Question 1

Relating equal loss and profit to compute CP The loss when selling at Rs 270 equals the profit when selling at 10% profit. What is the cost price of the article?

Accepted Answer

Introduction / Context: Equal loss and profit comparisons are classic reverse-percentage problems. Express both situations in terms of CP and equate the magnitudes to solve for CP. Given Data / Assumptions: Loss at SP = Rs 270 equals profit at SP corresponding to 10% gain. Find CP. Concept / Approach: Loss at 270 is CP - 270. Profit at 10% is 0.10 × CP. Set them equal and solve for CP. Step-by-Step Solution: CP - 270 = 0.10 CP.0.90 CP = 270.CP = 270 / 0.90 = 300. Verification / Alternative check: Loss at 270 = 300 − 270 = 30; 10% profit on 300 = 30 (equal, as stated). Why Other Options Are Wrong: 90, 110, 363, 330 do not satisfy the equality condition when checked. Common Pitfalls: Equating 270 directly to 10% of CP or misinterpreting the statement as equal selling prices rather than equal magnitudes. Final Answer: Rs 300

Question 2

Equivalent single discount from a series Find the single equivalent discount for the successive series: 10%, then 20%, then 40%.

Accepted Answer

Introduction / Context: Successive discounts multiply the retained fractions of price, not the percentages directly. The single equivalent discount is 1 minus the product of retention factors. Given Data / Assumptions: Discounts: 10%, 20%, 40% applied successively. Concept / Approach: Retention after each discount: 90% = 0.90, then 80% = 0.80, then 60% = 0.60. Multiply to get overall retention; subtract from 1 for the net discount. Step-by-Step Solution: Overall retention = 0.90 × 0.80 × 0.60 = 0.432.Equivalent single discount = 1 − 0.432 = 0.568 = 56.8%. Verification / Alternative check: If marked price is 100, final price after series = 100 × 0.432 = 43.2, so discount = 56.8, i.e., 56.8%. Why Other Options Are Wrong: 50% and 70% ignore compounding; 70.28% is not the product-based result; 60% is a rough guess, not exact. Common Pitfalls: Adding discounts arithmetically (10 + 20 + 40 = 70) instead of compounding multiplicatively. Final Answer: 56.80%

Question 3

Relating CP and SP as percentages If the cost price of an article is 40% of its selling price, what percent is the selling price of the cost price?

Accepted Answer

Introduction / Context: We are given CP as a fraction of SP and asked to invert the relationship to express SP as a percent of CP. This is a straightforward ratio inversion. Given Data / Assumptions: CP = 40% of SP = 0.40 SP. Concept / Approach: From CP = 0.40 SP ⇒ SP/CP = 1/0.40 = 2.5. Convert to percentage by multiplying by 100. Step-by-Step Solution: SP/CP = 2.5 ⇒ SP is 2.5 × CP.As a percent, 2.5 × 100 = 250%. Verification / Alternative check: Let SP = 100. Then CP = 40. SP as percent of CP = 100 / 40 × 100 = 250% (matches). Why Other Options Are Wrong: 240% is close but incorrect; 40%, 60%, 200% arise from misreading the base. Common Pitfalls: Using CP as 40% of SP but then forgetting to invert correctly when expressing SP relative to CP. Final Answer: 250

Question 4

Target gain with 'x for a rupee' pricing Toffees are bought at 8 for a rupee. To gain 60%, at what rate should they be sold?

Accepted Answer

Introduction / Context: Items priced as 'x for a rupee' require converting to per-unit cost. To achieve a target gain, compute the necessary per-unit selling price and convert it back to the 'y for a rupee' form. Given Data / Assumptions: CP: 8 for Rs 1 ⇒ CP per toffee = Rs 1/8 = Rs 0.125. Target gain = 60% on CP. Concept / Approach: Required SP per toffee = CP × (1 + gain%). Then take the reciprocal to express as 'k for a rupee'. Step-by-Step Solution: Required SP per toffee = 0.125 × 1.60 = 0.20.'k for a rupee' implies 1/k rupee per toffee = 0.20 ⇒ k = 5. Verification / Alternative check: At 5 for Rs 1, SP per toffee = 0.20. Profit per toffee = 0.20 − 0.125 = 0.075. Gain% = 0.075/0.125 × 100 = 60%. Why Other Options Are Wrong: 6 for Rs 1 yields SP per toffee ≈ 0.1667 (gain < 60%); 9 for Rs 2 ⇒ 0.222... (gain > 60%); 24 for Rs 5 ⇒ ≈ 0.2083 (gain > 60%); 4 for Rs 1 ⇒ 0.25 (too high). Common Pitfalls: Adding 60% to the '8' instead of to the price, or inverting the 'k for a rupee' step. Final Answer: 5 for a rupee

