Question 1

Ravi sells a smartphone for Rs. 30,000. If he had offered a discount of 10% on this selling price, he would still have earned a profit of 35%. What is the original cost price of the smartphone?

Accepted Answer

Introduction / Context:This question blends the ideas of marked price, discount, and profit. Ravi sells a smartphone at a certain price but is asked to consider a hypothetical scenario where he gives a discount on this selling price and still makes a profit. We must work backwards from this hypothetical situation to find the true cost price of the phone. Such questions test comfort with reversing percentage calculations and dealing with multiple conditions around the same cost price. Given Data / Assumptions: Actual selling price (SP1) of the smartphone = Rs. 30,000. If Ravi had given a discount of 10% on Rs. 30,000, then the selling price in that case (SP2) would be 90% of 30,000. At this discounted selling price, Ravi would have made a profit of 35% on cost price. Let the cost price be C. We need to find C. Concept / Approach:The structure is: discounted selling price = cost price * (1 + profit%). We know the discounted selling price indirectly as 90% of the original selling price. So we first compute the hypothetical discounted price, then equate it to 1.35 * C because a 35% profit means the selling price equals 135% of cost price. Solving this equation yields the cost price. Note that the original selling price of 30,000 is not used directly to find profit; it only helps us find the hypothetical discount price. Step-by-Step Solution:Original selling price SP1 = Rs. 30,000.If a discount of 10% is offered on this, then the new selling price SP2 would be SP1 * 0.90.Compute SP2: 30000 * 0.90 = Rs. 27,000.We are told that at this price Ravi would earn a 35% profit on cost price.So SP2 = C * 1.35.Therefore, 1.35 * C = 27,000.C = 27,000 / 1.35.Compute C = Rs. 20,000.Thus, the cost price of the smartphone is Rs. 20,000. Verification / Alternative check:With cost price C = Rs. 20,000, a 35% profit implies SP2 = 1.35 * 20000 = Rs. 27,000.This SP2 is exactly 90% of Rs. 30,000, which matches the discount description.So if he had sold at Rs. 27,000, he would have a 35% profit, as required. Why Other Options Are Wrong:If C = Rs. 22,000, then 35% profit would give SP2 = 29,700, not equal to 27,000.If C = Rs. 24,000, then SP2 = 32,400, which again does not match the needed 27,000.If C = Rs. 26,000, then SP2 = 35,100, also inconsistent with the condition.Only Rs. 20,000 satisfies the relationship between discounted selling price and profit. Common Pitfalls:Some students mistakenly apply the 35% profit to the original selling price instead of the cost price.Another common error is to compute the discount on the cost price, even though the question clearly applies it to the selling price.Not carefully distinguishing between SP1 and SP2 often leads to incorrect equations and wrong answers. Final Answer:The original cost price of the smartphone is Rs. 20,000.

Question 2

By selling an article for Rs. 595, a trader gains 19%. What would be the trader's gain or loss percentage if the article were instead sold for Rs. 475?

Accepted Answer

Introduction / Context:This problem requires finding the cost price from one selling situation and then using it to evaluate another selling situation. First, the article is sold at a known profit percentage, allowing us to compute the cost price. Then, by comparing a different selling price with the same cost price, we determine whether there is a gain or a loss and by what percentage. Such problems directly test understanding of profit and loss definitions and the ability to work backwards. Given Data / Assumptions: When sold for Rs. 595, the trader gains 19%. Let the cost price be C. In a different scenario, the article is sold for Rs. 475. We must determine the new gain or loss percentage compared with C. All values are in rupees and there are no additional costs. Concept / Approach:A gain of 19% means selling price equals 119% of cost price. Thus, SP1 = 1.19 * C. From this, we can find C by dividing the known selling price by 1.19. After finding C, we compare the new selling price with C. If the new selling price is less than C, it is a loss; if greater, it is a gain. The percentage is always calculated as (difference / cost price) * 100, where difference is profit or loss amount. Step-by-Step Solution:Let cost price be C.We have 595 = 1.19 * C (because 19% gain means selling price is 119% of cost).So C = 595 / 1.19.Compute C = Rs. 500.Now, in the second scenario, selling price SP2 = Rs. 475.Compare SP2 with C: 475 is less than 500, so this is a loss.Loss amount = C − SP2 = 500 − 475 = Rs. 25.Loss percentage = (Loss / C) * 100 = (25 / 500) * 100 = 5%. Verification / Alternative check:At SP1 = Rs. 595 and C = Rs. 500, profit = 95, which is 19% of 500, so the first scenario checks out.At SP2 = Rs. 475, loss = 500 − 475 = 25, which is exactly 5% of 500.Both calculations agree with the problem statement, confirming the correctness of the result. Why Other Options Are Wrong:Gain 5% would imply a selling price greater than the cost price, which contradicts 475 being less than 500.Loss 10% would require a loss of 50, meaning a selling price of 450, not 475.Gain 10% is clearly impossible as the price is below cost.Only loss of 5% fits the calculations. Common Pitfalls:A frequent error is to assume 19% of 595 is the profit instead of understanding that 595 itself is 119% of the cost price.Some students compute the percentage based on selling price instead of cost price when evaluating loss.It is also easy to mix up whether the new price represents gain or loss if the cost price is not clearly computed first. Final Answer:If the article is sold for Rs. 475, the trader incurs a loss of 5%.

Question 3

In a business, investor B invests an amount for 15 months, while investor A invests Rs. 1,200 more than B and keeps it invested for 4 months longer than B (that is, 19 months). The total profit is Rs. 1,240, and B's share of profit is Rs. 280 less t…

