Question 1

What is the effective single discount equivalent to two successive discounts of 20% and 25% on an article?

Accepted Answer

Introduction / Context: Here we are dealing with two successive discounts and asked to find a single discount that produces the same final selling price. Many people initially think that discounts simply add, but that is incorrect because each discount is applied to a reduced base. Understanding effective discount is important in retail mathematics and competitive exam questions dealing with price reductions. Given Data / Assumptions: First discount = 20 percent. Second discount = 25 percent, applied after the first discount. We need the equivalent single discount on the original marked price. We can assume a convenient marked price, for example 100 units, because results are based on percentages. Concept / Approach: After a 20 percent discount, 80 percent of the original price remains, which is a factor of 0.80. After a further 25 percent discount, the customer pays 75 percent of the already reduced price, a factor of 0.75. The overall remaining fraction is the product 0.80 * 0.75. The effective discount D_eq is found by comparing this final fraction with the original whole, using the relation final fraction = 1 - D_eq / 100. Solving for D_eq gives the effective discount percentage. Step-by-Step Solution: Assume marked price = 100 units. After a 20 percent discount, remaining price = 100 * (1 - 0.20) = 100 * 0.80 = 80 units. After an additional 25 percent discount, remaining price = 80 * (1 - 0.25) = 80 * 0.75 = 60 units. So final price after both discounts is 60 units out of the original 100 units. Thus the total reduction = 100 - 60 = 40 units. Effective discount percentage = (40 / 100) * 100 = 40 percent. Verification / Alternative check: Using the remaining fraction method, we can confirm the same result. Remaining fraction after both discounts = 0.80 * 0.75 = 0.60. Then 1 - D_eq / 100 = 0.60, implying D_eq / 100 = 0.40, so D_eq = 40 percent. This method shows that the effective discount is independent of the initial assumed marked price and is purely a result of the given percentage reductions. Why Other Options Are Wrong: An effective discount of 45 percent would imply a final price of 55 units, but our calculation shows that the final price is 60 units. A 50 percent effective discount would reduce the price to 50 units, which is too low. A 60 percent discount would leave only 40 units to be paid, which is much smaller than 60. Only 40 percent agrees with the computed overall effect of both discounts. Common Pitfalls: The main mistake is to simply add the two discounts and state that the effective discount is 45 percent (20 percent + 25 percent). This overlooks the fact that the second discount is applied to an already reduced price, not to the original marked price. Another error is mixing up remaining fractions with discount fractions. To avoid these, always multiply the remaining fractions, find the final fraction of the original price, and compute the single discount as one minus this fraction expressed as a percentage. Final Answer: The effective single discount equivalent to successive discounts of 20 percent and 25 percent is 40%.

Question 2

What is the value of 20% of 500% of 50?

Accepted Answer

Introduction / Context: This is a basic but important percentage composition problem. It involves applying one percentage to the result of another percentage applied to a number. Questions of this type build comfort with nested percentage operations and reinforce the fact that percentage of a percentage is equivalent to multiplication of their decimal forms. Given Data / Assumptions: We need to compute 20 percent of 500 percent of 50. All percentages are taken in the usual sense: x percent means x / 100 times the quantity. The operations are applied sequentially: first compute 500 percent of 50, then take 20 percent of that result. Concept / Approach: To find 500 percent of 50, we note that 500 percent corresponds to 500 / 100 = 5 times the original number. So 500 percent of 50 is 5 * 50. After that, to find 20 percent of the result, we multiply by 20 / 100 = 0.20. Overall, the expression is 0.20 * (5 * 50). We can also combine the percentages into a single factor: (20 / 100) * (500 / 100) times 50. This equals (0.20 * 5) * 50. Step-by-Step Solution: First compute 500 percent of 50. 500 percent = 500 / 100 = 5 as a multiplier. So 500 percent of 50 = 5 * 50 = 250. Now compute 20 percent of this result. 20 percent = 20 / 100 = 0.20. So 20 percent of 250 = 0.20 * 250. Compute 0.20 * 250 = 50. Therefore, 20 percent of 500 percent of 50 equals 50. Verification / Alternative check: Alternatively, we can combine all operations in one expression: (20 / 100) * (500 / 100) * 50. This equals (0.20 * 5) * 50 = 1 * 50 = 50. Since both step by step computation and combined computation give the same result, we are confident that the answer is correct. This method also shows that percentages behave like ordinary multiplicative factors when chained together. Why Other Options Are Wrong: A value of 0.5 would arise from misplacing decimal points or mistakenly dividing instead of multiplying. A result of 5000 would come from multiplying 500 percent and 50 directly and then adding an extra factor, which is incorrect. A result of 500 would correspond to 20 percent of 2500 or 200 percent of 250, not the expression given here. Only 50 fits the correct chain of operations as described in the problem. Common Pitfalls: Learners sometimes misinterpret 500 percent as 500 divided by 100 twice, or they forget that 500 percent means five times the number. Others may apply 20 percent to the original 50 directly, ignoring the intermediate result. To avoid these issues, follow the order of operations exactly as stated: first apply 500 percent to 50, then apply 20 percent to that result. Converting each percentage to a decimal multiplier and multiplying in the correct order keeps the process clear and error free. Final Answer: The value of 20 percent of 500 percent of 50 is 50.

Question 3

The number 29 is 0.8% of which number?