Question 5

Profit and Loss – Paper sheets and packing boxes: Jimmy buys paper sheets for Rs 7200, spends Rs 200 on transport, and pays Rs 600 for having 330 boxes made. He then sells all 330 boxes at Rs 28 each. Calculate his overall profit percentage on the e…

Accepted Answer

Introduction / Context: In profit and loss problems, total cost price (CP) includes every expense such as purchase cost, transport, and making charges. Total selling price (SP) equals quantity sold multiplied by selling price per unit. Profit percent is computed on CP. Given Data / Assumptions: Paper sheets cost = Rs 7200 Transport expense = Rs 200 Box making charges = Rs 600 Number of boxes = 330 Selling price per box = Rs 28 Concept / Approach: Compute CP as the sum of all costs. Compute SP as units * unit price. Profit = SP - CP. Profit% = (Profit / CP) * 100. Step-by-Step Solution: CP = 7200 + 200 + 600 = 8000SP = 330 * 28 = 9240Profit = 9240 - 8000 = 1240Profit% = (1240 / 8000) * 100 = 15.5% Verification / Alternative check: Check arithmetic: 33 * 28 = 924; therefore 330 * 28 = 9240, consistent. CP components clearly sum to 8000. Why Other Options Are Wrong: 40% and 60% are much larger than 1240/8000. 12% underestimates the ratio. “None” is incorrect because 15.5% matches computation. Common Pitfalls: Ignoring transport or making charges, or dividing by SP instead of CP. Final Answer: 15.5%

Question 6

Profit and Loss – Effect on revenue when price and quantity change: The price of a toy increases by 20%, and because of this the quantity sold decreases by 15%. What is the net effect on total sales revenue of the shop?

Accepted Answer

Introduction / Context: This question tests combined percentage changes. Sales revenue equals price * quantity. When both change, multiply their individual factors. Given Data / Assumptions: Price increases by 20% ⇒ factor 1.20 Quantity decreases by 15% ⇒ factor 0.85 Concept / Approach: Net revenue factor = price factor * quantity factor. Convert percentage to multiplicative factors before multiplying. Step-by-Step Solution: Net factor = 1.20 * 0.85 = 1.02Net change = (1.02 - 1.00) * 100% = 2% increase Verification / Alternative check: Assume initial price = 100 and quantity = 100; initial revenue = 10000. New revenue = 120 * 85 = 10200, which is 2% higher. Why Other Options Are Wrong: 2% decrease and 4% decrease contradict the product 1.20 * 0.85. 4% increase overstates the effect. No change is false since 1.02 ≠ 1.00. Common Pitfalls: Adding percentages (20% - 15% = 5%) instead of multiplying factors. Final Answer: 2% increase

Question 7

Profit and Loss – Short weight deception at “cost price”: A dealer claims to sell at cost price but uses a 900 g weight as if it were 1 kg. What is his actual gain percentage?

Accepted Answer

Introduction / Context: Using a short weight increases the effective price per kilogram, creating a hidden gain even if the stated price equals the cost price per kilogram. Given Data / Assumptions: Claimed unit: 1 kg Actual delivered: 900 g Quoted price equals cost price per 1 kg Concept / Approach: If customer pays for 1 kg but receives only 0.9 kg, the dealer collects the price of 1 kg while parting with 0.9 kg that costs him less. Gain% is computed on dealer’s cost for 0.9 kg. Step-by-Step Solution: Let cost price per kg = Rs 100 (any convenient number)Dealer sells “1 kg” at Rs 100 but gives 0.9 kg whose cost = 0.9 * 100 = Rs 90Gain = 100 - 90 = Rs 10Gain% = 10 / 90 * 100 = 11.111...% = 11 1/9% Verification / Alternative check: Formula: gain% = (1000 - 900) / 900 * 100 = 11.111...% Why Other Options Are Wrong: 11%, 10%, and 9% are approximations that do not match the exact 11 1/9%. 12.5% is too high. Common Pitfalls: Using 1000 as the denominator or computing profit on SP rather than CP. Final Answer: 11 1/9%

Question 8

Profit and Loss – Equal selling price with opposite percent changes: A dealer sells two TV sets at Rs 3700 each. On one he gains 10% and on the other he loses 10%. What is the overall percentage result (profit or loss) on the combined transaction?