Accepted Answer

Introduction / Context:This is a partnership and profit-sharing problem. The partners invest different amounts for different periods, and their profit shares are proportional to the product of capital and time. We are given the relationship between the profit shares of A and B and the fact that A invests more money for a longer duration. From the total profit and the difference in shares, we must work backwards to determine A's invested capital. Problems of this type are standard in aptitude tests, especially in the section on simple partnerships. Given Data / Assumptions: B invests some amount, say B rupees, for 15 months. A invests (B + 1,200) rupees for 19 months (which is 4 months more than B). Total profit from the business = Rs. 1,240. B's profit share is Rs. 280 less than A's profit share. Profits are shared in the ratio of (capital * time) for each partner. Concept / Approach:In simple partnership problems, the profit ratio equals the ratio of investments multiplied by the time for which the money remains invested. Let A's and B's profit shares be Pa and Pb respectively. We know that Pa + Pb = 1,240 and Pa − Pb = 280. From these two equations, we find Pa and Pb. Once we know the ratio Pa:Pb, we equate it to the ratio of (capital * time) for A and B. From there, we can solve for the unknown capital of B and hence of A. Step-by-Step Solution:Let A's profit share be Pa and B's profit share be Pb.Given: Pa + Pb = 1240 and Pa − Pb = 280.Add the equations: (Pa + Pb) + (Pa − Pb) = 1240 + 280 ⇒ 2Pa = 1520 ⇒ Pa = 760.Then Pb = 1240 − 760 = 480.So the profit ratio A : B = Pa : Pb = 760 : 480.Simplify this ratio by dividing by 40: 760/40 : 480/40 = 19 : 12.Now express the ratio of capital * time.Let B's capital be b; then A's capital = b + 1200.B's investment product = b * 15; A's investment product = (b + 1200) * 19.Thus, (b + 1200) * 19 : b * 15 = 19 : 12.This implies (b + 1200) * 19 / (b * 15) = 19 / 12.Cancel 19 from both sides: (b + 1200) / (15b) = 1 / 12.Cross multiply: 12(b + 1200) = 15b ⇒ 12b + 14400 = 15b ⇒ 3b = 14400 ⇒ b = 4800.Hence A's capital = b + 1200 = 4800 + 1200 = Rs. 6,000. Verification / Alternative check:A's investment product = 6000 * 19 = 114,000.B's investment product = 4800 * 15 = 72,000.Ratio = 114000 : 72000 = 19 : 12, which matches the profit ratio.Total profit = 1,240, and splitting in 19 : 12 gives A = 760, B = 480, with a difference of 280, consistent with the problem. Why Other Options Are Wrong:If A's capital were 7,000, then the ratio of capital * time would not simplify to 19 : 12.Similarly, 5,000 or 8,000 fail to satisfy both the total profit and the difference of 280 between profits.Only Rs. 6,000 fits all given conditions simultaneously. Common Pitfalls:Some learners mix up the given difference in profit with the difference in investments, which are not the same.Another mistake is to use 4 months instead of 19 months for A's time without adding it to B's 15 months.It is also easy to mishandle the ratio simplification and lose the factor of 19, leading to incorrect calculations. Final Answer:The amount invested by A in the business is Rs. 6,000.

Question 4

A man purchases a bullock and a cart together for Rs. 1,800. He sells the bullock at a profit of 20% and the cart at a profit of 30%. His overall profit on the combined sale is 155/6%. What was the cost price of the bullock?

Accepted Answer

Introduction / Context:This problem combines percentage profit on individual items with an overall percentage profit on their combined cost price. The man buys a bullock and a cart together, sells each at different profit rates, and is given the overall profit percentage. We are asked to find the cost price of just the bullock. This type of question is commonly used to test algebraic modeling of word problems in profit and loss. Given Data / Assumptions: Total cost price of bullock and cart together = Rs. 1,800. Bullock is sold at a profit of 20%. Cart is sold at a profit of 30%. Overall profit on the combined transaction = 155/6%. Let cost price of bullock be x and cost price of cart be 1800 − x. Concept / Approach:We use profit percentage formulas and write expressions for selling prices based on cost prices. Bullock selling price is 1.20 times its cost; cart selling price is 1.30 times its cost. The overall selling price for both items combined is then calculated using the overall profit percentage. Equating the sum of individual selling prices to the overall selling price expression gives a linear equation in x, which we solve to find the cost price of the bullock. Step-by-Step Solution:Let the cost price of the bullock be x.Then the cost price of the cart is 1800 − x.Bullock is sold at a 20% profit, so its selling price = 1.20 * x.Cart is sold at a 30% profit, so its selling price = 1.30 * (1800 − x).Overall cost = 1800.Overall profit percentage = 155/6% = 155 / 600 as a decimal ≈ 0.2583.Overall selling price = 1800 * (1 + 155/600) = 1800 * (755/600).Compute: 1800 * (755/600) = 3 * 755 = Rs. 2,265.So, 1.20x + 1.30(1800 − x) = 2265.Expand: 1.20x + 2340 − 1.30x = 2265.Combine like terms: (1.20 − 1.30)x + 2340 = 2265 ⇒ −0.10x + 2340 = 2265.So −0.10x = 2265 − 2340 = −75 ⇒ x = 750.Therefore, the cost price of the bullock is Rs. 750. Verification / Alternative check:Bullock cost = 750, selling price = 1.20 * 750 = Rs. 900.Cart cost = 1800 − 750 = 1050, selling price = 1.30 * 1050 = Rs. 1,365.Total cost = 750 + 1050 = 1800; total selling price = 900 + 1365 = 2265.Overall profit = 2265 − 1800 = 465.Profit percentage = (465 / 1800) * 100 = 25.833...%, which equals 155/6%, matching the question. Why Other Options Are Wrong:If bullock cost were Rs. 650 or Rs. 800 or Rs. 900, recomputing selling prices would not give overall profit of 155/6%.Only Rs. 750 as the bullock cost price satisfies both the individual profit conditions and the overall profit condition. Common Pitfalls:Misreading 155/6% as 155.6% instead of 155 divided by 6 is a common error.Some learners incorrectly assume equal cost division between bullock and cart instead of using variables.Others forget that the overall profit applies to the total cost, not separately to each item. Final Answer:The cost price of the bullock was Rs. 750.

Question 5

The printed price of a home theatre set is Rs. 4,950. If two successive discounts of 20% and 15% are offered on this marked price, what is the final selling price of the home theatre?