Accepted Answer

Introduction / Context: This question is an example of reversing a percentage. Instead of finding a percentage of a number, we know a value and the percentage it represents of some unknown number. This is common in topics such as finance, statistics, and data interpretation, where we often know a part and its percentage share, and we must find the total. Given Data / Assumptions: 29 is equal to 0.8 percent of some number, which we call N. 0.8 percent means 0.8 / 100 in decimal form. We need to find the value of N such that 0.8 percent of N = 29. Concept / Approach: If x percent of N equals a given number V, then we can write the equation (x / 100) * N = V. To find N, we rearrange the equation as N = V * 100 / x. Here x = 0.8 and V = 29. Keep in mind that 0.8 percent is a small fraction, so the original number N must be quite large relative to 29. Substituting the values into the formula lets us quickly compute N. Step-by-Step Solution: Let the required number be N. We are given that 0.8 percent of N equals 29. By definition, 0.8 percent of N = (0.8 / 100) * N. So, (0.8 / 100) * N = 29. This implies N = 29 * 100 / 0.8. Compute 29 * 100 = 2900. Now divide 2900 by 0.8: 2900 / 0.8 = 3625. Therefore, 29 is 0.8 percent of 3625. Verification / Alternative check: To verify, calculate 0.8 percent of 3625 and confirm that the result is 29. Express 0.8 percent as 0.008. Then 0.008 * 3625 = 29. This perfect match shows that the computed value of N is correct. Any other number would not yield 29 when 0.8 percent of it is taken. Why Other Options Are Wrong: If N were 1450, then 0.8 percent of 1450 would be 0.008 * 1450 = 11.6, not 29. For N = 7250, 0.8 percent would be 0.008 * 7250 = 58, which is double the required value. For N = 10875, 0.8 percent would be 87, which is even larger. Only 3625 produces 29 when 0.8 percent of it is calculated. Common Pitfalls: One pitfall is misreading 0.8 percent as 8 percent, which would use 0.08 instead of 0.008 and lead to a much smaller N. Another common error is dividing 29 by 0.8 and forgetting to multiply by 100, or incorrectly multiplying by 0.8 instead of dividing. A careful setup of the equation (percentage / 100) * N = value, followed by correct algebraic inversion, helps avoid such mistakes. Final Answer: The number of which 29 is 0.8 percent is 3625.

Question 4

The price of a fan is decreased by 40% and its sales increase by 50%. What is the overall percentage change in revenue?

Accepted Answer

Introduction / Context: This question relates price changes and sales volume changes to the total revenue of a seller. When price per unit decreases but the quantity sold increases, the final effect on revenue depends on the product of the new price and the new quantity. This kind of analysis frequently appears in economics and business mathematics, particularly when evaluating the impact of discounts or promotions. Given Data / Assumptions: Initial price of the fan is P (unknown but not needed explicitly). Initial quantity sold is Q units. Price decreases by 40 percent, so new price is lower. Sales volume increases by 50 percent, so new quantity is higher. We must find the net percentage change in revenue (price * quantity). Concept / Approach: Revenue is given by R = price * quantity. Let initial revenue be R0 = P * Q. After a 40 percent price decrease, the new price is P * (1 - 0.40) = 0.60 * P. After a 50 percent increase in quantity, the new quantity is Q * (1 + 0.50) = 1.50 * Q. So new revenue R1 = 0.60 * P * 1.50 * Q = 0.90 * P * Q. This means the new revenue is 90 percent of the original revenue, resulting in a 10 percent decrease overall. We can express the percentage change as (R1 - R0) / R0 * 100. Step-by-Step Solution: Let initial price be P and initial quantity be Q. Initial revenue R0 = P * Q. Price decreases by 40 percent, so new price = P * (1 - 0.40) = 0.60 * P. Sales increase by 50 percent, so new quantity = Q * (1 + 0.50) = 1.50 * Q. New revenue R1 = (0.60 * P) * (1.50 * Q). Compute the factor: 0.60 * 1.50 = 0.90. So R1 = 0.90 * P * Q = 0.90 * R0. This means the new revenue is 90 percent of the original revenue. Percentage change in revenue = (R1 - R0) / R0 * 100 = (0.90R0 - R0) / R0 * 100. Compute (0.90R0 - R0) / R0 = -0.10, so percentage change = -10 percent. Thus, revenue decreases by 10 percent. Verification / Alternative check: We can verify with simple numbers. Suppose the original price P = 100 and quantity Q = 10. Then R0 = 100 * 10 = 1000. New price after 40 percent reduction is 60. New quantity after 50 percent increase is 15. New revenue R1 = 60 * 15 = 900. The decrease in revenue is 1000 - 900 = 100, which is 10 percent of 1000. This confirms the 10 percent decrease result. Why Other Options Are Wrong: A 15 percent increase or decrease would imply new revenue at 115 percent or 85 percent of the original, which does not match the factor 0.90 we derived. A 10 percent increase would imply revenue of 110 percent of the original, contradicting the fact that we clearly have 0.90 times the previous revenue. Only a 10 percent decrease correctly represents the net effect of the 40 percent price cut and 50 percent rise in quantity sold. Common Pitfalls: Some students mistakenly subtract 40 percent and add 50 percent to get a net 10 percent increase, which is incorrect because price and quantity affect revenue multiplicatively, not additively. Others may forget to convert percentage changes into decimal multipliers before multiplying. To avoid mistakes, always treat each percentage change as a multiplicative factor, multiply the factors, and then compare the product with 1 to determine the net percentage change. Final Answer: The overall revenue experiences a 10% decrease.

Question 5

The marked price of an item is Rs. 400. The discount is 6% on buying 1 item and 24% on buying 4 items. Rachita buys 5 items in total. What is the effective discount percentage on her total bill?