Accepted Answer

Introduction / Context: When items are sold at the same selling price and experience equal but opposite percentage changes in profit and loss, the result is always a net loss. Given Data / Assumptions: SP1 = SP2 = Rs 3700 Gain on first = 10% Loss on second = 10% Concept / Approach: Compute each cost price. Then total CP vs total SP gives the overall percentage. Alternatively, use the identity: equal SP with +a% and -a% yields net loss = (a^2 / 100)%. Step-by-Step Solution: CP1 = 3700 / 1.10 = 3363.636...CP2 = 3700 / 0.90 = 4111.111...Total CP ≈ 7474.747..., Total SP = 7400Loss ≈ 74.747..., Loss% ≈ 74.747 / 7474.747 * 100 ≈ 1% Verification / Alternative check: Using formula: a = 10 ⇒ loss% = 10^2 / 100 = 1%. Why Other Options Are Wrong: 1% gain and no-profit-no-loss contradict the identity. 0.1% and 2% are incorrect magnitudes. Common Pitfalls: Averaging +10% and -10% to get 0% instead of using product effects. Final Answer: 1% loss

Question 9

Profit and Loss – Equal selling price again with ±5%: A man sells two houses for Rs 7.81 lakhs each. On one he gains 5% and on the other he loses 5%. What is the overall percentage effect on the whole sale?

Accepted Answer

Introduction / Context: This is the same structure as the classic equal selling price with opposite percentage changes. The result is a small net loss given by a^2 / 100. Given Data / Assumptions: SP1 = SP2 = Rs 7.81 lakhs One item at +5%, the other at -5% Concept / Approach: For equal SP and opposite percentage of the same magnitude a, overall loss% = a^2 / 100. Step-by-Step Solution: a = 5Loss% = 5^2 / 100 = 25 / 100 = 0.25% Verification / Alternative check: Compute CP1 = SP / 1.05 and CP2 = SP / 0.95, then compare total CP with total SP; it will be a 0.25% loss. Why Other Options Are Wrong: 0.25% gain and no profit contradict the identity. 2.5% and 1% are wrong magnitudes. Common Pitfalls: Assuming gains and losses cancel because they “average” to zero. Final Answer: 0.25% loss

Question 10

Profit and Loss – Equal profit and loss amounts at two selling prices: The profit when selling a commodity for Rs 425 equals the loss when selling it for Rs 355. What is the cost price of the commodity?

Accepted Answer

Introduction / Context: This is a symmetric profit–loss setup: the deviation of the selling price above cost equals the deviation below cost at another selling price. Given Data / Assumptions: SP at profit = Rs 425 SP at loss = Rs 355 Profit amount = Loss amount Concept / Approach: If CP = x, then 425 - x = x - 355. Solve for x. Step-by-Step Solution: 425 - x = x - 3552x = 425 + 355 = 780x = 780 / 2 = 390 Verification / Alternative check: Profit at Rs 425 is 35; loss at Rs 355 is also 35; they match. Why Other Options Are Wrong: 385, 395, 400, and 380 do not make equal deviations from both selling prices. Common Pitfalls: Adding or subtracting incorrectly; forgetting that deviations are symmetric around CP. Final Answer: Rs 390

Question 11

Profit and Loss – Solving a two-variable price system: If two mixers and one TV cost Rs 7000, while two TVs and one mixer cost Rs 9800, find the price of one TV set.

Accepted Answer

Introduction / Context: We are given a pair of linear equations in two variables representing item prices. Solve for the TV price. Given Data / Assumptions: Let mixer price = m Let TV price = t 2m + t = 7000 m + 2t = 9800 Concept / Approach: Use substitution or elimination to solve simultaneous linear equations. Step-by-Step Solution: From 2m + t = 7000 ⇒ t = 7000 - 2mSubstitute in m + 2t = 9800 ⇒ m + 2(7000 - 2m) = 9800m + 14000 - 4m = 9800 ⇒ -3m = -4200 ⇒ m = 1400Then t = 7000 - 2 * 1400 = 4200 Verification / Alternative check: Check second equation: 1400 + 2 * 4200 = 9800, correct. Why Other Options Are Wrong: 2100, 2800, 3500, 3900 do not satisfy both equations simultaneously. Common Pitfalls: Arithmetic slips when substituting or eliminating variables. Final Answer: Rs 4200

Question 12

Profit and Loss – Comparing +10% gain vs -10% loss difference: An article yields Rs 6 more when sold at a gain of 10% than when sold at a loss of 10%. What is the cost price of the article?

