Q: If the selling price of 12 articles equals the cost price of 15 articles of the same kind, compute the gain percentage.

Introduction: Ratio statements that compare totals at selling and cost prices allow you to infer the per-unit selling price relative to per-unit cost price. From that relation, the profit percentage follows directly. Given Data / Assumptions: 12 units at selling price equal 15 units at cost price. All units are homogeneous. Concept / Approach: Let s be SP per unit and c be CP per unit. Then 12s = 15c implies s = (15/12)c = 1.25c. Profit% = (s - c)/c * 100. Step-by-Step Solution: From 12s = 15c, s = 1.25cProfit per unit = s - c = 0.25cProfit% = 0.25c / c * 100 = 25% Verification / Alternative check: Assume c = 100. Then s = 125. For 12 units, SP = 1500 and CP of 15 units is also 1500, which is consistent with the premise and confirms 25% profit per unit. Why Other Options Are Wrong: 66 2/3% and 80%: far too large; misinterpret the ratio. 20%: arises from mixing article counts or using partial differences incorrectly. Common Pitfalls: Using 12/15 directly as profit percentage or subtracting counts without converting to unit prices. Final Answer: 25%

Q: An article sold for Rs 200 yields a 25 percent profit. If 6 such articles are sold for Rs 1056, determine the overall profit or loss percentage and state it clearly.

Introduction: When the selling price at a known profit percentage is given for a single unit, you can recover the unit cost price. Scaling to multiple units and comparing the total selling price with the total cost price yields the overall percentage outcome. Given Data / Assumptions: Single unit: SP = Rs 200 at 25% profit. Six units sold together for Rs 1056. Concept / Approach: If SP = 200 corresponds to 25% profit, then CP per unit = SP / 1.25. Multiply by 6 to get total CP for six units and compare with the given total SP to find the net percentage. Step-by-Step Solution: Unit CP = 200 / 1.25 = 160Total CP for 6 units = 6 * 160 = 960Total SP for 6 units = 1056Net profit = 1056 - 960 = 96Profit% = 96 / 960 * 100 = 10% Verification / Alternative check: Compute average SP per unit from the group sale: 1056 / 6 = 176. Since CP is 160, unit margin = 16, which is 10% of 160. This reconfirms the overall 10% profit. Why Other Options Are Wrong: 10% loss: sign error. 5% loss or 5% profit: magnitude error from arithmetic slips. Common Pitfalls: Using 25% of 200 as the profit to reverse CP incorrectly. Forgetting to scale the costs and revenues to the same quantity. Final Answer: 10 per cent profit

Q: Two chairs and three tables cost Rs 1025, while three chairs and two tables cost Rs 1100. Determine the absolute difference between the cost of one table and one chair.

Introduction: Linear pairs of purchases create a system of two equations in two unknowns. Often, adding or subtracting the equations directly isolates a clean expression for either the sum or difference of unit prices. Given Data / Assumptions: 2C + 3T = 1025 (C = price of a chair, T = price of a table) 3C + 2T = 1100 Concept / Approach: Subtract the equations to eliminate one variable and isolate the difference between T and C. We are asked for |T - C|, the absolute difference. Step-by-Step Solution: (3C + 2T) - (2C + 3T) = 1100 - 1025C - T = 75Therefore, T - C = -75, and |T - C| = 75 Verification / Alternative check: Optionally solve fully. From C - T = 75 and 2C + 3T = 1025, substitute C = T + 75 to get 2(T + 75) + 3T = 1025, so 5T + 150 = 1025, hence T = 175 and C = 250. The difference is 75, matching the result. Why Other Options Are Wrong: Rs. 35 and Rs. 125: not supported by the equations. Cannot be determined: incorrect because we have two independent equations for two unknowns. Common Pitfalls: Adding rather than subtracting, which does not isolate the difference efficiently. Computational slip when substituting back to check values. Final Answer: Rs. 75

Question 1

Anna sells his car to Boney at a 20% profit; Boney sells to Chakori at a 10% profit; Chakori sells to a mechanic at a 9.09% loss; the mechanic spends 10% on repairs and sells at an 8.33% profit back to Anna. What is Anna’s overall loss percentage?