Accepted Answer

Introduction / Context:This problem is a straightforward application of successive discounts on a marked price. The home theatre has a listed price, and the seller offers two discounts, one after the other. We need to compute the final selling price after both discounts are applied. Such questions are basic in the discount and profit and loss chapter and reinforce the multiplicative nature of successive percentage changes. Given Data / Assumptions: Marked price (MP) of the home theatre = Rs. 4,950. First discount = 20% on the marked price. Second discount = 15% on the reduced price after the first discount. We need to find the final selling price. Concept / Approach:Successive discounts are not added directly; instead, each discount is applied sequentially to the current price. A discount of d% means we multiply the current price by (1 − d/100). Therefore, with discounts of 20% and 15% applied successively, the final price factor is 0.80 * 0.85. Multiplying this combined discount factor by the marked price gives the final selling price. Step-by-Step Solution:Marked price MP = Rs. 4,950.After the first discount of 20%, price becomes MP * (1 − 20/100) = 4950 * 0.80.Compute: 4950 * 0.80 = Rs. 3,960.After the second discount of 15%, price becomes 3960 * (1 − 15/100) = 3960 * 0.85.Calculate: 3960 * 0.85 = 3,960 * 85 / 100 = 336,600 / 100 = Rs. 3,366.Thus, the final selling price is Rs. 3,366. Verification / Alternative check:We can also compute the combined multiplier directly: 0.80 * 0.85 = 0.68.Final price = 4950 * 0.68.Compute: 4950 * 0.68 = 4950 * 68 / 100 = (4950 * 68) / 100 = 336,600 / 100 = Rs. 3,366.Both methods produce the same final selling price. Why Other Options Are Wrong:Rs. 6,633 and Rs. 6,363 are greater than the marked price and therefore cannot be the result of discounts.Rs. 3,636 would correspond to a different pair or order of discounts and does not match the exact calculation.Only Rs. 3,366 matches the correct compounded discount result. Common Pitfalls:A frequent mistake is to add the discounts directly (20% + 15% = 35%) and apply a single 35% discount, which is incorrect.Another error is applying the second discount to the original marked price instead of the reduced price.Students sometimes miscalculate the decimal equivalents, using 0.2 and 0.15 incorrectly. Final Answer:The final selling price of the home theatre set is Rs. 3,366.

Question 6

If the ratio of the cost price to the selling price of an article is 4 : 5, what is the profit percentage earned on the article?

Accepted Answer

Introduction / Context:This is a simple question where the ratio of cost price to selling price is given directly. From this ratio, we must compute the profit percentage. Such problems are fundamental in the profit and loss section and help reinforce the understanding of how to transform a ratio into an actual profit percentage without needing explicit rupee values. Given Data / Assumptions: Ratio of cost price (CP) to selling price (SP) = 4 : 5. This means CP : SP = 4 : 5. We assume CP and SP are positive and correspond to the same article. We need to calculate profit percentage on the basis of cost price. Concept / Approach:When a ratio CP : SP = 4 : 5 is given, it is convenient to assume CP = 4 units and SP = 5 units. Then profit = SP − CP in the same units. The profit percentage is then (Profit / CP) * 100. Because the ratio is scale-invariant, these unit values directly give the correct profit percentage even without rupee amounts. Step-by-Step Solution:Assume CP = 4 units.Then SP = 5 units, following the given ratio 4 : 5.Profit = SP − CP = 5 − 4 = 1 unit.Profit percentage = (Profit / CP) * 100 = (1 / 4) * 100.Compute: (1 / 4) * 100 = 25%.Thus, the profit percentage is 25. Verification / Alternative check:Take an example with real rupee values: let CP = Rs. 400 (scaling by 100).Then SP must be Rs. 500 to maintain the 4 : 5 ratio.Profit = 500 − 400 = Rs. 100.Profit percentage = (100 / 400) * 100 = 25%.This confirms that the ratio-based calculation is correct. Why Other Options Are Wrong:A profit percentage of 20 or 10 would require different CP : SP ratios, such as 5 : 6 or 10 : 11.0.1 is not a reasonable profit percentage in this context and clearly does not match the 4 : 5 ratio.Only 25 is compatible with a CP : SP ratio of 4 : 5. Common Pitfalls:Students may invert the ratio and mistakenly treat it as SP : CP = 4 : 5, leading to a completely different percentage.Another mistake is to forget that profit percentage is based on cost price and accidentally use SP in the denominator.Some candidates also misinterpret the options as ratios instead of percentages. Final Answer:The profit percentage earned on the article is 25%.

Question 7

An item is sold at two successive gains of 30% and 20%. If the final selling price after both gains is Rs. 31,200, what is the original cost price of the item?

Accepted Answer

Introduction / Context:This problem involves successive gains on the same item. Instead of a single profit percentage, the seller first increases the price by 30% and then further increases the new price by 20%. The final selling price after these two increases is given, and we are asked to determine the original cost price. This type of question helps build understanding of successive percentage changes and reverse calculation from selling price to cost price. Given Data / Assumptions: Let the original cost price be C. First gain = 30%, so first selling price = C * 1.30. Second gain = 20%, so final selling price = (C * 1.30) * 1.20. Final selling price after both gains = Rs. 31,200. We need to find the original cost price C. Concept / Approach:Successive percentage gains multiply as factors. A gain of 30% corresponds to multiplying the current price by 1.30. A subsequent gain of 20% corresponds to multiplying by 1.20. Together, the combined multiplier is 1.30 * 1.20. We equate this combined factor times the cost price to the known final selling price and solve for the cost price by dividing by the factor. This is a standard reverse-percentage technique. Step-by-Step Solution:Let cost price be C.After the first gain of 30%, price becomes C * 1.30.After the second gain of 20%, price becomes C * 1.30 * 1.20.Therefore, final selling price SP = C * 1.30 * 1.20.Compute combined multiplier: 1.30 * 1.20 = 1.56.We are given SP = 31,200, so 1.56 * C = 31,200.Thus C = 31,200 / 1.56.Compute C = Rs. 20,000.Hence, the original cost price of the item is Rs. 20,000. Verification / Alternative check:Starting from C = Rs. 20,000, apply 30% gain: 20,000 * 1.30 = Rs. 26,000.Then apply 20% gain on 26,000: 26,000 * 1.20 = Rs. 31,200.This matches the given final selling price, confirming that C = Rs. 20,000 is correct. Why Other Options Are Wrong:If C = 15,000, final SP would be 15000 * 1.56 = 23,400, not 31,200.If C = 22,250, final SP would be 22,250 * 1.56, which exceeds 34,000, inconsistent with the given 31,200.If C = 24,000, final SP would be 24,000 * 1.56 = 37,440, also not matching.Only C = 20,000 produces SP = 31,200. Common Pitfalls:A common mistake is to add the percentages directly (30% + 20% = 50%) and treat the final price as 150% of C, which is incorrect.Another pitfall is dividing by 1.50 instead of using the correct combined factor of 1.56.Some students also mis-handle decimals and end up with approximate values that do not match any option. Final Answer:The original cost price of the item is Rs. 20,000.

Question 8

The cost price of 25 books is equal to the selling price of 20 books of the same kind. What is the profit percentage earned on each book?