Accepted Answer

Introduction / Context: The two selling prices differ because of equal percentage gain and loss applied to the same cost price. Their difference directly gives a fraction of the CP. Given Data / Assumptions: Gain scenario = +10% Loss scenario = -10% Difference in SPs = Rs 6 Concept / Approach: If CP = x, then SP at gain = 1.10x and SP at loss = 0.90x. Difference = 1.10x - 0.90x = 0.20x. Step-by-Step Solution: 0.20x = 6x = 6 / 0.20 = 30 Verification / Alternative check: SP at +10% = 33; SP at -10% = 27; difference = 6, consistent. Why Other Options Are Wrong: 20, 24, 25, and 36 do not satisfy 0.20x = 6. Common Pitfalls: Using 10% of 6 or misinterpreting the difference as 20% of SP. Final Answer: Rs 30

Question 13

Profit and Loss – Calculating rate of discount from marked and selling price: An umbrella is marked at Rs 80 and sold for Rs 68. What is the rate of discount allowed?

Accepted Answer

Introduction / Context: The discount rate is the reduction from the marked price relative to the marked price. Given Data / Assumptions: Marked price (MP) = Rs 80 Selling price (SP) = Rs 68 Concept / Approach: Discount% = (MP - SP) / MP * 100. Step-by-Step Solution: Discount = 80 - 68 = 12Discount% = 12 / 80 * 100 = 15% Verification / Alternative check: 15% of 80 is 12, so SP becomes 68, which matches. Why Other Options Are Wrong: 12% and 10% use wrong bases or arithmetic; 17.5% and 20% are too high. Common Pitfalls: Dividing by SP instead of MP. Final Answer: 15%

Question 14

Profit and Loss – Markup followed by discount: The marked price is 10% higher than the cost price. A discount of 10% is then given on the marked price. In this sale, does the seller gain or lose, and by what percent?

Accepted Answer

Introduction / Context: Successive percentage changes are multiplicative, not additive. A markup followed by an equal discount usually does not return to the original price. Given Data / Assumptions: MP = 1.10 * CP Discount on MP = 10% ⇒ SP = 0.90 * MP Concept / Approach: Compute SP relative to CP and compare. Step-by-Step Solution: SP = 0.90 * (1.10 * CP) = 0.99 * CPHence, SP is 1% below CP ⇒ 1% loss Verification / Alternative check: Let CP = 100; MP = 110; SP = 99; loss = 1. Why Other Options Are Wrong: No-profit-no-loss is false because 0.99 ≠ 1. 1% gain and 2% effects are incorrect directions or magnitudes. Common Pitfalls: Averaging +10% and -10% to get 0%. Final Answer: 1% loss

Question 15

Profit and Loss – Markup and target profit: A dealer marks his goods 20% above cost price. After allowing a discount he realizes an 8% profit. What rate of discount did he allow on the marked price?

Accepted Answer

Introduction / Context: We relate cost price, marked price, selling price, and discount rate. Markup is applied over CP; discount is applied on MP. Given Data / Assumptions: MP = 1.20 * CP SP = 1.08 * CP Let discount rate be d Concept / Approach: SP = (1 - d) * MP. Substitute MP and SP in terms of CP and solve for d. Step-by-Step Solution: 1.08 * CP = (1 - d) * 1.20 * CP1 - d = 1.08 / 1.20 = 0.90d = 0.10 = 10% Verification / Alternative check: Assume CP = 100; MP = 120; with 10% discount SP = 108, which is 8% over CP. Why Other Options Are Wrong: 12%, 6%, 4%, 14% do not yield SP = 1.08 * CP. Common Pitfalls: Subtracting percentages directly instead of using the relationship through MP. Final Answer: 10%

Question 16

Profit and Loss – Percentage gain equals cost price (in rupees): By selling an article for Rs 144, a man gains such that the numerical value of the percentage gain equals the cost price. What is the cost price of the article?