Accepted Answer

Introduction / Context: This question tests understanding of effective discount when different units of the same item are sold at different discount rates. Rachita buys some items with a small discount and some items with a larger discount. We are asked to find one overall discount percentage on the entire marked price value of all items combined. This is similar to calculating a weighted average of discounts based on the marked price contribution of each group of items. Given Data / Assumptions: Marked price (MP) per item = Rs. 400. Discount on buying 1 item = 6 percent. Discount on buying 4 items together = 24 percent. Rachita buys 1 item at 6 percent discount and 4 items at 24 percent discount, total 5 items. We must find the effective discount percentage on the total marked price of 5 items. Concept / Approach: We first compute the total marked price for all 5 items, then compute the total amount actually paid after applying the different discounts to the respective groups. The difference between total marked price and total paid amount gives the total discount in rupees. The effective discount percentage is then (total discount / total marked price) * 100. This is effectively a weighted average discount with weights equal to the marked price contributions of each group of items. Step-by-Step Solution: Marked price per item = Rs. 400. Total items bought by Rachita = 5. Total marked price for 5 items = 5 * 400 = 2000. She buys 1 item at 6 percent discount. Marked price for that 1 item = 400, discount = 6 percent of 400 = 0.06 * 400 = 24, so she pays 400 - 24 = 376. She buys 4 items at 24 percent discount. Marked price for 4 items = 4 * 400 = 1600, discount = 24 percent of 1600 = 0.24 * 1600 = 384, so she pays 1600 - 384 = 1216. Total amount paid = 376 + 1216 = 1592. Total discount in rupees = total marked price - total amount paid = 2000 - 1592 = 408. Effective discount percentage = (408 / 2000) * 100 = 20.4 percent. Verification / Alternative check: We can also think of the effective discount as the ratio of total discount to total marked price. Since the calculations above give 408 as total discount and 2000 as total marked price, the fraction is 0.204. Converting to percentage gives 0.204 * 100 = 20.4 percent. This matches our direct computation, confirming internal consistency. Any other effective discount value would not match the computed payment of Rs. 1592. Why Other Options Are Wrong: An effective discount of 34 percent would mean she pays only 66 percent of 2000, that is 1320, which is less than the 1592 she actually pays. A discount of 12.8 percent would imply a total discount of 256, not 408. A discount of 23.25 percent would give a total discount of 465, which is larger than the calculated discount. Only 20.4 percent matches the actual total discount she receives on the combined purchase. Common Pitfalls: Many students incorrectly average the two discount percentages directly (for example, (6 percent + 24 percent) / 2), ignoring the fact that the number of items and total marked value are different for each discount. Others mistakenly average based on the count of items without considering the same marked price per item, which in this case would give the same result for counts but is conceptually confusing. The safe method is always to work in rupees: compute total marked price, compute total amount paid with actual discounts, and then calculate the effective discount from the overall difference. Final Answer: The effective discount on Rachita's total purchase is 20.4 percent.

Question 6

Two students appeared for an examination. One scored 13 marks more than the other and his marks were 76% of the sum of their marks. What were the marks obtained by each student?

Accepted Answer

Introduction / Context: This problem combines basic algebra with percentages. We are given a relationship between the marks of two students in terms of their difference and the fact that the higher mark is a certain percentage of the sum of both marks. The aim is to set up equations and solve for the individual marks. Such questions are standard in aptitude tests and help practice translating verbal conditions into algebraic expressions. Given Data / Assumptions: There are two students; let their marks be x and y, with x greater than y. The higher scoring student scored 13 marks more than the other, so x = y + 13. The higher mark x is equal to 76 percent of the sum of both marks, that is 76 percent of (x + y). We must find the pair of marks that satisfies these conditions. Concept / Approach: We translate the information into two equations. First, x = y + 13 expresses the difference in marks. Second, x = 0.76 * (x + y) captures the percentage relation. Solving these two equations simultaneously will yield the values of x and y. We can express x in terms of y from the first equation and substitute into the second equation, reducing everything to a single variable. After solving for y, we find x and then check whether the values satisfy the conditions and match one of the option pairs. Step-by-Step Solution: Let the marks of the higher scoring student be x and the other student be y. Given: x = y + 13. Given: x is 76 percent of the sum of their marks, so x = 0.76 * (x + y). Substitute x = y + 13 into x = 0.76 * (x + y). So y + 13 = 0.76 * ((y + 13) + y) = 0.76 * (2y + 13). Expand the right side: 0.76 * (2y + 13) = 1.52y + 9.88. Set up the equation: y + 13 = 1.52y + 9.88. Bring terms with y to one side: y - 1.52y = 9.88 - 13. Compute: -0.52y = -3.12, so y = -3.12 / -0.52 = 6. Now find x: x = y + 13 = 6 + 13 = 19. Therefore, the two students scored 19 and 6 marks respectively. Verification / Alternative check: Check both conditions with x = 19 and y = 6. Difference: 19 - 6 = 13, which satisfies the first condition. Sum of marks: 19 + 6 = 25. Now compute 76 percent of 25: 0.76 * 25 = 19. This equals the higher mark, so the second condition is also satisfied. Thus the pair (19, 6) is fully consistent with the problem statement. Why Other Options Are Wrong: For 34 and 21, difference is 13 but 76 percent of their sum 55 equals 41.8, not 34. For 102 and 89, difference is 13 but 76 percent of 191 is 145.16, which does not match 102. For 92 and 79, difference is also 13, but 76 percent of 171 is 129.96, not 92. Only the pair 19 and 6 satisfies both the difference condition and the 76 percent sum condition. Common Pitfalls: A common mistake is to interpret 76 percent of the sum incorrectly, such as using only one of the marks in the sum or writing 0.76 * x instead of 0.76 * (x + y). Others may fail to use both equations together and try to guess answers from options without verification. To avoid errors, always write both conditions clearly as equations, substitute one into the other, and solve systematically. Checking the final values against the original conditions is an essential final step. Final Answer: The two students obtained marks of 19 and 6 respectively.