Accepted Answer

Introduction / Context:This is a classic profit and loss problem where an equality between the cost of several items and the selling price of fewer items is given. From this, we infer the relationship between cost price and selling price of a single item and compute the profit percentage. It is widely used in exams to test understanding of ratios and percentages without needing explicit rupee values. Given Data / Assumptions: Cost price of 25 books = selling price of 20 books. Let cost price per book be C. Let selling price per book be S. Total cost price of 25 books = 25C. Total selling price of 20 books = 20S. We are told that 25C = 20S. Concept / Approach:From the equality 25C = 20S, we can find the ratio S : C. Once S is expressed as a multiple of C, we can compute the profit per book as S − C. Profit percentage is then (S − C)/C * 100. Because only the ratio matters, C and S themselves need not be known; their ratio captures the entire profit behavior. Step-by-Step Solution:Given: 25C = 20S.Rearrange to find S/C: divide both sides by 5 ⇒ 5C = 4S.So S = (5/4) * C.Profit per book = S − C = (5/4)C − C = (1/4)C.Profit percentage = (Profit / C) * 100 = (1/4) * 100 = 25%.Thus, the profit percentage on each book is 25%. Verification / Alternative check:Assume C = Rs. 4 per book.Then S = (5/4) * 4 = Rs. 5 per book.Cost of 25 books = 25 * 4 = Rs. 100.Selling price of 20 books = 20 * 5 = Rs. 100.This matches the given condition, confirming the ratio is correct.Profit per book = 5 − 4 = Rs. 1, which is 25% of the cost price. Why Other Options Are Wrong:20%, 22%, and 24% would correspond to different S : C ratios and would not satisfy the equation 25C = 20S.Only a profit of 25% produces the precise relationship stated in the problem. Common Pitfalls:Some learners mistakenly treat 25 and 20 as the number of books sold at different times, instead of using them to connect CP and SP.Another pitfall is misreading the equality and forming 20C = 25S, which completely changes the ratio.A few students divide incorrectly and calculate S/C improperly, leading to wrong profit percentages. Final Answer:The profit percentage earned on each book is 25%.

Question 9

Two shopkeepers both mark a sewing machine at Rs. 700. The first shopkeeper offers successive discounts of 30% and 6%, while the second offers successive discounts of 20% and 16%. What is the difference between the two final selling prices?

Accepted Answer

Introduction / Context:This question compares two different schemes of successive discounts on the same marked price. Students must compute each shopkeeper's final selling price and then find the difference between the two. It reinforces the idea that successive discounts multiply and are not simply added, and it highlights how different discount structures can produce different effective price reductions even if the total of the percentages looks similar. Given Data / Assumptions: Marked price of the sewing machine = Rs. 700 for both shopkeepers. First shopkeeper offers two successive discounts: 30% and 6%. Second shopkeeper offers two successive discounts: 20% and 16%. We must find the absolute difference between their final selling prices. Concept / Approach:A discount of d% on a price P means the new price is P * (1 − d/100). When there are successive discounts, we multiply the factors corresponding to each discount. For example, discounts of 30% and 6% correspond to multiplying the marked price by 0.70 and then by 0.94. We compute each shopkeeper's final selling price separately using the respective compound discount factors and then subtract the smaller selling price from the larger one to find the difference. Step-by-Step Solution:Marked price MP = Rs. 700.First shopkeeper: discounts 30% and then 6%.First discount factor = 1 − 30/100 = 0.70; second factor = 1 − 6/100 = 0.94.Final selling price S1 = 700 * 0.70 * 0.94.Compute: 700 * 0.70 = 490; then 490 * 0.94 = 460.6.Second shopkeeper: discounts 20% and then 16%.Discount factors: 1 − 20/100 = 0.80 and 1 − 16/100 = 0.84.Final selling price S2 = 700 * 0.80 * 0.84.Compute: 700 * 0.80 = 560; then 560 * 0.84 = 470.4.Difference between selling prices = S2 − S1 = 470.4 − 460.6 = Rs. 9.8. Verification / Alternative check:Instead of computing intermediate values, we can directly multiply the factors with 700.For the first shopkeeper: 700 * (0.70 * 0.94) = 700 * 0.658 = 460.6.For the second shopkeeper: 700 * (0.80 * 0.84) = 700 * 0.672 = 470.4.Difference remains 470.4 − 460.6 = Rs. 9.8, confirming the earlier result. Why Other Options Are Wrong:Rs. 16.8, Rs. 22.4, and Rs. 36.4 arise from incorrect handling of percentage discounts or from assuming a single equivalent discount rather than successive ones.Only Rs. 9.8 matches the precise computed difference between S1 and S2. Common Pitfalls:A common mistake is to subtract percentage discounts (for example, 30% + 6% = 36%) and apply that directly, which ignores the compounding effect.Another error is to apply both shopkeepers' discounts to the same intermediate price instead of recalculating individually from the marked price.Rounding too early in calculations can also lead to small deviations, pushing the answer away from the correct option. Final Answer:The difference between the final selling prices offered by the two shopkeepers is Rs. 9.8.

Question 10

Twelve copies of a book are sold for Rs. 1,800, and in doing so the seller gains an amount equal to the cost price of three copies. What is the cost price of one copy of the book?

Accepted Answer

Introduction / Context:This profit and loss problem describes a situation where the total profit from selling a set of books is equal to the cost of a smaller number of those books. From this information, we are asked to find the cost price of a single copy. The language is typical of exam problems that require converting verbal profit conditions into clear algebraic equations. Given Data / Assumptions: Number of books sold = 12. Total selling price of 12 books = Rs. 1,800. Let the cost price of 1 book be C. Total cost price of 12 books = 12C. Total profit is equal to the cost price of 3 books, which is 3C. We assume all books are identical and sold at the same selling price per copy. Concept / Approach:The total profit from selling all 12 books is the difference between total selling price and total cost price. According to the question, this profit equals the cost of 3 books. Thus, (Total selling price − Total cost price) = 3C. Using this relationship, we can form an equation in C and solve for the cost price per book. Once C is known, it can be matched to the given options. Step-by-Step Solution:Let cost price of one book be C.Total cost price of 12 books = 12C.Total selling price of 12 books = Rs. 1,800.Total profit = total selling price − total cost price = 1800 − 12C.Given that this total profit equals cost price of 3 books, so 1800 − 12C = 3C.Rearrange: 1800 = 12C + 3C = 15C.Thus, C = 1800 / 15 = Rs. 120.Therefore, the cost price of one copy of the book is Rs. 120. Verification / Alternative check:If each book costs Rs. 120, the total cost of 12 books is 12 * 120 = Rs. 1,440.Total selling price is Rs. 1,800, so profit = 1800 − 1440 = Rs. 360.Cost price of 3 books at Rs. 120 each is 3 * 120 = Rs. 360.Thus, the calculated cost price satisfies the condition that profit equals cost price of 3 books. Why Other Options Are Wrong:If C = Rs. 150, then total cost would be 12 * 150 = 1,800, leaving zero profit, which contradicts the condition.Rs. 1,200 and Rs. 1,500 as cost per book are far too large and would make the total cost many times the selling price.Only Rs. 120 gives a realistic and correct solution consistent with the problem statement. Common Pitfalls:A common mistake is to misinterpret “gaining cost price of 3 copies” as selling 3 extra books rather than profit equal to 3C.Students sometimes treat 1,800 as the profit instead of total selling price.Another pitfall is forgetting to multiply the cost price by 12 when computing total cost. Final Answer:The cost price of one copy of the book is Rs. 120.