Accepted Answer

Introduction: Track value through successive percentage changes. Use a convenient base cost for Anna initially, propagate sale prices and costs through the chain, and finally compare Anna’s buyback price with his original outlay to express the net loss percentage for the full round trip. Given Data / Assumptions: Let Anna’s original cost = 100 (arbitrary base) Anna sells to Boney at +20% ⇒ 120 Boney sells to Chakori at +10% ⇒ 132 Chakori sells to mechanic at −9.09% (= 1/11) ⇒ 132 * (10/11) = 120 Mechanic spends 10% of purchase price ⇒ 120 + 12 = 132 cost basis Mechanic sells at +8.33% (= 1/12) ⇒ 132 * (13/12) = 143 back to Anna Concept / Approach: Compare Anna’s final buyback price (143) with his original cost (100). The extra cash outflow over the cycle reflects his net loss relative to the initial base. Step-by-Step Solution: Original cost (Anna) = 100; buyback price = 143Overall loss in % relative to original = (143 − 120) with respect to 100? Consider the round trip: Anna received 120 upon selling, later paid 143 to reacquire.Net cash loss over the cycle = 143 − 120 = 23Expressed as % of Anna’s original cost (100): 23% Verification / Alternative check: Using actual rupees scales the same way due to percentage chaining; 1/11 and 1/12 are exact reciprocals of 9.09% and 8.33% approximations, ensuring arithmetic consistency. Why Other Options Are Wrong: 29%/40%/50% are not supported by the exact chain multipliers. Common Pitfalls: Comparing 143 directly to 100 (which suggests 43% difference, not the correct net cash loss metric for the round trip). Final Answer: 23%

Question 2

I had just enough money to buy a watch at list price P. With a 25% discount I could also buy another watch worth Rs 940 for my sister. What price did I pay for my own watch?

Accepted Answer

Introduction: “Just sufficient” for the list price means the amount of money equals the marked price. With a 25% discount, the saving is 25% of P, which exactly funds a second watch priced at Rs 940. We back out P from this relation and then compute the paid price (75% of P). Given Data / Assumptions: Total money M = P (the list price of my watch) Discount = 25% ⇒ paid price = 0.75P Leftover = P − 0.75P = 0.25P = Rs 940 Concept / Approach: Set 0.25P = 940 to get P. Then find the actual amount paid for the first watch as 0.75P. Step-by-Step Solution: 0.25P = 940 ⇒ P = 940 * 4 = 3760Amount paid for my watch = 0.75 * 3760 = Rs 2820 Verification / Alternative check: Money M = 3760; after paying 2820, remaining = 940, matching the second watch price. Why Other Options Are Wrong: 2700/1800 underestimate 75% of 3760; 3760 is the list price, not the amount paid. Common Pitfalls: Confusing “price paid” with list price; applying 25% to 940 instead of to P. Final Answer: Rs. 2820

Question 3

Partners A and B invest Rs 54,000 and Rs 90,000. Total profit is Rs 3,600, including A’s commission at a fixed percentage of total profit (as working partner). A receives Rs 1,800 in total. Find A’s commission as a percentage of total profit.

Accepted Answer

Introduction: Working partners can receive a commission on total profit before the remaining profit is divided in the ratio of capital. We set up an equation in the commission rate using A’s total receipt and solve it algebraically. Given Data / Assumptions: A invests 54,000; B invests 90,000 Total profit = 3,600 Let commission rate = r (on total profit) A’s total receipt = commission + share from remaining profit = 1,800 Concept / Approach: Remaining profit after commission = 3,600 * (1 − r). A’s capital share fraction = 54,000 / (54,000 + 90,000) = 3/8 = 0.375. Form the equation: 3,600r + 0.375 * 3,600(1 − r) = 1,800. Step-by-Step Solution: Compute: 3,600r + 1,350(1 − r) = 1,800⇒ 3,600r + 1,350 − 1,350r = 1,800⇒ 2,250r = 450 ⇒ r = 0.2Commission percentage = 20% Verification / Alternative check: Commission = 720; remaining profit = 2,880; A’s share = 0.375 * 2,880 = 1,080; total to A = 720 + 1,080 = 1,800 (matches). Why Other Options Are Wrong: 10%/5%/25% do not reproduce Rs 1,800 total. Common Pitfalls: Dividing the entire profit by capital ratios before deducting commission; miscomputing A’s fraction as 54/90 instead of 54/(54+90). Final Answer: 20%

Question 4

A trader sells at k% above cost but delivers only 880 g instead of 1 kg. If his overall profit is 25%, find k.

