Question 1

A shopkeeper sells dried apricots at Rs 1310 per kilogram and incurs a loss of 13%. If he raises the selling price to Rs 1441 per kilogram, what will be his new percentage gain or loss?

Accepted Answer

Introduction / Context: This question is similar in structure to other profit and loss problems where a new selling price changes the magnitude of loss or profit. Initially, dried apricots are sold at a certain loss percent. After increasing the selling price, the shopkeeper still may have a loss, but usually a smaller one. The task is to compute the new percentage gain or loss after the price change, using the fact that cost price remains fixed. Given Data / Assumptions: Initial selling price SP1 = Rs 1310 per kg. Initial loss = 13%. New selling price SP2 = Rs 1441 per kg. We must determine whether SP2 leads to profit or loss, and its percentage. Cost price per kg is constant between both scenarios. Concept / Approach: We again use the loss formula to find cost price: Loss 13% means SP1 = 0.87 * CP. Thus CP = SP1 / 0.87. Compare SP2 with CP using percentage formula: (SP2 - CP) / CP * 100. A positive result gives profit; a negative result gives loss. Step-by-Step Solution: Step 1: Let cost price per kg = CP. Step 2: Loss of 13% implies SP1 = 0.87 * CP. Step 3: SP1 = 1310, so 1310 = 0.87 * CP. Step 4: CP = 1310 / 0.87. Step 5: Express 0.87 as 87 / 100, so CP = 1310 * 100 / 87 = 131000 / 87. Step 6: New selling price SP2 = 1441. Step 7: Profit or loss fraction = (SP2 - CP) / CP. Step 8: Compute SP2 - CP in fractional form: SP2 - CP = 1441 - 131000 / 87. Step 9: Convert 1441 to denominator 87: 1441 = 1441 * 87 / 87 = 125367 / 87. Step 10: Difference = (125367 - 131000) / 87 = -5633 / 87, which is negative, so it is a loss. Step 11: Loss fraction = (5633 / 87) / (131000 / 87) = 5633 / 131000 ≈ 0.043. Step 12: Loss percentage ≈ 0.043 * 100 = 4.3% loss. Verification / Alternative check: Approximate CP numerically: CP ≈ 1310 / 0.87 ≈ Rs 1505.75. Difference between CP and SP2 = 1505.75 - 1441 ≈ 64.75. Loss percentage ≈ 64.75 / 1505.75 * 100 ≈ 4.3%. This confirms that even with the increased selling price, the shopkeeper still faces a small loss of about 4.3% per kilogram. Why Other Options Are Wrong: 8.6 percent loss: This is larger than the computed loss and does not correspond to the new price. 4.3 percent gain: Incorrect because SP2 is still lower than CP, so a gain is impossible. 8.6 percent gain: Also impossible because a selling price below cost price can never create profit. Only 4.3 percent loss matches both exact fractional and approximate numerical calculations. Common Pitfalls: One frequent error is taking 1310 as cost price and computing profit directly from 1441. This ignores the initial loss percentage and leads to incorrect conclusions. Another mistake is to treat the 13% loss as being on the selling price instead of on cost price. Always remember: loss percentage is defined relative to cost price unless otherwise stated. Correctly reconstructing CP from SP1 is the key step. Final Answer: At the new selling price of Rs 1441 per kilogram, the shopkeeper incurs a 4.3 percent loss on dried apricots.

Question 2

A shopkeeper sells 22 pairs of Skechers shoes and earns a total profit equal to the selling price of 6 pairs of the same shoes. What is his profit percentage on each pair?

Accepted Answer

Introduction / Context: This question is about interpreting a verbal description of profit in terms of number of items sold. The shopkeeper's total profit from selling 22 pairs of shoes is equal to the selling price of 6 pairs. From this information, you must derive the profit percentage per pair. This style of question is common in profit and loss topics and emphasizes translation of words into algebraic equations. Given Data / Assumptions: Number of pairs sold = 22. Total profit from selling these 22 pairs equals the selling price of 6 pairs. Let SP be the selling price per pair. Let CP be the cost price per pair. We assume all pairs are identical and sold at the same price. Concept / Approach: We translate the condition into an equation: Total selling price for 22 pairs = 22 * SP. Total cost price for 22 pairs = 22 * CP. Total profit = 22 * SP - 22 * CP. Given: Total profit = selling price of 6 pairs = 6 * SP. We solve for the ratio SP / CP and then compute profit percentage = ((SP - CP) / CP) * 100. Step-by-Step Solution: Step 1: Let SP = selling price per pair, CP = cost price per pair. Step 2: Total SP for 22 pairs = 22 * SP. Step 3: Total CP for 22 pairs = 22 * CP. Step 4: Total profit = 22 * SP - 22 * CP. Step 5: Given condition: total profit = selling price of 6 pairs = 6 * SP. Step 6: So 22 * SP - 22 * CP = 6 * SP. Step 7: Rearrange: 22SP - 6SP = 22CP. Step 8: 16SP = 22CP. Step 9: Divide both sides by 16CP: SP / CP = 22 / 16 = 11 / 8. Step 10: Profit per pair = SP - CP = (11 / 8)CP - CP = (3 / 8)CP. Step 11: Profit percentage = (Profit / CP) * 100 = (3 / 8) * 100 = 37.5%. Verification / Alternative check: Assign a simple numerical CP, for example CP = Rs 8: Then SP = (11 / 8) * 8 = Rs 11. Profit per pair = 11 - 8 = Rs 3. Profit percentage = 3 / 8 * 100 = 37.5%. Total profit on 22 pairs = 22 * 3 = Rs 66. Selling price of 6 pairs = 6 * 11 = Rs 66. The total profit equals the selling price of 6 pairs, matching the given condition and confirming that the profit percentage is correct. Why Other Options Are Wrong: 27.2 percent, 54.4 percent, and 16.9 percent do not correspond to SP / CP = 11 / 8. If any of these percentages were used, the profit from 22 pairs would not exactly equal the selling price of 6 pairs. Only 37.5 percent yields the exact algebraic match to the problem statement. Common Pitfalls: A common mistake is to misinterpret the phrase "profit equal to the selling price of 6 pairs" as meaning the profit percentage is 6 / 22 of something, which is incorrect. Another error is to set equations based on per pair values incorrectly, forgetting to multiply by the number of pairs. Always translate the given condition into a precise mathematical equation using total cost and total selling price for all items sold. Final Answer: The shopkeeper's profit percentage on each pair of Skechers shoes is 37.5 percent.