Question 11

For an article, the profit is 190% of the cost price. If the cost price increases by 10% but the selling price remains the same, then the new profit is what percentage (approximately) of the selling price?

Accepted Answer

Introduction / Context:This question explores how profit relationships change when cost price changes but selling price remains constant. Initially, profit is very high, equal to 190% of the cost price. Then the cost price increases by 10%, but the selling price does not change. We are asked to express the new profit as a percentage of the selling price instead of the cost price. This is a multi-step percentage problem that tests careful reasoning and algebraic manipulation. Given Data / Assumptions: Initial profit is 190% of the cost price. Let the original cost price be C. Thus, original profit P1 = 1.90 * C. Original selling price S = C + P1. Cost price then increases by 10% to a new cost price C2 = 1.10 * C. Selling price remains S. We need to find the new profit as a percentage of S. Concept / Approach:First, we express the original selling price in terms of C. Since profit is 190% of C, P1 = 1.90C and S = C + 1.90C = 2.90C. After increasing the cost price by 10%, the new cost price becomes 1.10C. The new profit is then S − C2. Once we express this new profit as a multiple of C, we can form the ratio (New profit / S) * 100 to get the required percentage of selling price. This requires careful handling of both old and new values in symbolic form. Step-by-Step Solution:Let original cost price be C.Given original profit P1 = 190% of C = 1.90C.Original selling price S = C + P1 = C + 1.90C = 2.90C.Now cost price increases by 10%, so new cost price C2 = 1.10C.Selling price remains S = 2.90C.New profit P2 = S − C2 = 2.90C − 1.10C = 1.80C.We must express P2 as a percentage of S.So required percentage = (P2 / S) * 100 = (1.80C / 2.90C) * 100.The C terms cancel, giving (1.80 / 2.90) * 100.Compute the fraction: 1.80 / 2.90 ≈ 0.6207.Therefore, percentage ≈ 0.6207 * 100 ≈ 62.07%.Approximately, the new profit is 62% of the selling price. Verification / Alternative check:Take a numerical example: let C = Rs. 100 for simplicity.Original profit = 190% of 100 = Rs. 190; original selling price S = 100 + 190 = Rs. 290.New cost price = 10% more than 100 = Rs. 110.New profit = S − new cost = 290 − 110 = Rs. 180.Express this as a percentage of selling price: (180 / 290) * 100 ≈ 62.07%.Rounded to the nearest integer, this is 62%, validating our algebraic solution. Why Other Options Are Wrong:54% and 73% deviate significantly from the precise ratio 180/290 and result from incorrect manipulation of percentages.163% confuses profit as a percentage of cost price with profit as a percentage of selling price.The approximation closest to the true value is 62%, which is the only correct choice. Common Pitfalls:A frequent misunderstanding is to treat the 190% profit as a percentage of selling price instead of cost price.Some learners add 10% directly to 190% to get 200% and attempt to use that for selling price calculations, which is incorrect.Others compute the new profit percentage with respect to the new cost price instead of the selling price as explicitly asked. Final Answer:After the 10% increase in cost price (with selling price unchanged), the new profit is approximately 62% of the selling price.

Question 12

In what ratio should sugar costing Rs 30 per kg be mixed with sugar costing Rs 45 per kg so that, when the mixture is sold at Rs 42 per kg, the shopkeeper earns a profit of 20% on the cost price?

Accepted Answer

Introduction / Context: This aptitude question on profit and loss and mixtures tests whether you can connect selling price, profit percentage, and weighted average cost. Two varieties of sugar are mixed and then sold at a common rate. You must determine in what ratio the cheaper and costlier sugar should be mixed so that the trader earns a 20% profit overall when selling the mixture at Rs 42 per kg. Given Data / Assumptions: Cheaper sugar costs Rs 30 per kg. Costlier sugar costs Rs 45 per kg. The mixture is sold at Rs 42 per kg. Required overall profit on cost price is 20%. We assume no wastage or extra cost of mixing. Concept / Approach: The key idea is that selling price (SP) and profit percentage determine the effective cost price (CP) of the mixture. If profit is 20%, then SP = 1.2 * CP. Knowing SP of the mixture, we first find CP per kg of the mixture. Then we treat the mixture as a weighted average of the two components with prices Rs 30 and Rs 45. The ratio in which they are mixed is obtained using the alligation or weighted average method. Step-by-Step Solution: Let CP of the mixture per kg be M. Given profit = 20%, SP = 42, so 42 = 1.2 * M. Therefore M = 42 / 1.2 = 35 rupees per kg. We now have cheaper = 30, mixture CP = 35, costlier = 45. By alligation, ratio of cheaper : costlier = (45 - 35) : (35 - 30) = 10 : 5 = 2 : 1. Verification / Alternative check: Suppose we take 2 kg of sugar at Rs 30 and 1 kg of sugar at Rs 45. The total cost is 2 * 30 + 1 * 45 = 60 + 45 = 105 rupees for 3 kg, so CP per kg = 105 / 3 = 35 rupees. If the mixture is sold at Rs 42 per kg, the profit per kg is 42 - 35 = 7 rupees. Profit percentage = (7 / 35) * 100 = 20%, which matches the requirement, confirming the ratio is correct. Why Other Options Are Wrong: The ratio 2 : 3 gives a weighted cost closer to the higher price and would not result in CP = 35. The ratio 5 : 2 gives a different weighted average cost, not equal to Rs 35. The ratio 3 : 7 heavily favors the costlier sugar and leads to a much higher CP, which cannot yield exactly 20% profit at Rs 42 per kg. Common Pitfalls: A common error is to apply alligation directly between 30 and 45 with 42 in the middle, without adjusting for the given profit percentage. Another mistake is to treat Rs 42 as the cost price instead of the selling price. Some learners also confuse the roles of cheaper and costlier components when forming the ratio and accidentally invert the ratio values. Final Answer: The required mixing ratio of sugar costing Rs 30 per kg to sugar costing Rs 45 per kg is 2 : 1.

