach:Equate SP expressions: 0.85 * MP = 1.19 * CP. Then compute MP/CP and convert to percent above cost = (MP − CP)/CP * 100%. Step-by-Step Solution: 0.85 * MP = 1.19 * CP MP / CP = 1.19 / 0.85 = 1.4 Hence, markup = 40% above cost price. Verification / Alternative check:Let CP = 100 ⇒ MP = 140. After 15% discount SP = 140*0.85 = 119, which is indeed 19% above 100. Why Other Options Are Wrong:34%, 25%, 30%, 36% do not satisfy the equality SP = 0.85*MP = 1.19*CP. Common Pitfalls:Adding percentages directly instead of forming the equation with multiplicative factors. Final Answer:40%

Question 18

Markup then discount: If the marked price of an article is 30% more than its cost price and a 10% discount is given, what is the profit percentage?

Accepted Answer

Introduction / Context:This is a straightforward chain of percentage changes: a markup from CP to MP, then a discount from MP to SP. The final profit percentage compares SP to CP. Given Data / Assumptions: MP = CP * 1.30 Discount = 10% ⇒ SP = MP * 0.90 Concept / Approach:Compute SP in terms of CP, then profit% = [(SP − CP)/CP] * 100%. Use an easy base (CP = 100) to simplify mental arithmetic. Step-by-Step Solution: Let CP = 100 ⇒ MP = 130 SP = 130 * 0.90 = 117 Profit% = (117 − 100)/100 * 100% = 17% Verification / Alternative check:General form: SP = 1.30*0.90*CP = 1.17*CP ⇒ profit is 17% of CP. Why Other Options Are Wrong:Other values do not match the computed 1.17 multiplier relative to CP. Common Pitfalls:Confusing 30% − 10% with the final profit; percentages compound multiplicatively, not additively. Final Answer:17%

Question 19

Discount given, profit achieved: A shopkeeper sells a book at a 10% discount on its marked price yet makes a 20% profit. What is the ratio of cost price to marked price?

Accepted Answer

Introduction / Context:Two simple relations define selling price: SP = 0.90*MP (due to 10% discount) and SP = 1.20*CP (due to 20% profit). Equating them yields CP : MP directly. Given Data / Assumptions: Discount = 10% ⇒ SP = 0.90 * MP Profit = 20% ⇒ SP = 1.20 * CP Concept / Approach:Equate SP expressions to connect CP and MP, then simplify to a ratio in the lowest terms. Step-by-Step Solution: 0.90*MP = 1.20*CP CP / MP = 0.90 / 1.20 = 3 / 4 Hence, CP : MP = 3 : 4 Verification / Alternative check:Let CP = 3k, MP = 4k ⇒ SP = 0.9*4k = 3.6k, profit = 3.6k − 3k = 0.6k, which is 20% of 3k. Why Other Options Are Wrong:Other ratios do not satisfy the simultaneous conditions implied by both discount and profit. Common Pitfalls:Mixing the order (MP : CP instead of CP : MP). Always match the requested ratio. Final Answer:3 : 4

Question 20

Markup then discount net profit: A shopkeeper marks an article 50% above cost and allows a 30% discount to customers. What is his profit percentage?

Accepted Answer

Introduction / Context:Another chained-percentage question. Apply markup to move from CP to MP, then discount to move from MP to SP. Compare SP with CP to get profit% or loss%. Given Data / Assumptions: Markup = 50% ⇒ MP = 1.50 * CP Discount = 30% ⇒ SP = 0.70 * MP Concept / Approach:Compute SP factor relative to CP: SP = 1.50 * 0.70 * CP = 1.05 * CP. Profit% is then (1.05 − 1)*100% = 5%. Step-by-Step Solution: Let CP = 100 MP = 150 SP = 150 * 0.70 = 105 Profit% = (105 − 100) / 100 * 100% = 5% Verification / Alternative check:Direct factor method: 1.50 * 0.70 = 1.05 ⇒ 5% profit. Why Other Options Are Wrong:10%, 12%, 15% do not follow from the exact multiplicative combination of 50% and 30%. Common Pitfalls:Adding percentages 50 − 30 = 20 and calling that profit. Percentages chain multiplicatively. Final Answer:5%

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