Accepted Answer

Introduction: A short-weight trick increases effective price per true kilogram. Combined with a markup k% on cost, the overall profit becomes 25%. We compute k so that revenue on a “1 kg” sale compared to the true cost of 0.88 kg delivered yields a 25% margin. Given Data / Assumptions: True cost per kg = C Delivered per “1 kg” bill = 0.88 kg Nominal SP per “1 kg” = C * (1 + k) Target overall profit = 25% Concept / Approach: Profit% on cost of goods delivered = [(Revenue − Cost)/Cost] * 100 with Cost = 0.88C and Revenue = C(1 + k). Set it equal to 25% and solve for k. Step-by-Step Solution: [(C(1 + k) − 0.88C) / (0.88C)] = 0.25(k + 0.12)/0.88 = 0.25 ⇒ k + 0.12 = 0.22 ⇒ k = 0.10Therefore k = 10% Verification / Alternative check: At k = 10%, revenue = 1.10C; cost for 0.88 kg = 0.88C; profit% = (0.22C)/(0.88C) = 25%. Why Other Options Are Wrong: 8.33%/8.25%/12.5% give overall margins different from 25% with 0.88 kg delivered. Common Pitfalls: Computing profit on SP; forgetting to account for the reduced quantity delivered. Final Answer: 10%

Question 5

Workforce and wage adjustment in a firm: the number of employees reduces in the ratio 3:2, while the average wage per employee increases in the ratio 20:27. Compute the overall percentage saving or gain on the total wage bill compared to the previou…

Accepted Answer

Introduction: Questions that combine changes in staff count and per-employee wages test the idea of multiplicative effects. Instead of averaging the given percentages or ratios, you must compare the total wage bill before and after the change to determine the overall saving or increase. Given Data / Assumptions: Headcount reduces from 3 parts to 2 parts (employee ratio 3:2). Average wage per employee increases from 20 parts to 27 parts (wage ratio 20:27). Total wage bill = number of employees * average wage per employee. Concept / Approach: Compute an index for the old and new wage bills using the product of the two ratios. Old bill is proportional to 3 * 20. New bill is proportional to 2 * 27. Compare these to find the net change as a percentage of the old bill. Step-by-Step Solution: Old wage bill index = 3 * 20 = 60New wage bill index = 2 * 27 = 54Absolute change = 60 - 54 = 6 (a reduction)Percentage change relative to old = 6 / 60 * 100 = 10% Verification / Alternative check: Scale to concrete numbers. Suppose initially there are 300 employees paid Rs 20 each: total = 6000. After change, employees = 200 and wage = Rs 27 each: total = 5400. Reduction = 600, which is 10% of 6000. This confirms the result. Why Other Options Are Wrong: 9.09%: arises from using the new wage bill as base instead of the old bill. 11.11%: comes from reversing the headcount ratio or misapplying percentages. None of these: incorrect because 10% is correct. Common Pitfalls: Averaging the ratios or converting them to percentages before combining. Basing the percentage reduction on the new bill rather than the old baseline. Final Answer: 10% reduction (a 10% saving on the previous wage bill)

Question 6

Successive discount versus a single discount: a motorcycle is displayed at Rs 50,000. Instead of a single 15% discount, the buyer is offered two successive discounts of 10% and 5%. Determine the single equivalent discount the buyer actually receives.