Question 7

An item is sold at a 25% discount and the buyer also receives 10% cashback on the amount paid. What is the effective discount percentage on the marked price?

Accepted Answer

Introduction / Context: This question involves two types of benefits given to a buyer: a discount on the marked price and a cashback on the amount actually paid. The effective discount is the total reduction in net cost to the buyer, expressed as a percentage of the original marked price. This type of mixed benefit scenario is common in modern retail promotions and is a useful application of percentage calculations. Given Data / Assumptions: Marked price (MP) of an item is assumed as a convenient value, say 100 units, since we work with percentages. There is a 25 percent discount on the marked price at the time of purchase. The buyer then receives 10 percent cashback on the amount paid after the discount. We must find the effective discount percentage relative to the original marked price. Concept / Approach: First, apply the 25 percent discount to the marked price to find the initial payment. Then apply the 10 percent cashback to this payment amount. The net amount actually borne by the buyer is payment minus cashback. The effective discount is equal to marked price minus net payment, divided by marked price, multiplied by 100. Using a convenient marked price of 100 makes the calculations very straightforward, and the percentage result is independent of the assumed value. Step-by-Step Solution: Assume marked price MP = 100 units. First discount = 25 percent, so amount of discount = 25 percent of 100 = 25 units. Price after discount = 100 - 25 = 75 units. Cashback rate = 10 percent of the amount paid (which is 75 units). Cashback amount = 10 percent of 75 = 7.5 units. Net amount actually paid by the buyer = 75 - 7.5 = 67.5 units. Total effective discount in units = marked price - net payment = 100 - 67.5 = 32.5. Effective discount percentage = (32.5 / 100) * 100 = 32.5 percent. Verification / Alternative check: We can express the process via multipliers. After a 25 percent discount, the payable fraction of the marked price is 0.75. A 10 percent cashback on this payment means the buyer effectively pays 0.90 of 0.75 of the marked price, so effective payment factor = 0.75 * 0.90 = 0.675. The net payment is 67.5 percent of the marked price. Therefore, effective discount = 100 percent - 67.5 percent = 32.5 percent, confirming our earlier calculation. Why Other Options Are Wrong: An effective discount of 35.75 percent or 35 percent would correspond to different net payment factors that are not equal to 0.675. A discount of 12.5 percent is far too small and ignores the substantial combined effect of the original discount and cashback. Only 32.5 percent aligns with the actual net cost to the buyer after both benefits are applied. Common Pitfalls: One typical mistake is to simply add 25 percent and 10 percent to conclude a 35 percent discount. This is incorrect because the 10 percent cashback is computed on the reduced price, not on the original marked price. Another error is to deduct cashback directly from the marked price without passing through the discounted price. The correct approach is always to follow the chronological order: apply discount first, then compute cashback on the resulting payment, and finally compare the net amount paid with the original marked price to find the effective discount. Final Answer: The effective discount on the marked price is 32.5 percent.

Question 8

A dealer allows a discount of 15%. A customer pays Rs. 318.75 for an article. At what price is the article listed (what is the marked price)?

Accepted Answer

Introduction / Context: This is a straightforward reverse percentage problem involving discount and marked price. We know the discount percentage and the final selling price after discount, and we must find the original marked price before the discount was applied. This type of question is common in commerce and aptitude exams and tests the ability to invert a percentage reduction. Given Data / Assumptions: Discount rate = 15 percent on the marked price. Selling price (SP) after discount = Rs. 318.75. Marked price (MP) is unknown and must be determined. Discount is calculated on the marked price, not on some other value. Concept / Approach: If the discount is 15 percent, then the customer pays (100 percent - 15 percent) = 85 percent of the marked price. In decimal form, this is 0.85 of MP. Therefore, SP = 0.85 * MP. To find the marked price, we invert this relation and compute MP = SP / 0.85. This direct method avoids confusion and quickly yields the original marked price from the selling price and discount percentage. Step-by-Step Solution: Let marked price be MP. Discount = 15 percent, so amount payable is 85 percent of MP. Therefore selling price SP = 0.85 * MP. We are given SP = Rs. 318.75. So 0.85 * MP = 318.75. Hence MP = 318.75 / 0.85. Compute 318.75 / 0.85 = 375. Therefore, the article was listed at Rs. 375.00. Verification / Alternative check: Check by computing 15 percent of 375. Discount amount = 0.15 * 375 = 56.25. Subtract from marked price: 375 - 56.25 = 318.75, which matches the given selling price. This confirms that the marked price of Rs. 375 is correct and consistent with a 15 percent discount leading to the final amount paid by the customer. Why Other Options Are Wrong: If the marked price were Rs. 366.50, then 15 percent discount would result in a selling price different from 318.75. A marked price of Rs. 350.00 with 15 percent discount would lead to a selling price of 297.50, which is too low. A marked price of Rs. 431.25 with 15 percent discount would produce a selling price much higher than 318.75. Only Rs. 375.00 gives the exact selling price after applying a 15 percent discount. Common Pitfalls: Some learners mistakenly compute MP = SP * 0.85 instead of dividing by 0.85, effectively applying the discount twice. Others confuse discount and profit formulas and use the wrong base for percentage calculations. To avoid errors, always write the fundamental relation clearly: SP = MP * (1 - discount percent / 100), and then solve for MP by dividing the selling price by the remaining fraction. This ensures a reliable and systematic solution method. Final Answer: The article is listed at a marked price of Rs. 375.00.