Question 13

A dealer sells two machines for Rs 12000 each; on the first machine the dealer gains 32% and on the second machine the dealer loses 32%. What is the overall percentage profit or loss on the entire transaction?

Accepted Answer

Introduction / Context: This profit and loss question focuses on the combined effect of a given percentage profit on one item and an equal percentage loss on another item when both are sold for the same selling price. Many students assume that a 32% gain and a 32% loss cancel each other, but that is not correct because the base amounts (cost prices) are different. Given Data / Assumptions: First machine is sold for Rs 12000 with 32% profit. Second machine is sold for Rs 12000 with 32% loss. We assume there are no additional costs or taxes. We must find the net percentage profit or loss on both machines together. Concept / Approach: Profit and loss percentages are always calculated on cost price, not on selling price. When the same selling price is used but the profit and loss percentages differ, the cost prices are different for the two items. We calculate individual cost prices from the given selling prices and percentages, sum the two cost prices to get total investment, then compare with the total selling price to determine overall gain or loss percentage. Step-by-Step Solution: Let CP1 be the cost price of the first machine. Given 32% profit, 12000 = CP1 * 1.32, so CP1 = 12000 / 1.32. Let CP2 be the cost price of the second machine. Given 32% loss, 12000 = CP2 * 0.68, so CP2 = 12000 / 0.68. Compute CP1 ≈ 9090.91 and CP2 ≈ 17647.06. Total CP = CP1 + CP2 ≈ 9090.91 + 17647.06 ≈ 26737.97. Total SP = 12000 + 12000 = 24000; net loss ≈ 26737.97 - 24000 ≈ 2737.97. Loss percentage ≈ (2737.97 / 26737.97) * 100 ≈ 10.24% loss. Verification / Alternative check: We can use the standard result that if an article is sold at gain x% and another at loss x% with same selling prices, there is always an overall loss. For actual calculation, using the cost price approach as above confirms a loss of approximately 10.24%. This fits the option that clearly states 10.24% loss. Why Other Options Are Wrong: “No gain and no loss” is incorrect because the gain and loss percentages do not cancel each other due to different cost bases. “1% loss” and “18% profit” are numerically far from the calculated percentage and do not match the derived net loss of around 10.24%. Common Pitfalls: A frequent mistake is to assume that +32% and -32% balance out to zero, leading to no gain or loss. Another common error is to average the percentages, which is also wrong. Ignoring the fact that profit and loss percentage is always on cost price, not selling price, causes incorrect reasoning in such problems. Final Answer: The dealer makes an overall loss of approximately 10.24% on the entire transaction.

Question 14

If a trader makes a profit of 20% on an article, what is the ratio of the cost price to the selling price of the article, respectively?

Accepted Answer

Introduction / Context: This is a basic profit and loss question that checks whether you can convert a given profit percentage into a simple ratio between cost price and selling price. Understanding this relationship is useful because many competitive exam questions are framed in terms of ratios instead of explicit prices. Given Data / Assumptions: Profit percentage is 20%. Profit is calculated on cost price. We need a simplified ratio of cost price (CP) to selling price (SP). No actual rupee values are given, so we take CP as an assumed convenient number. Concept / Approach: By definition, profit percentage = (Profit / CP) * 100. If profit is 20%, then SP = CP + 20% of CP. That is SP = CP * (1 + 20/100) = CP * 1.2. By choosing a convenient CP value, we can represent both CP and SP as whole numbers and obtain the CP : SP ratio. Since percentage is relative, the choice of CP does not affect the final ratio. Step-by-Step Solution: Assume CP = 100 units (for convenience). Profit at 20% = 20% of 100 = 20 units. Selling price SP = CP + profit = 100 + 20 = 120 units. Thus, CP : SP = 100 : 120. Divide both terms by 20 to simplify the ratio: (100 / 20) : (120 / 20) = 5 : 6. Verification / Alternative check: We can also use direct multiplication: SP = 1.2 * CP. Treat CP = 5, then SP = 1.2 * 5 = 6. Hence CP : SP = 5 : 6, which confirms the same ratio. Any other assumed cost price will yield an equivalent ratio that simplifies to 5 : 6. Why Other Options Are Wrong: The ratio 4 : 5 corresponds to a 25% profit, not 20%. The ratio 2 : 5 implies an extreme profit that is not consistent with 20%. The ratio 3 : 4 corresponds to a profit of 33.33%, which is also incorrect for 20% profit. Therefore, only 5 : 6 correctly represents a 20% profit. Common Pitfalls: Learners sometimes reverse the ratio and write SP : CP instead of CP : SP. Others may incorrectly add 20 to both numbers instead of working with percentages. Always remember that profit percentage relates to cost price, and the ratio must be simplified after calculating SP from CP. Final Answer: The required ratio of cost price to selling price at 20% profit is 5 : 6.

Question 15

The marked price of an article is 40% more than its cost price, and a discount of 15% is allowed on the marked price. What is the final profit percentage earned by the seller?

Accepted Answer

Introduction / Context: This question involves combined concepts of marked price, discount, and profit percentage. It tests your ability to move step by step from cost price to marked price, then to selling price after discount, and finally to calculate overall profit percentage based on cost price. Such questions are common in retail and shopkeeper style word problems in aptitude exams. Given Data / Assumptions: Marked price (MP) is 40% more than cost price (CP). Discount of 15% is given on the marked price. We must find overall profit percentage based on the original cost price. There are no extra costs like transport or taxes. Concept / Approach: First, express the marked price in terms of cost price using the 40% increase. Then apply the discount on the marked price to determine the selling price. Finally, compute profit or gain percentage as (SP - CP) / CP * 100. Using a convenient assumed value for CP makes the arithmetic easier without changing the answer. Step-by-Step Solution: Assume CP = 100 units. Marked price MP = CP * (1 + 40/100) = 100 * 1.4 = 140 units. Discount = 15% of MP, so discount = 0.15 * 140 = 21 units. Selling price SP = MP - discount = 140 - 21 = 119 units. Profit = SP - CP = 119 - 100 = 19 units. Profit percentage = (19 / 100) * 100 = 19%. Verification / Alternative check: We can also treat the combined effect directly: MP = 1.4 * CP and SP = 0.85 * MP = 0.85 * 1.4 * CP = 1.19 * CP. This shows that SP is 1.19 times CP, meaning a 19% profit. Both approaches confirm the same percentage. Why Other Options Are Wrong: A 25% profit would require SP = 1.25 * CP which would be 125 units instead of 119. A 15% profit would put SP at 115 units. A 21% profit would require SP = 121 units. None of these match the calculated selling price of 119 units, so 19% is the only correct answer. Common Pitfalls: Candidates often subtract discount from cost price instead of marked price, which leads to wrong results. Another error is to forget that profit must always be calculated on cost price, not on marked price or selling price. Careless percentage calculations and skipping the simplification step also cause mistakes. Final Answer: The profit percentage earned after a 15% discount on a marked price that is 40% above cost is 19%.