Accepted Answer

Introduction: Successive discounts do not add arithmetically; they combine multiplicatively. Converting a pair of discounts to a single equivalent discount is a standard skill in profit and loss and pricing questions. Given Data / Assumptions: Marked price reference: any convenient base (e.g., Rs 100) works. Two successive discounts: first 10%, then 5% on the reduced price. We must find the single equivalent discount. Concept / Approach: Let M be the marked price. After 10% off, price becomes 0.90M. After a further 5% off, price becomes 0.95 * 0.90M = 0.855M. The equivalent discount D satisfies price = (1 - D)M, i.e., 1 - D = 0.855. Step-by-Step Solution: Net price factor = 0.90 * 0.95 = 0.855Equivalent discount D = 1 - 0.855 = 0.145Therefore, D = 14.5% Verification / Alternative check: Using M = Rs 50,000 for concreteness: after 10% off, Rs 45,000; after 5% more, Rs 42,750. Single discount from Rs 50,000 to Rs 42,750 is Rs 7,250, which is 7,250 / 50,000 * 100 = 14.5%. Why Other Options Are Wrong: 15%: simple addition ignores multiplicative compounding. 15.5%: an overcorrection; incorrect rounding. None of these: incorrect because 14.5% is exact. Common Pitfalls: Adding percentages directly for successive discounts. Applying the second discount to the original price instead of the reduced price. Final Answer: 14.5%

Question 7

Effect on profit or loss percentage Z when both CP (C) and SP (S) are increased by the same absolute amount: determine whether Z increases, decreases, or remains constant.

Accepted Answer

Introduction: Profit or loss percentage depends on the ratio between profit (or loss) and cost price. When both the cost price (CP) and selling price (SP) increase by the same absolute amount, the numerator (SP - CP) does not change, but the denominator used for the percentage typically does. Understanding this sensitivity clarifies the direction of change in percentage Z. Given Data / Assumptions: Original CP = C, SP = S, percentage Z is based on CP unless otherwise specified. Both CP and SP are increased by the same amount k. We consider the usual definition: profit% = (S - C)/C * 100, loss% similar. Concept / Approach: After adding k to both, profit in absolute terms remains (S - C). However, the new CP becomes (C + k), which increases the denominator used to compute percentage Z. A larger denominator with the same numerator yields a smaller percentage magnitude. Step-by-Step Solution: Original percentage: Z = (S - C)/C * 100New percentage: Z_new = (S + k - (C + k)) / (C + k) * 100Note that S + k - (C + k) = S - C (unchanged)Therefore Z_new = (S - C)/(C + k) * 100Since C + k > C for k > 0, Z_new < Z Verification / Alternative check: Take C = 100, S = 120 (20% profit). Add k = 10: new CP = 110, new SP = 130, profit is still 20. New profit% = 20/110 * 100 = 18.18%, which is smaller than 20%. Why Other Options Are Wrong: Z increases: false because denominator increases while numerator remains the same. Remains constant: would require the denominator to remain unchanged, which it does not. None of these: incorrect because Z decreases is correct. Common Pitfalls: Confusing absolute profit (unchanged) with percentage profit (changes due to the base CP). Using selling price as the base for the percentage instead of cost price. Final Answer: Z decreases

Question 8

If the selling price of 12 articles equals the cost price of 15 articles of the same kind, compute the gain percentage.

Accepted Answer

Introduction: Ratio statements that compare totals at selling and cost prices allow you to infer the per-unit selling price relative to per-unit cost price. From that relation, the profit percentage follows directly. Given Data / Assumptions: 12 units at selling price equal 15 units at cost price. All units are homogeneous. Concept / Approach: Let s be SP per unit and c be CP per unit. Then 12s = 15c implies s = (15/12)c = 1.25c. Profit% = (s - c)/c * 100. Step-by-Step Solution: From 12s = 15c, s = 1.25cProfit per unit = s - c = 0.25cProfit% = 0.25c / c * 100 = 25% Verification / Alternative check: Assume c = 100. Then s = 125. For 12 units, SP = 1500 and CP of 15 units is also 1500, which is consistent with the premise and confirms 25% profit per unit. Why Other Options Are Wrong: 66 2/3% and 80%: far too large; misinterpret the ratio. 20%: arises from mixing article counts or using partial differences incorrectly. Common Pitfalls: Using 12/15 directly as profit percentage or subtracting counts without converting to unit prices. Final Answer: 25%

Question 9

An article sold for Rs 200 yields a 25 percent profit. If 6 such articles are sold for Rs 1056, determine the overall profit or loss percentage and state it clearly.