Question 3

A vendor buys bananas at the rate of 2 for Re 1 and sells them at the rate of 10 for Rs 7. What is his overall profit or loss percentage on the bananas?

Accepted Answer

Introduction / Context: This question checks your understanding of unit cost and unit selling price when items are bought and sold in different group sizes. The vendor buys bananas in one ratio (2 for Re 1) and sells them in another ratio (10 for Rs 7). You need to convert both to a common per unit basis to find the profit or loss percentage. Such questions are classic in profit and loss sections of aptitude tests. Given Data / Assumptions: Buying rate: 2 bananas for Re 1. Selling rate: 10 bananas for Rs 7. We assume no wastage and that all bananas purchased are sold. We must find the profit or loss percentage. Concept / Approach: The easiest method is to find cost price and selling price per banana: CP per banana = total cost / number of bananas when buying. SP per banana = total selling price / number of bananas when selling. Then profit per banana = SP per banana - CP per banana. Profit percentage = (Profit / CP per banana) * 100. Since the numbers are small and simple, calculations are straightforward. Step-by-Step Solution: Step 1: Compute cost price per banana. Step 2: 2 bananas cost Re 1, so CP per banana = 1 / 2 = Rs 0.50. Step 3: Compute selling price per banana. Step 4: 10 bananas sell for Rs 7, so SP per banana = 7 / 10 = Rs 0.70. Step 5: Profit per banana = SP - CP = 0.70 - 0.50 = Rs 0.20. Step 6: Profit percentage = (0.20 / 0.50) * 100. Step 7: 0.20 / 0.50 = 0.4. Step 8: Profit percentage = 0.4 * 100 = 40%. Verification / Alternative check: Consider buying and selling the same number of bananas, for example 10 bananas: To buy 10 bananas at 2 for Re 1: for every 2 bananas, cost is Re 1, so 10 bananas cost 5 rupees. To sell 10 bananas at the given selling rate: 10 bananas sell for Rs 7. Profit on 10 bananas = 7 - 5 = Rs 2. Cost price of 10 bananas = Rs 5, profit percentage = 2 / 5 * 100 = 40%. This check confirms the same answer using a batch approach instead of per-unit calculations. Why Other Options Are Wrong: 40 percent loss: Incorrect because selling price per banana (Rs 0.70) is clearly higher than cost price (Rs 0.50). 28.57 percent gain: This percentage often comes from mixing up ratios, but does not match the computed profit ratio of 0.4. 28.5 percent loss: Also clearly wrong because there is a gain, not a loss. Only 40 percent gain matches both per unit and batch-based calculations exactly. Common Pitfalls: A common mistake is to compare the total buy and sell numbers directly without adjusting for quantity, for example comparing 2 for 1 with 10 for 7 in a confusing way. Always convert both rates to the same base, usually cost and selling price per single unit or for a common number of units like 10 or 20. Careless handling of decimal values like 0.5 and 0.7 can also cause errors, so work slowly and check your arithmetic. Final Answer: The vendor makes a 40 percent gain on the bananas.