Accepted Answer

Introduction / Context: The phrase “percentage gain equals the cost price” means the numerical value of gain% equals CP measured in rupees. This leads to a quadratic equation in CP. Given Data / Assumptions: SP = Rs 144 Let CP = x Gain% (numerical) = x Concept / Approach: Gain = SP - CP. Also, Gain% = (Gain / CP) * 100. Set Gain% = x and solve. Step-by-Step Solution: Gain = 144 - x(144 - x) / x * 100 = x14400 - 100x = x^2 ⇒ x^2 + 100x - 14400 = 0Discriminant = 10000 + 57600 = 67600 ⇒ sqrt = 260x = (-100 + 260) / 2 = 80 (reject negative root) Verification / Alternative check: CP = 80 ⇒ Gain = 64 ⇒ Gain% = 64 / 80 * 100 = 80, which equals CP numerically. Why Other Options Are Wrong: 60, 64, 72, 96 do not satisfy the quadratic relation. Common Pitfalls: Interpreting “equals” as rupees-to-rupees rather than a numerical equality of percentage and CP value. Final Answer: Rs 80

Question 17

Profit and Loss – Successive discounts on printed price: An electric heater has a printed price of Rs 160. If two successive discounts of 20% and 10% are offered, how much does the customer pay?

Accepted Answer

Introduction / Context: Successive discounts multiply their factors, not add the percentages. Given Data / Assumptions: Marked price = Rs 160 Discounts: 20% then 10% Concept / Approach: Apply the first discount to get an intermediate price, then apply the second discount on that intermediate price. Step-by-Step Solution: Price after 20% off = 160 * 0.80 = 128Price after an additional 10% off = 128 * 0.90 = 115.20 Verification / Alternative check: Combined factor = 0.8 * 0.9 = 0.72 ⇒ 160 * 0.72 = 115.20. Why Other Options Are Wrong: 112, 119.60, 129.60, 108.80 result from incorrect arithmetic or additive treatment of discounts. Common Pitfalls: Adding discounts to get 30% and applying once. Final Answer: Rs 115.20

Question 18

Profit and Loss – Target price for desired profit given a loss price: There would be a 10% loss if rice is sold at Rs 5.40 per kg. At what price per kg should it be sold to earn a 20% profit?

Accepted Answer

Introduction / Context: From a given loss-selling price, compute cost price, then apply the desired profit percentage to find the required selling price. Given Data / Assumptions: SP at 10% loss = Rs 5.40 Desired gain = 20% Concept / Approach: For loss L%: SP = (1 - L/100) * CP ⇒ CP = SP / (1 - L/100). For target gain G%: Required SP = (1 + G/100) * CP. Step-by-Step Solution: CP = 5.40 / 0.90 = 6.00Required SP = 6.00 * 1.20 = 7.20 Verification / Alternative check: At Rs 7.20, gain = 1.20 on CP 6 ⇒ 20%. Why Other Options Are Wrong: 6.48, 7.02, 6.84 do not produce 20% gain on CP 6. Rs 6.00 is just CP. Common Pitfalls: Applying both percentages to SP rather than CP. Final Answer: Rs 7.20

Question 19

Profit and Loss – Simple gain percent on a small transaction: A person buys a book for ₹ 200 and sells it for ₹ 225. What is the gain percentage?

Accepted Answer

Introduction / Context: Compute a basic profit percentage from given cost and selling prices. Given Data / Assumptions: CP = ₹ 200 SP = ₹ 225 Concept / Approach: Profit% = (SP - CP) / CP * 100. Step-by-Step Solution: Profit = 225 - 200 = 25Profit% = 25 / 200 * 100 = 12.5% Verification / Alternative check: 12.5% of 200 equals 25, which matches the profit. Why Other Options Are Wrong: 13% and 14% are close but incorrect; 18.4% and 10% are wrong magnitudes. Common Pitfalls: Dividing by SP instead of CP. Final Answer: 12.5%

Question 20

Profit and Loss – Simple loss percent on a small transaction: A person buys a watch for ₹ 500 and sells it for ₹ 300. What is the loss percentage?

Accepted Answer

Introduction / Context: This is a straightforward loss percentage computation using CP and SP. Given Data / Assumptions: CP = ₹ 500 SP = ₹ 300 Concept / Approach: Loss% = (CP - SP) / CP * 100. Step-by-Step Solution: Loss = 500 - 300 = 200Loss% = 200 / 500 * 100 = 40% Verification / Alternative check: 40% of 500 is 200; subtracting yields SP 300, consistent. Why Other Options Are Wrong: 30%, 35%, 45%, and 50% do not equal 200 / 500 * 100. Common Pitfalls: Using SP as the denominator. Final Answer: 40%

Profit and Loss Questions