Question 9

Kamal had some apples. He sold 40% more apples than he ate. If he sold 70 apples, how many apples did he eat?

Accepted Answer

Introduction / Context: This question involves a comparison between two related quantities using a percentage phrase, "40 percent more than." The number of apples sold is described as being 40 percent more than the number eaten. We are given the number sold and must find how many were eaten. This is a simple algebraic application of percentage increase, reinforcing how to translate verbal relationships into equations. Given Data / Assumptions: Let the number of apples Kamal ate be A. He sold 40 percent more apples than he ate. Number of apples sold = 70. We assume that "40 percent more than A" means A plus 40 percent of A. Concept / Approach: If one quantity is 40 percent more than another quantity A, then it is A + 40 percent of A = A + 0.40A = 1.40A. In this problem, the number sold equals 1.40 times the number eaten. Since the number sold is given as 70, we can write the equation 1.40A = 70 and solve for A. This kind of direct proportional equation is straightforward once the verbal phrase is converted into algebraic form. Step-by-Step Solution: Let the number of apples eaten by Kamal be A. He sold 40 percent more apples than he ate. So, apples sold = A + 40 percent of A = A + 0.40A = 1.40A. We are given that apples sold = 70. Therefore, 1.40A = 70. To find A, divide both sides by 1.40: A = 70 / 1.40. Compute 70 / 1.40 = 50. Thus, Kamal ate 50 apples. Verification / Alternative check: We can verify by checking the percentage relationship. If Kamal ate 50 apples, then 40 percent of 50 is 0.40 * 50 = 20. He sold 50 + 20 = 70 apples. This matches the given number sold, confirming that 50 is correct. Any other assumed number of apples eaten would not yield exactly 70 when increased by 40 percent. Why Other Options Are Wrong: If he had eaten 18 apples, then apples sold would be 1.40 * 18 = 25.2, not 70. If he had eaten 42 apples, apples sold would be 1.40 * 42 = 58.8, again not 70. If he had eaten 90 apples, apples sold would be 1.40 * 90 = 126, which is much higher than 70. Only 50 apples eaten leads to exactly 70 apples sold with the given 40 percent more condition. Common Pitfalls: A recurring mistake is to interpret "40 percent more than" as simply 40 percent of the quantity, rather than 140 percent of it. Another error is to subtract 40 percent instead of adding it, which would incorrectly model a decrease. Some students also misplace the percentage base, taking 40 percent of 70 instead of 40 percent of the eaten quantity. Carefully translating verbal descriptions into the correct algebraic form is essential to avoid these mistakes. Final Answer: Kamal ate 50 apples.

Question 10

In an ornament, the ratio of gold to copper is 3 : 2. Based on this ratio, what percentage of the total metal in the ornament is gold?

Accepted Answer

Introduction / Context: In many aptitude and quantitative exams, questions on ratios and percentages test a learner's ability to convert a given ratio into a percentage of the whole. This question talks about an ornament made of gold and copper mixed in a specific ratio and asks what percentage of the ornament is gold. Understanding the basic idea that a ratio compares parts of a whole is the key to solving such questions quickly and accurately. Given Data / Assumptions: The ornament is made of gold and copper only. The ratio of gold to copper is 3 : 2. No other metal is mixed in the ornament. We are required to find the percentage of gold in the entire ornament. Concept / Approach: The ratio 3 : 2 means that out of a total of 3 + 2 equal parts, 3 parts are gold and 2 parts are copper. To convert a ratio part into a percentage, we divide the required part by the total number of parts and then multiply by 100. So, percentage of gold = (gold parts / total parts) * 100. This approach works even if the actual total mass or volume of the ornament is not given, because the ratio already expresses the relative composition. Step-by-Step Solution: Step 1: Identify the number of parts for each metal. Gold = 3 parts, copper = 2 parts. Step 2: Calculate the total number of parts in the ornament. Total parts = 3 + 2 = 5. Step 3: Express the fraction of gold as gold parts divided by total parts. Fraction of gold = 3 / 5. Step 4: Convert this fraction into a percentage. Percentage of gold = (3 / 5) * 100. Step 5: Simplify the calculation. (3 / 5) * 100 = 60. Step 6: Therefore, gold constitutes 60 percent of the ornament. Verification / Alternative check: An alternative way is to imagine a convenient total quantity for the ornament. For example, assume the total weight is 5 grams to match the total parts (3 + 2). Then gold would be 3 grams and copper would be 2 grams. Percentage of gold = (3 / 5) * 100 = 60. This confirms the earlier calculation and shows that the answer is independent of the actual total mass, because the ratio remains the same. Why Other Options Are Wrong: 60 is correct because it equals 3 parts out of 5 in percentage form. Option 40 would correspond to copper, not gold. Option 30 and option 20 are smaller fractions and do not match 3 out of 5. Therefore, these values cannot represent the percentage of gold in the ornament. Common Pitfalls: A common mistake is to treat one of the ratio numbers directly as a percentage. For example, some learners might incorrectly say that gold is 3 percent, which ignores the total number of parts. Another error is to forget to add the parts when calculating the total. Always remember that ratios indicate parts of a whole, and the percentage must be computed with respect to the sum of all parts. Final Answer: The percentage of gold in the ornament is 60 percent.