Question 4

Puneet buys 240 articles and labels each with the same marked price. He sells 160 articles initially at 20% discount on the labelled price. Then he sells rest articles at an additional discount of 25% on the discounted price. Thus, he gets total of …

Accepted Answer

Concept & Profit Calculation: The core concept involves relating Cost Price (CP), Selling Price (SP), and Marked Price (MP). Profit percentage is always calculated on the base Cost Price: Profit % = \frac{SP - CP}{CP} × 100 Step-by-Step Solution: • Let the Cost Price (CP) of 1 article be 1 unit. Total CP for 240 articles = 240. • Let the Marked Price (MP) of each article be M. • The total Selling Price (SP) is ₹Z. Since there is an overall profit of 10%, the total SP must be 110% of the total CP: Total SP = 240 × 1.10 = 264 units. • Now, let's calculate the SP based on the discounts: • First 160 articles are sold at a 20% discount on MP. SP_1 = 160 × (M × (1 - 0.20)) = 160 × 0.8M = 128M • The remaining 80 articles are sold at an *additional* 25% discount on the *already discounted* price (0.8M). New Discounted Price = 0.8M × (1 - 0.25) = 0.8M × 0.75 = 0.6M SP_2 = 80 × 0.6M = 48M • Total SP in terms of M = 128M + 48M = 176M. • Equate the two total SP values: 176M = 264 M = (264/176) = 1.5 units. • The Marked Price (MP) is 1.5 per article, while the Cost Price (CP) is 1 per article. • If no discount is offered, the new SP equals the MP (1.5). • Profit = 1.5 - 1 = 0.5. • Profit % = ((0.5/1)) × 100% = 50%. Exam Strategy & Shortcut: Assume the CP of one article is 100 to avoid decimals. Total CP = 24000. Total SP = 26400 (10% profit). Equating the sales: (160 × 80% × M) + (80 × 60% × M) = 26400 \implies 128M + 48M = 26400 \implies 176M = 26400 \implies M = 150. If CP is 100 and MP is 150, the profit percentage without discount is simply 50%. Common Pitfall: A common error is applying the second 25% discount to the original marked price rather than the already discounted price (successive discount). "Additional discount on the discounted price" means it compounds on the 80% value, becoming 60% overall. Final Answer: Therefore, the correct answer is 50%.

Question 5

Accepted Answer

Concept & Equation Solving Strategy: This is a comprehensive Data Interpretation puzzle integrating quadratic equations, number series, and profit & loss concepts. We must decode the underlying variables (n, m, a, b) first. Key formulas: Profit = SP - CP Discount\ % = (MP - SP/MP) × 100 Step-by-Step Solution: 1. Find n (from quadratic equation): • Equation: K^2 - 32K + 252 = 0 • Roots are 14 and 18 (since 14 × 18 = 252 and 14 + 18 = 32). • The larger root is 18. Therefore, n = 4 × 18 = 72. 2. Find m (from sequence): • Sequence: 140, 136, 161, x, 329, -200 • Differences: 136 - 140 = -4 (-2^2) • 161 - 136 = 25 (+5^2) • Notice the pattern of alternating signs and squares of alternate prime numbers (2, 5, 11, 17, 23). • Next difference should be -11^2 = -121. So, x = 161 - 121 = 40. • Verify with next: 40 + 17^2 = 40 + 289 = 329. (Matches perfectly) • Therefore, m = 2 × 40 = 80. 3. Find a (from Article T): • CP_T = 4a + (80/2) = 4a + 40 • MP_T = 13a - (72/2) + 6 = 13a - 30 • Markup is 1280 \implies MP_T - CP_T = 1280 • (13a - 30) - (4a + 40) = 1280 \implies 9a - 70 = 1280 \implies 9a = 1350 \implies a = 150. 4. Find b (from Article S): • Markup of T (1280) is 28% more than Profit on S. • Profit_S = (1280/1.28) = 1000. • SP_S = 5(80) + 7(72) + 4(150) + 296 = 400 + 504 + 600 + 296 = 1800. • CP_S = SP_S - Profit_S = 1800 - 1000 = 800. • From table, CP_S = 5b - m - n - 48 = 5b - 80 - 72 - 48 = 5b - 200. • Equating: 5b - 200 = 800 \implies 5b = 1000 \implies b = 200. 5. Evaluate Question for L: • CP_T = 4(150) + 40 = 640. • CP_P is 87.5% ((7/8)) more than CP_T \implies CP_P = 640 × (15/8) = 1200. • Profit_P = 40% \implies SP_P = 1200 × 1.4 = 1680. • MP_P = 10.8(200) + 3(80) = 2160 + 240 = 2400. • Discount given = 2400 - 1680 = 720. Discount % = ((720/2400)) × 100 = 30%. • Given Discount % = 2L - 210 \implies 2L - 210 = 30 \implies 2L = 240 \implies L = 120. 6. Verify Options: • I. 1.5m = 1.5(80) = 120 (True) • II. b - n - 8 = 200 - 72 - 8 = 120 (True) • III. 2.4(b - a) = 2.4(200 - 150) = 2.4(50) = 120 (True) • IV. 240 
eq 120 (False) Exam Strategy & Shortcut: By finding the base values (a=150, b=200, m=80, n=72) accurately on your scratchpad first, both associated questions collapse into standard arithmetic. Memorizing fractional equivalents (like 87.5% = (7/8)) saves massive calculation time on step 5. Common Pitfall: A frequent error is misinterpreting the number series. Noticing that differences (-4, 25) are squares of prime numbers with alternating signs is non-intuitive. Always test alternating logic if simple differences yield no standard geometric/arithmetic progression. Final Answer: Therefore, the correct answer is I, II, and III only.