Question 16

A trader allows a discount of 15% on a trolley bag whose list price is Rs 1360 and still earns a profit of 15.6%. What is the cost price, in rupees, of the trolley bag?

Accepted Answer

Introduction / Context: This question combines the ideas of list price (also called marked price), discount, and profit percentage. The aim is to work backwards from the selling price and known profit to find the original cost price. This type of question is very common in shop or retail based profit and loss problems in aptitude exams. Given Data / Assumptions: List price (marked price) of the trolley bag is Rs 1360. Discount offered on the list price is 15%. The trader earns a profit of 15.6% on the cost price. We are required to find the cost price (CP) of the trolley bag. No other expenses or taxes are involved. Concept / Approach: First, calculate the selling price (SP) after applying the 15% discount on the list price. Next, relate that selling price to the cost price using the profit percentage: SP = CP * (1 + profit percentage). Rearranging this formula gives CP = SP / (1 + profit percentage). Substituting the numbers yields the original cost price. Step-by-Step Solution: List price = Rs 1360. Discount = 15% of 1360 = 0.15 * 1360 = Rs 204. Selling price SP = list price - discount = 1360 - 204 = Rs 1156. Profit percentage = 15.6%, so SP = CP * (1 + 15.6/100) = CP * 1.156. Thus CP = SP / 1.156 = 1156 / 1.156 = Rs 1000. Verification / Alternative check: Using CP = Rs 1000, profit at 15.6% is 1000 * 0.156 = Rs 156. Then SP should be 1000 + 156 = Rs 1156. This matches the selling price obtained from applying 15% discount to the list price. Therefore, the cost price of Rs 1000 is consistent from both directions. Why Other Options Are Wrong: If CP were Rs 1005 or Rs 1050, then multiplying by 1.156 would give selling prices that are not equal to Rs 1156. Similarly, Rs 1156 as cost price would imply zero discount or incorrect profit calculations. Hence only Rs 1000 correctly satisfies both the given discount and profit data. Common Pitfalls: A common mistake is to apply the profit percentage on the list price instead of cost price. Some learners also miscalculate discount and do not correctly subtract it from the list price. Another frequent error is to add instead of dividing by the profit factor when solving for cost price. Final Answer: The cost price of the trolley bag is Rs 1000.

Question 17

Mohit sells a table at a profit of 25%. If he reduces the selling price of the same table by Rs 240, he incurs a loss of 5%. What was the initial selling price of the table, in rupees?

Accepted Answer

Introduction / Context: This profit and loss question involves two different selling prices of the same article, with a profit at the higher selling price and a loss at the lower selling price. The objective is to determine the original selling price using both profit and loss conditions. This tests algebraic formulation of profit and loss relationships. Given Data / Assumptions: At the initial selling price, Mohit makes a profit of 25%. If he reduces the selling price by Rs 240, he makes a loss of 5% on cost price. The cost price of the table is assumed constant in both scenarios. We are required to find the initial selling price in rupees. Concept / Approach: Let the unknown cost price be CP. First selling price SP1 gives 25% profit, so SP1 = CP * 1.25. Second selling price SP2 gives a loss of 5%, so SP2 = CP * 0.95. We know that SP2 is less than SP1 by Rs 240, so SP1 - SP2 = 240. Substituting in terms of CP gives an equation that can be solved easily for CP and then for SP1. Step-by-Step Solution: Let CP = x rupees. Initial selling price SP1 = x * 1.25. Reduced selling price SP2 = x * 0.95. Given SP1 - SP2 = 240, so 1.25x - 0.95x = 240. This simplifies to 0.30x = 240, hence x = 240 / 0.30 = 800 rupees. Now SP1 = 1.25 * 800 = Rs 1000. Verification / Alternative check: With CP = Rs 800 and SP1 = Rs 1000, profit = 1000 - 800 = 200 rupees, which is 25% of 800. For SP2, subtract 240 from SP1: 1000 - 240 = 760 rupees. Loss = 800 - 760 = 40 rupees, which is 5% of 800. Both conditions match the given data, confirming that the original selling price is Rs 1000. Why Other Options Are Wrong: If SP1 were 800, 1040, or 1120, then either the profit or the loss or the difference of Rs 240 would not be satisfied simultaneously. Only when SP1 is 1000 and CP is 800 do both profit and loss percentages and the Rs 240 difference hold true. Common Pitfalls: Many students incorrectly assume CP is 1000 or directly subtract percentages instead of relating them via algebra. Another mistake is to apply the 25% and 5% changes successively to selling price instead of to cost price, which leads to wrong equations. Final Answer: The initial selling price of the table was Rs 1000.

Question 18

Rajeev sells a machine for Rs 55 lakhs at a loss. If instead he had sold it for Rs 67 lakhs, his gain would have been five times the former loss. What is the cost price of the machine in lakhs of rupees?