Question 11

If 40% of x is equal to y, then y% of 40 is equal to what percentage of x?

Accepted Answer

Introduction / Context: This question tests your understanding of how percentages of variables relate to one another. It combines two percentage statements: 40 percent of x equals y, and then asks what y percent of 40 is in terms of x. Problems like this improve algebraic thinking and the ability to translate word statements into mathematical expressions involving percentages. Given Data / Assumptions: 40% of x is equal to y. We are asked to compute y% of 40. The final expression should be written as a percentage of x. All variables represent real numbers and no additional conditions are imposed. Concept / Approach: We translate percentage statements into algebraic equations. If 40% of x equals y, then y = (40 / 100) * x. To find y% of 40, we write it as (y / 100) * 40. Then we substitute y in terms of x from the first equation into this second expression. Finally, we simplify the result so that it becomes k% of x, and compare k with the options given in the question. Step-by-Step Solution: Step 1: Express 40% of x in algebraic form. 40% of x = (40 / 100) * x = 0.4x. Step 2: According to the question, 40% of x equals y, so y = 0.4x. Step 3: Now we need to find y% of 40. By definition, y% of 40 = (y / 100) * 40. Step 4: Substitute y = 0.4x into this expression. So y% of 40 = (0.4x / 100) * 40. Step 5: Simplify the multiplication: (0.4x / 100) * 40 = 0.4x * 40 / 100. Step 6: Evaluate 0.4 * 40 = 16, so we get 16x / 100. Step 7: Therefore, y% of 40 = 16x / 100, which is 16% of x. Verification / Alternative check: To verify, assume a simple numerical value for x. Let x = 100. Then 40% of 100 is 40, so y = 40. Now compute y% of 40, that is 40% of 40, which equals (40 / 100) * 40 = 16. As a percentage of x = 100, this value 16 is exactly 16% of x. This confirms that the expression is indeed 16% of x. Why Other Options Are Wrong: 4% of x would be 4x / 100, which is much smaller than 16x / 100. 8% of x is also only half of the correct value. 160% of x would give 1.6x, which is far larger than the simplified expression 16x / 100. Therefore none of these match the computed result, and only 16% of x is correct. Common Pitfalls: Learners often confuse which quantity is being expressed as a percentage of which. Another common error is to treat y% as simply y / 100 without multiplying by the base quantity (here 40). It is also easy to make mistakes when simplifying fractions or decimals. Carefully writing each algebraic step and simplifying gradually helps avoid such mistakes. Final Answer: y% of 40 is equal to 16% of x.

Question 12

The original price of a television set is Rs. 6000. Its price is first discounted by 20% and then the reduced price is increased by 10% as a service charge. What is the final price charged by the shopkeeper?

Accepted Answer

Introduction / Context: Successive percentage changes on prices are very common in real life, especially when shops offer discounts and then add service charges or taxes. This question asks you to apply two percentage operations in sequence to the original price of a television. It tests the understanding that these operations act on the current price at each step, and not directly on the original amount for both steps together. Given Data / Assumptions: Original price of the television set = Rs. 6000. First change: a discount of 20% on the original price. Second change: an increase of 10% on the discounted price as a service contract charge. We have to calculate the final price that the customer pays. Concept / Approach: When a discount or increment is applied successively, we must apply each percentage change to the price that exists at that stage. The general idea is: new price after first change = original price * (1 minus discount rate). Then, the new price after the second change = previous price * (1 plus increase rate). We should avoid the mistake of trying to directly add or subtract the percentages because they are applied on different bases. Step-by-Step Solution: Step 1: Calculate the price after a 20% discount on Rs. 6000. Step 2: A 20% discount means the customer pays 80% of the original amount. So discounted price = 6000 * (80 / 100). Step 3: Compute 6000 * (80 / 100) = 6000 * 0.8 = Rs. 4800. Step 4: Now a 10% increase is applied on this discounted price of Rs. 4800. Step 5: A 10% increase corresponds to multiplying by 1.10. So final price = 4800 * 1.10. Step 6: Calculate 4800 * 1.10 = 5280. Step 7: Therefore, the price charged by the shopkeeper is Rs. 5280. Verification / Alternative check: Instead of two separate steps, we can think in terms of combined multiplication factors. First factor: 80% or 0.8. Second factor: 110% or 1.10. Overall factor = 0.8 * 1.10 = 0.88. Therefore final price = 6000 * 0.88 = 5280, which matches our previous answer. This confirms that our calculations are consistent and the method is correct. Why Other Options Are Wrong: Rs. 5400 is higher than the correct final amount and would correspond to a different combination of percentage changes. Rs. 5100 is also not consistent with applying 20% discount followed by 10% increase. Rs. 4200 is even less, and would imply a much larger effective discount. None of these values match the actual stepwise computation, so they are incorrect. Common Pitfalls: A frequent mistake is to add 20% and 10% to get 30% and then assume a single net change. However, 20% discount and 10% increase do not cancel or simply add, because they are applied on different amounts. Another error is miscalculating percentages of large numbers under time pressure. Carefully writing the intermediate price after each step prevents such confusion. Final Answer: The final price charged by the shopkeeper is Rs. 5280.

Question 13

If 35% of the income of A is equal to 25% of the income of B, then what is the ratio of the income of A to the income of B?