Question 6

Accepted Answer

Concept & Profit Logic Strategy: This problem utilizes the decoded variables from the central puzzle to connect the Marked Price of one article to the Cost Price of another. The core formula utilized here connects Discounts to Percentages: Discount\ % = (Discount\ Amount/Marked\ Price) × 100 Step-by-Step Solution: 1. Recall Decoded Base Variables: • From decoding the initial notes (see previous explanations): a = 150, b = 200, m = 80, n = 72. 2. Calculate Parameters for T: • MP_T = 13a - (n/2) + 6 • MP_T = 13(150) - (72/2) + 6 = 1950 - 36 + 6 = 1920. 3. Relate to Article R: • The problem states MP_T is ₹80 less than CP_R. • Therefore, CP_R = MP_T + 80 = 1920 + 80 = 2000. • From the main table, Article R has a 20% profit. • SP_R = CP_R × 1.20 = 2000 × 1.2 = 2400. 4. Apply Discount Data for R: • Given discount amount = ₹400. • MP_R = SP_R + Discount = 2400 + 400 = 2800. • Actual Discount % = ((400/2800)) × 100 = (100/7)%. • We are given that the discount % is ((5L/14))%. • Equating the two: (5L/14) = (100/7) \implies 5L = 200 \implies L = 40. Exam Strategy & Shortcut: Instead of recalculating variable a from scratch, store derived variables immediately in a table on your rough sheet during Data Interpretation blocks. From there, tracing the path MP_T \rightarrow CP_R \rightarrow SP_R \rightarrow MP_R is a highly linear arithmetic chain that takes less than 30 seconds to execute. Common Pitfall: A very common trap is applying the discount directly on the Selling Price rather than the Marked Price. Always remember that MP = SP + Discount, and the discount percentage is universally calculated with respect to the MP as the base denominator. Final Answer: Therefore, the correct answer is 40.

Question 7

Accepted Answer

Concept & Profit and Loss Strategy: Deciphering the base variables from the shared Data Interpretation notes provides the Cost Price of S and Marked Price of Q. We apply the standard fractional relationships for profit and discount to find the Cost Price of Q. SP = MP × (1 - Discount%) CP = (SP/1 + Profit%) Step-by-Step Solution: 1. Recall Base Variables: • From decoding the initial puzzle (solving the quadratic and number sequence): n = 72, m = 80, a = 150, b = 200. • From Note (ii) and (iii), CP_S is found to be 800. 2. Analyze Article Q: • MP_Q = 12a - n = 12(150) - 72 = 1800 - 72 = 1728. • From Note (iii), Discount on Q = 16.66% \approx (1/6). • SP_Q = MP_Q × (1 - (1/6)) = 1728 × (5/6) = 288 × 5 = 1440. 3. Calculate CP of Q: • Given Profit% is thrice the Discount%: Profit% = 3 × 16.66% = 50% = (1/2). • SP_Q = CP_Q × (1 + (1/2)) = 1.5 × CP_Q. • 1440 = 1.5 × CP_Q \implies CP_Q = (1440/1.5) = 960. 4. Find the Difference: • Difference = CP_Q - CP_S = 960 - 800 = 160. Exam Strategy & Shortcut: Recognizing 16.66% as (1/6) and 50% as (1/2) is crucial for speed. Instead of complex decimals, use fraction multipliers: SP = MP × (5/6) and CP = SP × (2/3). This turns the calculation into mental math: 1728 × (5/6) = 1440 \implies 1440 × (2/3) = 960. Common Pitfall: A common mistake is applying the 50% profit calculation as a markdown from the Selling Price (i.e., finding 50% of 1440 and subtracting). Remember that profit percentage is always based on the Cost Price: SP = CP × (1 + P%). Final Answer: Therefore, the correct answer is 160.

Question 8

Accepted Answer

Concept & Profit and Loss Strategy: This question requires calculating individual profit and discount percentages for articles T and S using the derived variables a, b, m, n. Key formulas: Profit\ % = (SP - CP/CP) × 100 Discount\ % = (MP - SP/MP) × 100 Step-by-Step Solution: 1. Recall Base Variables: • a = 150, b = 200, m = 80, n = 72. • From Note (iii), SP_S = 5(80) + 7(72) + 4(150) + 296 = 1800. 2. Analyze Article T (Find L%): • CP_T = 4a + (m/2) = 4(150) + (80/2) = 600 + 40 = 640. • MP_T = 13a - (n/2) + 6 = 13(150) - (72/2) + 6 = 1950 - 36 + 6 = 1920. • Discount on T = (b - a)% = (200 - 150)% = 50%. • SP_T = MP_T × (1 - 0.5) = 1920 × 0.5 = 960. • Profit = SP_T - CP_T = 960 - 640 = 320. • Profit% (L%) = (320/640) × 100 = 50%. Thus, L = 50. 3. Analyze Article S (Find D%): • MP_P = 10.8b + 3m = 10.8(200) + 3(80) = 2160 + 240 = 2400. • Given MP_S is ₹400 less than MP_P: MP_S = 2400 - 400 = 2000. • Discount on S = MP_S - SP_S = 2000 - 1800 = 200. • Discount% (D%) = (200/2000) × 100 = 10%. Thus, D = 10. 4. Final Calculation: • We need to find (L% - D%) = 50% - 10% = 40%. Exam Strategy & Shortcut: Notice that SP_T (960) is exactly halfway between MP_T (1920) and 0, making the discount 50%. Since CP_T is 640, the profit of 320 is exactly half of 640, making profit 50%. Spotting these halving relationships bypasses the need for the formal percentage formula. Common Pitfall: Be careful not to mix up the absolute values (L, D) with their percentage representations. The question asks for the difference in the calculated percentages. Always cross-check the base (MP for discount, CP for profit). Final Answer: Therefore, the correct answer is 40%.