Accepted Answer

Introduction / Context: This problem tests your understanding of how profit and loss relate to cost price and selling price in two hypothetical scenarios. Rajeev sells the same machine at two different prices: in one case he incurs a loss, and in another case he earns a gain that is a multiple of that loss. The goal is to set up an equation using the relationship between these two situations to find the unknown cost price. Given Data / Assumptions: First selling price (SP1) is Rs 55 lakhs, which results in a loss. Second selling price (SP2) is Rs 67 lakhs, which results in a gain. The gain at SP2 is five times the loss at SP1. The cost price (CP) of the machine is the same for both scenarios. We need CP in lakhs of rupees. Concept / Approach: Loss is CP minus SP when SP is less than CP. Gain is SP minus CP when SP is greater than CP. Let the loss at Rs 55 lakhs be L. Then L = CP - 55. The gain at Rs 67 lakhs is 67 - CP. Given that gain equals five times the loss, we write 67 - CP = 5 * (CP - 55). This equation in CP can be solved to obtain the cost price. Step-by-Step Solution: Let CP = x lakhs. Loss at SP1 (55 lakhs) is L = x - 55. Gain at SP2 (67 lakhs) is G = 67 - x. Given G = 5L, so 67 - x = 5(x - 55). Expand the right side: 67 - x = 5x - 275. Bring like terms together: 67 + 275 = 5x + x, so 342 = 6x. Thus x = 342 / 6 = 57 lakhs. Verification / Alternative check: If CP is 57 lakhs, loss at SP1 is 57 - 55 = 2 lakhs. Gain at SP2 is 67 - 57 = 10 lakhs. The gain of 10 lakhs is exactly five times the loss of 2 lakhs, which matches the condition given. So CP = 57 lakhs is fully consistent. Why Other Options Are Wrong: A cost price of 65, 78, or 49 lakhs would not satisfy the relationship that gain at 67 lakhs is five times the loss at 55 lakhs. Checking each quickly shows that the resulting gains and losses do not match the required multiple. Common Pitfalls: Many test takers incorrectly write the equation with reversed signs or treat gain and loss as percentages when the question uses absolute rupee values. Another common error is to try to average the two selling prices, which does not use the five times relationship and produces a wrong answer. Final Answer: The cost price of the machine is Rs 57 lakhs.

Question 19

A trader has 6 quintals of wheat. He sells part of it at a profit of 7% and the remainder at a profit of 17%, so that his overall profit percentage is 11%. How many kilograms of wheat does he sell at 17% profit?

Accepted Answer

Introduction / Context: This mixture type profit and loss question involves selling different parts of the same commodity at two different profit percentages. The overall gain percentage is given, and you must determine the quantity sold at the higher profit rate. This is a standard weighted average or allegation type problem commonly seen in aptitude exams. Given Data / Assumptions: Total wheat = 6 quintals = 6 * 100 = 600 kg. Part of the wheat is sold at 7% profit. The rest is sold at 17% profit. Overall profit percentage on the entire wheat is 11%. We need to find the quantity sold at 17% profit, in kilograms. Concept / Approach: Let the quantity sold at 7% profit be x kg, so the quantity at 17% profit is 600 - x kg. If the cost price per kg is the same for all wheat, the effective profit percentage is a weighted average of individual profit percentages, weighted by the respective quantities. Equating the weighted average to 11% allows us to solve for x and then obtain the quantity sold at 17% profit. Step-by-Step Solution: Let the cost price per kg be 1 unit (for simplicity). Let quantity at 7% profit be x kg; then quantity at 17% profit is 600 - x kg. Total cost = 600 * 1 = 600 units. Total selling price = 1.07x + 1.17(600 - x). Given overall profit = 11%, so total SP = 1.11 * 600 = 666 units. Thus, 1.07x + 1.17(600 - x) = 666. Simplify: 1.07x + 702 - 1.17x = 666 → -0.10x + 702 = 666 → 0.10x = 36 → x = 360 kg. Hence quantity at 17% profit = 600 - 360 = 240 kg. Verification / Alternative check: We can also apply the alligation method on profit rates. Putting 7% and 17% with mean 11% gives ratio of quantities as (17 - 11) : (11 - 7) = 6 : 4 = 3 : 2. So out of total 600 kg, quantity at 7% is (3/5) * 600 = 360 kg and at 17% is (2/5) * 600 = 240 kg, confirming the result. Why Other Options Are Wrong: 360 kg is the quantity at 7% profit, not at 17%. Quantities 120 kg or 480 kg at 17% are not consistent with the ratio required to obtain an overall 11% gain. Only 240 kg satisfies both the total quantity and the overall profit condition. Common Pitfalls: A usual mistake is to assume half the quantity is sold at each rate or to average the percentages arithmetically without considering quantities. Another error is mixing up which quantity corresponds to which profit rate when using the alligation cross differences. Final Answer: The trader sells 240 kg of wheat at 17% profit.

Question 20

Raheem sells a machine for Rs 48 lakhs at a loss. If instead he had sold it for Rs 60 lakhs, his gain would have been five times the former loss. What is the cost price of the machine in lakhs of rupees?

Accepted Answer

Introduction / Context: This question is structurally similar to earlier profit and loss problems where a single cost price is linked to two different selling prices, one giving a loss and another giving a gain. The relation that the gain is a multiple of the loss allows us to write an algebraic equation and determine the cost price. Given Data / Assumptions: First selling price SP1 = Rs 48 lakhs, giving a loss. Second selling price SP2 = Rs 60 lakhs, giving a gain. The gain at Rs 60 lakhs is five times the loss at Rs 48 lakhs. The cost price CP is the same in both cases. Required: CP in lakhs of rupees. Concept / Approach: When SP is less than CP, loss = CP - SP. When SP is greater than CP, gain = SP - CP. Let the loss at SP1 be L. Then L = CP - 48. The gain at SP2 is 60 - CP and is given to be 5L. Using the equation 60 - CP = 5 * (CP - 48), we can solve for CP directly. Step-by-Step Solution: Let CP = x lakhs. Loss at SP1 = x - 48. Gain at SP2 = 60 - x. Given 60 - x = 5(x - 48). Expand: 60 - x = 5x - 240. Rearrange: 60 + 240 = 5x + x → 300 = 6x. So x = 300 / 6 = 50 lakhs. Verification / Alternative check: With CP = 50 lakhs, loss at 48 lakhs is 50 - 48 = 2 lakhs. Gain at 60 lakhs is 60 - 50 = 10 lakhs. Here gain is exactly five times the loss (10 = 5 * 2), which matches the condition. Therefore CP = 50 lakhs is consistent with both selling prices. Why Other Options Are Wrong: If CP were 58 or 69.6 or 42 lakhs, then the loss at 48 lakhs and gain at 60 lakhs would not satisfy the exact 5 times relation. Quick substitution shows that the ratio of gain to loss would be different from five in those cases. Common Pitfalls: A typical mistake is misinterpreting the sentence and writing the equation with loss equal to five times gain instead of the other way around. Another common error is to treat the given values as profit percentages, when in fact the question uses absolute rupee amounts for gain and loss. Final Answer: The cost price of the machine is Rs 50 lakhs.

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