Accepted Answer

Introduction: When the selling price at a known profit percentage is given for a single unit, you can recover the unit cost price. Scaling to multiple units and comparing the total selling price with the total cost price yields the overall percentage outcome. Given Data / Assumptions: Single unit: SP = Rs 200 at 25% profit. Six units sold together for Rs 1056. Concept / Approach: If SP = 200 corresponds to 25% profit, then CP per unit = SP / 1.25. Multiply by 6 to get total CP for six units and compare with the given total SP to find the net percentage. Step-by-Step Solution: Unit CP = 200 / 1.25 = 160Total CP for 6 units = 6 * 160 = 960Total SP for 6 units = 1056Net profit = 1056 - 960 = 96Profit% = 96 / 960 * 100 = 10% Verification / Alternative check: Compute average SP per unit from the group sale: 1056 / 6 = 176. Since CP is 160, unit margin = 16, which is 10% of 160. This reconfirms the overall 10% profit. Why Other Options Are Wrong: 10% loss: sign error. 5% loss or 5% profit: magnitude error from arithmetic slips. Common Pitfalls: Using 25% of 200 as the profit to reverse CP incorrectly. Forgetting to scale the costs and revenues to the same quantity. Final Answer: 10 per cent profit

Question 10

Two chairs and three tables cost Rs 1025, while three chairs and two tables cost Rs 1100. Determine the absolute difference between the cost of one table and one chair.

Accepted Answer

Introduction: Linear pairs of purchases create a system of two equations in two unknowns. Often, adding or subtracting the equations directly isolates a clean expression for either the sum or difference of unit prices. Given Data / Assumptions: 2C + 3T = 1025 (C = price of a chair, T = price of a table) 3C + 2T = 1100 Concept / Approach: Subtract the equations to eliminate one variable and isolate the difference between T and C. We are asked for |T - C|, the absolute difference. Step-by-Step Solution: (3C + 2T) - (2C + 3T) = 1100 - 1025C - T = 75Therefore, T - C = -75, and |T - C| = 75 Verification / Alternative check: Optionally solve fully. From C - T = 75 and 2C + 3T = 1025, substitute C = T + 75 to get 2(T + 75) + 3T = 1025, so 5T + 150 = 1025, hence T = 175 and C = 250. The difference is 75, matching the result. Why Other Options Are Wrong: Rs. 35 and Rs. 125: not supported by the equations. Cannot be determined: incorrect because we have two independent equations for two unknowns. Common Pitfalls: Adding rather than subtracting, which does not isolate the difference efficiently. Computational slip when substituting back to check values. Final Answer: Rs. 75

Question 11

An item costs Rs 200 and is sold at a 10% loss. If the selling price is reduced by a further 5% (on the current selling price), compute the new selling price.

Accepted Answer

Introduction: This problem mixes a loss from cost price and a further percentage reduction from selling price. It reinforces that the base of a percentage cut must be the current value at each step rather than the original cost price unless explicitly stated. Given Data / Assumptions: Cost price = Rs 200. Initial loss = 10% on CP. Additional reduction = 5% on the selling price obtained after the first reduction. Concept / Approach: First compute the selling price after a 10% loss on CP. Then apply a 5% reduction on that selling price. Multiply sequential factors to avoid mixing bases incorrectly. Step-by-Step Solution: SP after 10% loss = 200 * (1 - 0.10) = 200 * 0.90 = 180New SP after further 5% off = 180 * (1 - 0.05) = 180 * 0.95 = 171 Verification / Alternative check: Sequential multipliers give the same result: 200 * 0.90 * 0.95 = 171. Any rounding occurs only if specified; here values are exact. Why Other Options Are Wrong: Rs. 179 and Rs. 175: stem from applying 5% to the cost price or arithmetic errors. Rs. 170: double rounding or using 15% straight off CP, which is not the process described. Common Pitfalls: Applying the second 5% reduction to the original cost price instead of the already reduced selling price. Adding 10% and 5% as if both were on the same base. Final Answer: Rs. 171

Question 12

Book prices vary between Rs 200 and Rs 350 for purchases, and selling prices vary between Rs 300 and Rs 425. What is the greatest possible profit from selling 8 books under these ranges?