Question 9

Mr Kashyap purchased an airconditioner for ₹ 12000 and sold it for ₹ 15000. What was the profit percentage? (Bank Recruitment, 2010)

Accepted Answer

Concept & Profit Percentage: Profit occurs when the Selling Price (SP) is greater than the Cost Price (CP). The profit percentage is always calculated based on the Cost Price. Profit % = ( \frac{SP - CP}{CP} ) × 100 Step-by-Step Solution: Given: • Cost Price (CP) = ₹ 12000 • Selling Price (SP) = ₹ 15000 Calculation: 1. Find the total profit amount by subtracting CP from SP. Profit = 15000 - 12000 = 3000 2. Substitute the values into the profit percentage formula. Profit % = ( (3000/12000) ) × 100 3. Simplify the fraction to find the final percentage. Profit % = (1/4) × 100 = 25% Exam Strategy & Shortcut: Look at the ratio of the numbers to save time. 12000 and 15000 are in the ratio of 4:5. An increase from 4 to 5 is an increase of 1 over a base of 4. Since 1/4 = 25%, you can arrive at the answer instantly without writing zeros. Common Pitfall: A common mistake is calculating the profit percentage over the Selling Price (3000/15000 = 20%), which leads to choosing the incorrect option (b). Final Answer: Therefore, the correct answer is 25.

Question 10

Mohanlal purchased a TV set for ₹ 12500 and spent ₹ 300 on transportation and ₹ 800 on installation. At what price should he sell it so as to earn an overall profit of 15%? (Specialist Officers, 2009)

Accepted Answer

Concept & Effective Cost Price: Overhead expenses such as transportation, repairs, and installation must be added to the initial purchase price to determine the true, effective Cost Price (CP). Profit is always calculated on this effective CP. Effective CP = Purchase Price + Overhead Expenses Step-by-Step Solution: Given: • Purchase Price of TV = ₹ 12500 • Transportation Cost = ₹ 300 • Installation Cost = ₹ 800 • Desired Profit = 15% Calculation: 1. Find the total effective Cost Price by adding all expenses. Effective CP = 12500 + 300 + 800 = 13600 2. Calculate the required selling price to achieve a 15% profit. SP = Effective CP × (1 + (15/100)) SP = 13600 × 1.15 3. Break the calculation down for simplicity: calculate 10% and 5% of 13600. 10% of 13600 = 1360 5% of 13600 = 680 4. Add the profit to the effective CP. Total Profit = 1360 + 680 = 2040 SP = 13600 + 2040 = 15640 Since ₹ 15640 is not among the given options (a, b, c, or d), the correct choice is "None of these". Exam Strategy & Shortcut: Use the Unit Digit trick to verify options quickly. 136 × 115. The last significant digit of 6 × 5 is 0. Move to the next digit: (6 × 1) + (3 × 5) = 6 + 15 = 21. So the tens digit before the zeros is a 4 (because 13600 × 15% \rightarrow 136 × 15 = 2040). 13600 + 2040 = 15640. You can quickly see none of the specific numerical options match. Common Pitfall: Forgetting to include the overhead expenses in the cost price and calculating the 15% profit purely on the ₹ 12500 purchase price (12500 × 1.15 = 14375), which is intentionally provided as distractor option (a). Final Answer: Therefore, the correct answer is (e) None of these.

Question 11

Alfred buys an old scooter for ₹ 4700 and spends ₹ 800 on its repairs. If he sells the scooter for ₹ 5800, his gain percent is

Accepted Answer

Concept & True Cost Price: Before calculating profit or loss percentages, any money spent on repairs, maintenance, or upgrades immediately after purchase must be added to the raw purchase price to establish the "True" or "Effective" Cost Price. Gain % = ( \frac{SP - True CP}{True CP} ) × 100 Step-by-Step Solution: Given: • Purchase Price = ₹ 4700 • Repair Cost = ₹ 800 • Selling Price (SP) = ₹ 5800 Calculation: 1. Find the True Cost Price (CP). True CP = 4700 + 800 = 5500 2. Calculate the gain (profit). Gain = SP - True CP = 5800 - 5500 = 300 3. Calculate the gain percentage based on the True CP. Gain % = ((300/5500)) × 100 4. Simplify the fraction. Gain % = (300/55) = (60/11) 5. Convert the improper fraction to a mixed number. (60/11) = 5 with a remainder of 5 = 5(5/11)% Exam Strategy & Shortcut: Whenever dealing with numbers ending in double zeros (300, 5500), immediately mentally strike them out to simplify the ratio to 3/55. Then multiply by 100: 300/55 \rightarrow 60/11. Knowing your fraction-to-mixed-number conversions makes 60/11 instantly recognizable as 5(5/11)%. Common Pitfall: The most common mistake is ignoring the repair costs and using ₹ 4700 as the denominator. This would result in a gain of 1100 / 4700, leading to a completely incorrect percentage. Always consolidate costs first. Final Answer: Therefore, the correct answer is (b) 5(5/11)%.