Accepted Answer

Introduction / Context: This problem focuses on converting percentage relations between two quantities into a simple ratio. Such questions appear frequently in aptitude tests and competitive examinations to check whether students can handle percentages and ratios together. Here, we know that a fixed percentage of the income of A is equal to another percentage of the income of B, and from this relation we must derive the ratio between their incomes. Given Data / Assumptions: 35% of A's income is equal to 25% of B's income. We denote the income of A by A and the income of B by B. We are required to find the ratio A : B. All incomes are assumed to be positive real numbers. Concept / Approach: We translate the percentage statement into an equation. If 35% of A equals 25% of B, we write (35 / 100) * A = (25 / 100) * B. Then, we simplify this equation to isolate the ratio A / B. Once we get A / B in fractional form, we express it in the simplest whole number ratio format, which is the standard way of representing ratios in such questions. Step-by-Step Solution: Step 1: Write the percentage condition as an equation: (35 / 100) * A = (25 / 100) * B. Step 2: Multiply both sides of the equation by 100 to remove the denominators. This gives 35A = 25B. Step 3: Rearrange the equation to express A / B. So, A / B = 25 / 35. Step 4: Simplify the fraction 25 / 35 by dividing numerator and denominator by their greatest common divisor, which is 5. Step 5: 25 / 35 simplifies to 5 / 7. Therefore A / B = 5 / 7. Step 6: Thus, the ratio of the income of A to the income of B is 5 : 7. Verification / Alternative check: To verify, assume A = 5 units and B = 7 units. Then 35% of A is (35 / 100) * 5 = 1.75 units. Similarly, 25% of B is (25 / 100) * 7 = 1.75 units. Both values are equal, which confirms that the ratio A : B = 5 : 7 satisfies the condition in the question. Therefore our derivation is correct. Why Other Options Are Wrong: Option 7:5 would correspond to A / B = 7 / 5, which would imply 35% of A being larger than 25% of B. Option 4:7 and 4:3 do not maintain the equality of 35% of A and 25% of B when tested with actual numbers. Only the ratio 5:7 ensures that these two percentages match exactly. Common Pitfalls: A common error is inverting the ratio. Another frequent mistake is incorrectly handling percentages, for example treating 35% as 35 instead of 35 / 100. Sometimes students attempt to plug in random values instead of solving the equation systematically, which can lead to confusion. Writing out the algebraic steps carefully and simplifying the fraction with care helps avoid these issues. Final Answer: The ratio of A's income to B's income is 5 : 7.

Question 14

When a discount of Rs. 42 is allowed on the marked price of an article, the reduced selling price becomes 86% of the original marked price. What is the marked price of the article?

Accepted Answer

Introduction / Context: Questions connecting absolute discounts in rupees with percentage reductions are very standard in profit and loss and percentage chapters. Here, we are given that after allowing a rupee discount, the selling price becomes a certain percentage of the original marked price. The goal is to reverse this information and find the original marked price. This type of question helps strengthen algebraic manipulation skills combined with percentage understanding. Given Data / Assumptions: Let the marked price of the article be P rupees. A discount of Rs. 42 is given on this marked price. After the discount, the new price becomes 86% of the original marked price. We need to find the value of P. Concept / Approach: The key idea is to express both the discounted price and the percentage based price in terms of the same unknown marked price P. The discounted price is P minus 42. The percentage based price is 86% of P which is (86 / 100) * P. By equating these two expressions, we obtain a linear equation in P. Solving this equation gives the original marked price. This approach is systematic and avoids guesswork. Step-by-Step Solution: Step 1: Let the marked price be P rupees. Step 2: After allowing a discount of Rs. 42, the new price is P - 42. Step 3: According to the question, this discounted price is 86% of the original marked price. So P - 42 = (86 / 100) * P. Step 4: Simplify the equation: P - 42 = 0.86P. Step 5: Bring all P terms to one side: P - 0.86P = 42. Step 6: Compute the difference: 0.14P = 42. Step 7: Solve for P by dividing both sides by 0.14. So P = 42 / 0.14 = 300. Step 8: Therefore, the marked price of the article is Rs. 300. Verification / Alternative check: We can verify the result by plugging P = 300 back into the situation. A discount of Rs. 42 gives a selling price of 300 - 42 = Rs. 258. Now, 86% of 300 is (86 / 100) * 300 = 0.86 * 300 = 258. Since both values match, the equation is satisfied and the computed marked price is consistent with the condition given in the question. Why Other Options Are Wrong: If P were Rs. 250, then 86% of 250 would be 215, which would not differ from 250 by Rs. 42. Similarly, for P = 350, 86% of 350 equals 301, but 350 minus 42 equals 308, so these do not match. For P = 400, 86% equals 344, while 400 minus 42 equals 358, again inconsistent. Only P = 300 satisfies both the amount discount and the percentage condition. Common Pitfalls: A typical mistake is reversing the direction of the percentage, for example treating 86% as the discount instead of the remaining price. Another common error is miscomputing 86% of P. Students sometimes also attempt trial and error with options without understanding the underlying equation, which can be time consuming. Writing down the algebraic expression and solving carefully is the most reliable method. Final Answer: The marked price of the article is Rs. 300.

Question 15

A student must secure 35% of the maximum marks to pass in a subject. The student obtained 82 marks and failed by 23 marks. What are the maximum marks for the subject?