Accepted Answer

Introduction: Range problems ask for extremal outcomes subject to stated bounds. When costs and selling prices are given as inclusive ranges, the maximum profit is achieved by choosing the minimum feasible cost and the maximum feasible selling price for each item independently, unless constraints link items across the set. Given Data / Assumptions: For each book: purchase price is between Rs 200 and Rs 350. For each book: selling price is between Rs 300 and Rs 425. We assume books can be chosen within the stated ranges independently (no coupling constraints provided). Concept / Approach: To maximize profit per book, select the lowest allowable purchase price and the highest allowable selling price. Multiply the best per-book margin by the number of books to get the total maximum profit. Step-by-Step Solution: Best per-book margin = 425 - 200 = 225Number of books = 8Greatest possible profit = 8 * 225 = 1800 Verification / Alternative check: Any selection with higher cost or lower selling price reduces the margin. Since no cross-book constraint is stated, the theoretical maximum of Rs 1800 is attainable in principle under the given ranges. Why Other Options Are Wrong: Rs. 400 and Rs. 600: much smaller than the computed bound. Cannot be determined: incorrect because the ranges suffice to compute an extremum when independence is allowed. Common Pitfalls: Assuming you must use every price in the range or that prices are linked across books, which is not stated. Using average prices rather than optimizing for extremes when asked for the greatest possible outcome. Final Answer: Rs 1800 (thus, None of these)

Question 13

By selling 8 dozen pencils, a shopkeeper gains an amount equal to the selling price of 1 dozen pencils. Determine the gain percentage.

Accepted Answer

Introduction: Profit statements expressed as a multiple of selling price are common. Converting these descriptions to algebra with per-dozen or per-unit prices helps to compute the gain percentage accurately. Given Data / Assumptions: Let S be the selling price per dozen pencils. By selling 8 dozen, the profit equals S (the price of 1 dozen). All dozens are sold at the same price. Concept / Approach: Total SP for 8 dozen is 8S. If profit equals S, then total cost for 8 dozen must be 8S - S = 7S. Profit percentage is profit divided by cost times 100. Step-by-Step Solution: Total SP for 8 dozen = 8SProfit = STotal CP = 8S - S = 7SProfit% = S / 7S * 100 = 100/7% = 14 2/7% Verification / Alternative check: Use numbers: suppose S = Rs 700 per dozen. Then 8S = Rs 5600; profit S = Rs 700; cost = Rs 4900. Profit% = 700/4900 * 100 = 14.2857...% = 14 2/7%. Why Other Options Are Wrong: 12.5%: too small; comes from mixing dozen and unit counts. 20%: too large; results from taking S over 5S or similar mistakes. None of these: incorrect because 14 2/7% is exact. Common Pitfalls: Treating S as CP rather than SP. Forgetting that percentage is on cost, not selling price. Final Answer: 14 2/7%

Question 14

A vendor sells 36 oranges and incurs a loss equal to the selling price of 4 oranges. Compute the loss percentage.

Accepted Answer

Introduction: Loss or gain expressed in terms of the selling price of some quantity is a classic framing. Turning it into algebra using per-unit selling price and comparing total selling price with total cost gives the required percentage. Given Data / Assumptions: Let s be the selling price per orange. Total oranges sold = 36. Loss amount = selling price of 4 oranges = 4s. Concept / Approach: Total SP = 36s. Since there is a loss of 4s, total CP must be SP + loss = 36s + 4s = 40s. Loss percentage is loss divided by cost times 100. Step-by-Step Solution: Total SP = 36sLoss = 4sTotal CP = 36s + 4s = 40sLoss% = 4s / 40s * 100 = 10% Verification / Alternative check: Assume s = Rs 10. Then SP = 360, loss = 40, CP = 400, giving 40/400 * 100 = 10%, consistent. Why Other Options Are Wrong: 12.5% and 11 1/9%: incorrect ratios from misplacing the base. None of these: incorrect because 10% is correct. Common Pitfalls: Computing percentage on selling price instead of on cost price. Interpreting the loss as 4 oranges out of 36 without converting rupee values. Final Answer: 10%

Question 15

A shopkeeper offers a 5% discount on a watch. If he instead offers a 7% discount, his profit decreases by Rs 15. Find the marked price of the watch.