Question 12

A shopkeeper purchased 70 kg of potatoes for ₹ 420 and sold the whole lot at the rate of ₹ 6.50 per kg. What will be his gain percent? (S.S.C., 2007)

Accepted Answer

Concept & Unit Price Method: Instead of calculating the total Selling Price for all items, it is often faster to find the Cost Price and Selling Price of a single unit. The gain percentage remains the same regardless of quantity. Gain % = ( \frac{SP per unit - CP per unit}{CP per unit} ) × 100 Step-by-Step Solution: Given: • Total Cost Price (CP) for 70 kg = ₹ 420 • Selling Price (SP) per kg = ₹ 6.50 Calculation: 1. Find the Cost Price (CP) of 1 kg of potatoes. CP per kg = (420/70) = 6 2. Calculate the gain per kg. Gain = SP per kg - CP per kg = 6.50 - 6 = 0.50 3. Calculate the gain percentage based on the CP per kg. Gain % = ((0.50/6)) × 100 4. Simplify the expression. Gain % = (50/6) = (25/3) 5. Convert the improper fraction to a mixed fraction. (25/3) = 8(1/3)% Exam Strategy & Shortcut: By identifying the per-unit costs quickly (420/70 = 6), you see the ratio of profit to cost is 0.5/6, which is 1/12. Memorizing standard fraction-to-percentage conversions ensures you know 1/12 = 8(1/3)% instantly, saving calculation time. Common Pitfall: A common mistake is calculating the total Selling Price (70 × 6.50 = 455), which adds an unnecessary multiplication step that increases the chance of a calculation error before finding the difference (455 - 420 = 35). Both methods work, but per-unit is faster. Final Answer: Therefore, the correct answer is 8(1/3)%.

Question 13

Sam purchased 20 dozens of toys at the rate of ₹ 375 per dozen. He sold each one of them at the rate of ₹ 33. What was his percentage profit?

Accepted Answer

Concept & Consistent Units: To calculate profit percentage, the Cost Price (CP) and Selling Price (SP) must be for the exact same quantity. If CP is given in dozens and SP in single units, convert both to a single unit (or both to a dozen) before calculating. Profit % = ( \frac{SP - CP}{CP} ) × 100 Step-by-Step Solution: Given: • CP per dozen = ₹ 375 • Quantity purchased = 20 dozens (Note: This is extra information not needed for the percentage calculation if we use per-unit values). • SP per toy = ₹ 33 • 1 dozen = 12 toys Calculation: 1. Calculate the Cost Price (CP) for a single toy. CP per toy = (375/12) = 31.25 2. Calculate the profit per toy. Profit = SP - CP = 33 - 31.25 = 1.75 3. Calculate the profit percentage based on the CP per toy. Profit % = ((1.75/31.25)) × 100 4. Eliminate decimals by multiplying numerator and denominator by 100. Profit % = ((175/3125)) × 100 5. Simplify the fraction by dividing by 25. Profit % = ((7/125)) × 100 = (700/125) 6. Divide to find the final percentage. (700/125) = 5.6 Exam Strategy & Shortcut: Instead of finding per-unit cost, convert SP to per-dozen to avoid dividing 375 by 12. SP per dozen = 33 × 12 = 396. Profit per dozen = 396 - 375 = 21. Profit % = (21 / 375) × 100. Divide 21 and 375 by 3 to get (7 / 125) × 100 = 700 / 125 = 5.6%. This avoids decimals completely until the final step. Common Pitfall: Calculating the total CP (20 × 375 = 7500) and total SP (20 × 12 × 33 = 7920) creates large numbers that are harder to subtract and divide (420/7500), costing valuable time on an exam. Final Answer: Therefore, the correct answer is 5.6.

Question 14

If an article is sold at 200 percent profit, then the ratio of its cost price to its selling price will be

Accepted Answer

Concept & Cost to Selling Price Ratio: Profit is calculated based on the Cost Price (CP). When the profit is given as a percentage, you can assume the CP is 100% (or 1 part) to easily deduce the Selling Price (SP). SP = CP + Profit Step-by-Step Solution: • Step 1: Assume a value for the Cost Price (CP). Let it be x. • Let CP = x • Step 2: Express the profit in terms of x. • Profit = 200% of CP = ((200/100)) × x = 2x • Step 3: Calculate the Selling Price (SP). • SP = CP + Profit • SP = x + 2x = 3x • Step 4: Find the ratio of Cost Price to Selling Price. • Ratio = \frac{CP}{SP} = (x/3x) • Ratio = 1 : 3 Exam Strategy & Shortcut: Always let CP = 100 for simple percentage problems. If Profit = 200, then SP = CP + Profit = 100 + 200 = 300. The ratio of CP : SP is simply 100 : 300, which reduces instantly to 1 : 3. Common Pitfall: A common mistake is assuming that "200 percent profit" means the Selling Price is twice the Cost Price. This confuses "profit" with "selling price". If SP is twice CP, the profit is only 100%. A 200% profit means the SP is three times the CP. Final Answer: Therefore, the correct answer is 1 : 3.

Question 15

If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is

Accepted Answer

Concept & Profit Percentage: The relationship between Cost Price (CP) and Selling Price (SP) can be used directly from their ratio to find the profit or loss. Profit % = (\frac{SP - CP}{CP}) × 100 Step-by-Step Solution: • Step 1: Let the common ratio multiplier be x. • Cost Price (CP) = 10x • Selling Price (SP) = 11x • Step 2: Calculate the profit. • Profit = SP - CP = 11x - 10x = 1x • Step 3: Calculate the percentage of profit. • Profit % = ((1x/10x)) × 100 • Profit % = ((1/10)) × 100 = 10% Exam Strategy & Shortcut: When given a ratio, you can ignore the variable x entirely and treat the ratio numbers as actual values. Assume CP = ₹ 10 and SP = ₹ 11. The profit is ₹ 1. The profit percentage is simply (1/10) × 100 = 10%. Common Pitfall: A common mistake is placing the Selling Price (11) in the denominator instead of the Cost Price (10), which would lead to an incorrect calculation of (1/11) \approx 9.09%. Final Answer: Therefore, the correct answer is 10.

Question 16

A trader sells an article and loses $12 \frac{1}{2}\%$. The ratio of cost price to the selling price is

Accepted Answer

Concept & Fractional Equivalents: Understanding the fractional equivalent of standard percentages makes ratio calculations instantaneous. Loss is calculated on the Cost Price (CP). SP = CP - Loss Step-by-Step Solution: • Step 1: Convert the loss percentage to a fraction. • 12 (1/2)% = (25/2)% = (25/200) = (1/8) • Step 2: Interpret the fraction. • A loss of (1/8) means for every 8 units of Cost Price, there is a loss of 1 unit. • Let CP = 8 units. • Loss = 1 unit. • Step 3: Calculate the Selling Price (SP). • SP = CP - Loss = 8 - 1 = 7 units. • Step 4: Determine the required ratio of Cost Price to Selling Price. • Ratio = CP : SP = 8 : 7 Exam Strategy & Shortcut: Memorize that 12.5% is exactly (1/8). This immediately tells you that the SP is 1 - (1/8) = (7/8) of the CP. Therefore, the ratio of CP to SP is simply 8 : 7. Common Pitfall: Pay close attention to the order requested in the question. Students often calculate the ratio correctly but accidentally choose 7 : 8 (which is SP to CP) instead of the requested CP to SP (8 : 7). Final Answer: Therefore, the correct answer is 8 : 7.

Question 17

A shopkeeper buys 144 eggs at 90 paise each. On the way 20 eggs were broken. He sold the remaining eggs at ₹ 1.20 each. The percentage gain or loss is

Accepted Answer

Concept & Total Cost vs. Total Revenue: To find the true overall profit or loss percentage, you must compare the Total Cost Price incurred (for all items, regardless of condition) against the Total Selling Revenue generated (from the items actually sold). Overall % = ( \frac{Total Revenue - Total Cost}{Total Cost} ) × 100 Step-by-Step Solution: • Step 1: Calculate the Total Cost Price (CP). • Total eggs bought = 144 • Price per egg = 90 paise = ₹ 0.90 • Total CP = 144 × 0.90 = ₹ 129.60 • Step 2: Calculate the saleable inventory. • Broken eggs = 20 • Remaining eggs = 144 - 20 = 124 eggs • Step 3: Calculate the Total Selling Price (SP). • Selling price per egg = ₹ 1.20 • Total SP = 124 × 1.20 • Total SP = 124 × (6/5) = (744/5) = ₹ 148.80 • Step 4: Determine Gain or Loss Amount. • Since Total SP (148.80) > Total CP (129.60), there is a gain. • Gain = 148.80 - 129.60 = ₹ 19.20 • Step 5: Calculate Gain Percentage. • Gain % = ((19.20/129.60)) × 100 • Remove decimals: ((192/1296)) × 100 • Simplify fraction: Divide by 4 \rightarrow (48/324); Divide by 12 \rightarrow (4/27) • Gain % = (400/27) \approx 14.814...% • Rounding to one decimal place, the gain is 14.8%. Exam Strategy & Shortcut: Work purely in ratios to avoid large decimals. Total CP = 144 × 9 = 1296 (working in units of 10 paise to keep numbers clean). Total SP = 124 × 12 = 1488. Ratio of CP : SP = 1296 : 1488. Divide by 24 \rightarrow 54 : 62 \rightarrow 27 : 31. A jump from 27 to 31 is an increase of 4. (4/27) × 100 \approx 14.8%. Common Pitfall: Calculating the profit per egg by comparing the initial 90 paise to the final ₹1.20 while completely ignoring the sunk cost of the 20 broken eggs. You must use aggregate totals. Final Answer: Therefore, the correct answer is 14.8% gain.

Question 18

Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of ₹ 1100. How much did he spend on repairs if he made a profit of 20%?