Accepted Answer

Introduction: When a seller changes the discount rate, the change in selling price equals the change in discount taken on the marked price. If this change translates directly to a change in profit (cost remaining the same), the rupee difference reveals the marked price. Given Data / Assumptions: Two scenarios: 5% discount and 7% discount. Profit difference between scenarios = Rs 15 (lower profit at 7%). Cost price is unchanged across scenarios. Concept / Approach: Let M be the marked price. The price drop when moving from 5% to 7% discount equals 2% of M. This drop causes the profit to fall by Rs 15. Hence 0.02M = 15, from which M can be found. Step-by-Step Solution: Change in discount rate = 7% - 5% = 2%2% of M = Rs 15M = 15 / 0.02 = 750 Verification / Alternative check: At 5% discount, SP = 0.95M = 712.50. At 7% discount, SP = 0.93M = 697.50. The difference is Rs 15, which matches the stated profit change when cost is fixed. Why Other Options Are Wrong: Rs. 697.50 and Rs. 712.50: these are selling prices under 7% and 5% discounts, not the marked price. Rs. 787.50: not aligned with a 2% difference of Rs 15. Common Pitfalls: Applying the 2% to selling price rather than to the marked price. Assuming cost price changes between scenarios. Final Answer: Rs. 750.00

Question 16

A sells a horse to B for Rs 4860 at a loss of 19%. B then sells it to C at the price that would have given A a 17% profit on A’s own cost. Compute B’s gain in rupees.

Accepted Answer

Introduction: This chain transaction compares B’s purchase price with a target price pegged to A’s cost. Converting percentage statements back to A’s cost price is the key step before computing B’s rupee gain. Given Data / Assumptions: A sells to B for Rs 4860 at 19% loss. Target price for the next sale is the price that would have given A a 17% profit on A’s cost. Concept / Approach: First derive A’s cost from the 19% loss sale. Then scale A’s cost by 1.17 to get the target price at which B sells to C. B’s gain equals that target price minus B’s purchase price of 4860. Step-by-Step Solution: Let A’s cost = X. Loss 19% implies 4860 = 0.81XX = 4860 / 0.81 = 6000Price giving A a 17% profit = 1.17 * 6000 = 7020B’s gain = 7020 - 4860 = 2160 Verification / Alternative check: Compute percentages directly: 19% of 6000 is 1140, so A’s selling price at loss is 6000 - 1140 = 4860. The 17% profit price is 6000 + 1020 = 7020. Difference remains 2160. Why Other Options Are Wrong: Rs. 2610 and Rs. 2260: arithmetic deviations from the correct target price. Rs. 1260: arises from mixing percentage bases. Common Pitfalls: Using B’s buying price as the base for the 17% profit rather than A’s cost, as stated. Final Answer: Rs. 2160

Question 17

An article yields Rs 6 more when sold at a 12% gain than when sold at a 12% loss. Determine the cost price of the article.

Accepted Answer

Introduction: When two selling scenarios differ only by the sign of the percentage (gain versus loss) on the same cost price, the difference of the two selling prices is twice the percentage factor times the cost price. This leads quickly to the cost price. Given Data / Assumptions: Gain scenario: SP1 = 1.12 * CP. Loss scenario: SP2 = 0.88 * CP. SP1 - SP2 = Rs 6. Concept / Approach: Subtract the two expressions to eliminate CP scaling: (1.12 - 0.88) * CP = 0.24 * CP = 6. Solve for CP. Step-by-Step Solution: SP1 - SP2 = (1.12 - 0.88) * CP0.24 * CP = 6CP = 6 / 0.24 = 25 Verification / Alternative check: Check with CP = 25: SP at 12% gain = 28; SP at 12% loss = 22; difference = 6, confirming the calculation. Why Other Options Are Wrong: Rs. 20, Rs. 24, Rs. 30: do not satisfy the difference of 6 when applying ±12%. Common Pitfalls: Using 12% of SP rather than CP. Forgetting that the two percentages are applied to the same base. Final Answer: Rs. 25

Question 18

When the price of a pressure cooker rises by 15%, sales fall by 15%. Determine the net percentage effect on total revenue (money receipt).