Accepted Answer

Concept & Base Cost Logic: In profit and loss, "Cost" refers to the initial purchase price, and the "Total Cost Price" includes the purchase price plus repair overheads. Profit is calculated on the Total Cost Price. Step-by-Step Solution: • Define Variables: • Let the original purchase cost of the scooter be C. • Cost of repairs = 10% of C = 0.10C. • Total Cost Price (CP_{total}) = Purchase Cost + Repair Cost = C + 0.10C = 1.10C. • Relate Profit Percentage to Profit Value: • Given Profit % = 20%. • Given Actual Profit = ₹ 1100. • We know: Profit = Profit % × CP_{total} • 1100 = 0.20 × 1.10C • 1100 = 0.22C • Solve for the Unknowns: • C = (1100/0.22) = (110000/22) = 5000. • The original purchase cost is ₹ 5000. • The amount spent on repairs is 10% of ₹ 5000 = ₹ 500. Exam Strategy & Shortcut: Work directly with ratios. The total cost represents 110% of the initial price. The profit is 20% of this total cost, which equals 22% of the initial price (1.1 × 0.2 = 0.22). If 22% equals 1100, then 10% (the repair cost) is strictly proportional. (1100/22) × 10 = 50 × 10 = 500. Common Pitfall: A common error is confusing the initial purchase cost with the total investment (which includes repairs). If you calculate 20% profit on C alone instead of 1.1C, you will get incorrect numbers. Final Answer: Therefore, the correct answer is ₹ 500.

Question 19

If an article is sold for ₹ $x$, there is a loss of $15\%$. If the same article is sold for ₹ $y$, there is a profit of $15\%$. The ratio of $(y - x)$ to $(y + x)$ is            (Hotel Mgmt, 2010)

Accepted Answer

Concept & Proportional Relations of Selling Price: When an article is sold at a loss or a profit, the selling price can be expressed as a percentage of the Cost Price (CP). A 15% loss means the selling price is 85% of the CP, while a 15% profit means it is 115% of the CP. The ratio of any two expressions involving these selling prices will be independent of the actual Cost Price. Selling Price = CP × (1 \pm \frac{Profit/Loss %}{100}) Step-by-Step Solution: • Let the Cost Price (CP) of the article be 100 units. • Given: Selling for ₹ x results in a 15% loss. • Therefore, x = 100 - 15 = 85 units. • Given: Selling for ₹ y results in a 15% profit. • Therefore, y = 100 + 15 = 115 units. • We need to find the ratio of (y - x) to (y + x). • First, calculate (y - x): 115 - 85 = 30. • Second, calculate (y + x): 115 + 85 = 200. • Form the ratio: (y - x/y + x) = (30/200). • Simplify the ratio by dividing both numerator and denominator by 10: (3/20). • The final ratio is 3 : 20. Exam Strategy & Shortcut: Instead of writing out 100 or using a variable like C, directly use the percentages. x = 85% of CP y = 115% of CP Ratio = (115 - 85/115 + 85) = (30/200) = (3/20) = 3 : 20. This avoids defining explicit variables and jumps straight to the solution. Common Pitfall: A common error is to set up a complex algebraic equation for CP involving x and y and trying to solve for variables independently. Since the question asks for a ratio, the absolute value of CP will always cancel out. Final Answer: Therefore, the correct answer is 3 : 20.

Question 20

If selling price is doubled, the profit triples. Find the profit percent.

Accepted Answer

Concept & Algebraic Formulation of Profit Conditions: When the relationships between changes in Selling Price (SP) and Profit (P) are given, translating these proportional changes into basic algebraic equations helps isolate the relationship between SP and Cost Price (CP). Profit (P) = Selling Price (SP) - Cost Price (CP) Step-by-Step Solution: • Let the Cost Price be C. • Let the original Selling Price be S. • The original Profit is P = S - C. • Given: The selling price is doubled. So, New Selling Price = 2S. • Given: The profit triples. So, New Profit = 3P. • We know the new profit is also equal to the new selling price minus the original cost price. • Therefore, New Profit = 2S - C. • Equate the two expressions for New Profit: 3P = 2S - C. • Substitute the original definition of P (S - C) into the equation: 3(S - C) = 2S - C. • Expand the left side: 3S - 3C = 2S - C. • Rearrange to solve for S: 3S - 2S = 3C - C \Rightarrow S = 2C. • Now we know the original Selling Price is twice the Cost Price. • Find the original Profit Percentage: Profit % = ((S - C/C)) × 100. • Substitute S = 2C: Profit % = ((2C - C/C)) × 100 = ((C/C)) × 100 = 100%. Exam Strategy & Shortcut: Use a test case based on options. If profit percent is 100%, then SP is twice the CP (e.g., CP = 10, SP = 20, Profit = 10). Double the SP: New SP = 40. New Profit = 40 - 10 = 30. Original profit was 10, new profit is 30. It tripled! The condition holds perfectly. Common Pitfall: Forgetting to substitute the initial relationship (P = S - C) back into the newly formed equation (3P = 2S - C) often leads to a dead end with too many variables and no way to isolate the ratio of S to C. Final Answer: Therefore, the correct answer is 100.

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