Accepted Answer

Introduction: Total revenue equals price multiplied by quantity sold. When both change by given percentages, multiply the corresponding factors to get the net effect. The combined effect is not the simple difference of the percentages. Given Data / Assumptions: Price increases by 15%: multiplier 1.15. Quantity decreases by 15%: multiplier 0.85. Concept / Approach: Revenue_new = Revenue_old * 1.15 * 0.85. Compare the product with 1 to obtain the overall percentage change. Step-by-Step Solution: Net multiplier = 1.15 * 0.85 = 0.9775Percentage change = (0.9775 - 1) * 100 = -2.25% Verification / Alternative check: Use Rs 100 revenue baseline. New revenue = 97.75, which is 2.25 less than 100, i.e., a 2.25% decrease. This matches the computed result. Why Other Options Are Wrong: No effect: would require the product of multipliers to be 1, which it is not. 15% decrease: incorrectly subtracts percentages. 7.5% increase: sign and magnitude are both wrong. Common Pitfalls: Adding +15 and -15 to conclude zero change. Applying the second percentage to the original base instead of the updated value. Final Answer: 2.25% decrease

Question 19

Subhash buys a tape recorder at 9/10 of its listed selling price and sells it at 8% above the listed selling price. Determine his gain percentage on cost.

Accepted Answer

Introduction: When purchase and sale are expressed relative to a common reference (the listed selling price), it is convenient to treat that reference as a unit, compute the actual cost and selling price, and then form the gain percentage on cost. Given Data / Assumptions: Let listed price be L. Cost price = 9/10 of L. Selling price = 1.08L (8% above L). Concept / Approach: Express both CP and SP in terms of L, then compute gain = SP - CP and divide by CP to get the percentage gain on cost. Step-by-Step Solution: CP = 0.9LSP = 1.08LGain = 1.08L - 0.9L = 0.18LGain% = 0.18L / 0.9L * 100 = 20% Verification / Alternative check: Let L = Rs 1000. Then CP = Rs 900, SP = Rs 1080, gain = Rs 180, which is 20% of Rs 900. The percentage is unchanged for any L since both prices scale with L. Why Other Options Are Wrong: 9% and 10%: arise from mixing the base (using SP instead of CP). 180%: a misread of the rupee gain 180 in the numeric example. Common Pitfalls: Computing percentage on SP rather than on CP. Confusing 8% of L with 8% of CP. Final Answer: 20%

Question 20

By selling 100 bananas, a fruit seller gains an amount equal to the selling price of 20 bananas. Compute his gain percentage.

Accepted Answer

Introduction: Stated profits in terms of selling price of some quantity can be translated into algebraic relations. Once the total selling price and profit are linked, the cost price follows, enabling the profit percentage calculation. Given Data / Assumptions: Let s be SP per banana. Total quantity = 100 bananas. Profit amount = SP of 20 bananas = 20s. Concept / Approach: Total SP for 100 bananas = 100s. With profit = 20s, total cost must be 100s - 20s = 80s. Profit percentage = profit / cost * 100. Step-by-Step Solution: SP_total = 100sProfit = 20sCost = 100s - 20s = 80sProfit% = 20s / 80s * 100 = 25% Verification / Alternative check: Take s = Rs 5. Then SP_total = 500, profit = 100, cost = 400, giving 100/400 * 100 = 25% gain. Why Other Options Are Wrong: 10% and 15%: underestimates from incorrect cost base. 20%: still too low; profit should be compared to cost, not to SP. Common Pitfalls: Treating the 20 bananas as 20% of selling price and assuming that equals the percentage gain directly. Final Answer: 25%

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