Accepted Answer

Introduction / Context: Examination and result based questions often involve pass marks expressed as a percentage of the maximum marks. The student's actual marks and the margin by which the student failed are used to back calculate the full mark of the paper. This question is a direct application of percentage and basic algebra and appears frequently in aptitude and competitive exams. Given Data / Assumptions: The pass mark is 35% of the maximum marks. The student scored 82 marks. The student failed by 23 marks, that is, the student needed 23 more marks to just pass. We need to find the maximum marks for the subject. Concept / Approach: The idea is to express the pass mark in terms of the unknown maximum marks. If we let the maximum marks be M, then the pass mark is 35% of M, which is (35 / 100) * M. The question says that the student scored 82 marks and is short by 23 marks from the pass mark. So, pass mark = 82 + 23. We equate this to 35% of M and solve for M. Step-by-Step Solution: Step 1: Let the maximum marks be M. Step 2: The pass mark is 35% of M, so pass mark = (35 / 100) * M = 0.35M. Step 3: The student obtained 82 marks and failed by 23 marks. So the pass mark must be 82 + 23 = 105. Step 4: Set up the equation: 0.35M = 105. Step 5: Solve for M by dividing both sides by 0.35. So M = 105 / 0.35. Step 6: Compute 105 / 0.35 = 300. Step 7: Therefore, the maximum marks for the subject is 300. Verification / Alternative check: We can verify the result by checking whether 35% of 300 actually gives a pass mark consistent with the story. 35% of 300 is (35 / 100) * 300 = 105. The student got 82 marks, and indeed 105 minus 82 equals 23 marks, which matches the statement that the student failed by 23 marks. This confirms that our calculation is correct. Why Other Options Are Wrong: For a maximum of 250 marks, 35% would be 87.5, and the shortfall from 82 would be only 5.5, not 23. For a maximum of 350 marks, 35% would be 122.5, which is far from the given difference. For 400 marks, 35% would be 140, so the student would fall short by 58 marks. None of these match the failure margin of 23 marks, so they are invalid options. Common Pitfalls: Students sometimes treat the 23 marks as 23% or misinterpret the phrase "failed by 23 marks". Another frequent mistake is to directly take 35% of 82 instead of relating 82 plus 23 to the pass mark. Always read carefully whether a number represents a percentage of the maximum or an absolute number of marks. Building the equation patiently usually leads to the correct answer. Final Answer: The maximum marks of the subject is 300.

Question 16

Two labourers, A and B, are paid a total of Rs. 650 per day. Labourer A is paid 160% of what B is paid. How much, in rupees, is labourer B paid per day?

Accepted Answer

Introduction / Context: This question is a typical example of percentage comparison between two incomes where their combined total is also given. It asks you to find the individual share of one labourer when the total daily payment and a percentage relation between their wages are known. Such questions are very common in aptitude exams, especially in topics like ratio, proportion, and percentage. Given Data / Assumptions: Total payment to labourers A and B together per day = Rs. 650. Payment to A is 160% of the payment to B. We need to find the daily wage of B. All amounts are per day, and there are only two labourers considered. Concept / Approach: Let the payment to B be some variable, say x rupees. Since A earns 160% of B, the payment to A is 160% of x, which is (160 / 100) * x = 1.6x. The total payment is then x + 1.6x. We know that this sum equals 650. This gives a simple linear equation in x which we can solve. Once x is found, that value represents the payment of B. Step-by-Step Solution: Step 1: Let the daily wage of B be x rupees. Step 2: Since A is paid 160% of B, wage of A = 1.6x rupees. Step 3: Total daily wages of A and B together is x + 1.6x. Step 4: According to the question, x + 1.6x = 650. Step 5: Combine like terms to get 2.6x = 650. Step 6: Solve for x: x = 650 / 2.6. Step 7: Calculate 650 / 2.6 = 250. Step 8: Therefore, B is paid Rs. 250 per day. Verification / Alternative check: Let us verify by finding A's wage from this value. If B earns Rs. 250, then A earns 160% of 250, which is (160 / 100) * 250 = 1.6 * 250 = 400. Now, total wages = 250 + 400 = 650, which matches the given total payment. Therefore the calculated value for B's wage is consistent and correct. Why Other Options Are Wrong: If B earned Rs. 400, A would earn 160% of 400, or 640, and their total would be 1040, not 650. If B earned Rs. 350, A would earn 560, total 910. If B earned Rs. 450, A would earn 720, total 1170. None of these totals match the given Rs. 650. Only Rs. 250 for B produces the correct total. Common Pitfalls: A common misunderstanding is to treat 160% as 1.60 times without connecting properly to the total. Some learners mistakenly think A's wage is 160% more than B (which would be 260% of B) instead of 160% of B. Reading the phrase carefully is crucial. Also, performing mental division in the last step may lead to arithmetic mistakes, so writing the calculation clearly as 650 / 2.6 is helpful. Final Answer: Labourer B is paid Rs. 250 per day.

Question 17

In a school, the ratio of the number of boys to the number of girls is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of all students are not scholarship holders?

Accepted Answer

Introduction / Context: This problem combines ratio and percentage concepts with a real life context about scholarship holders in a school. It tests your ability to move from ratios to actual fractions of a total, apply different percentages to subgroups, and then compute the overall percentage of students who do not receive scholarships. These skills are very important in data interpretation and quantitative reasoning. Given Data / Assumptions: Ratio of boys to girls = 3 : 2. 20% of the boys are scholarship holders. 25% of the girls are scholarship holders. We assume all students are either boys or girls and there are no other categories. We must find the percentage of total students who are not scholarship holders. Concept / Approach: First convert the boy girl ratio into fractional parts of the total students. Then apply the given scholarship percentages separately to boys and girls to find the fraction of scholarship holders in each gender group. Add these fractions to find the total proportion of scholarship holders in the school. The complement of this proportion (that is, one minus the scholarship fraction) gives the proportion of non scholarship students, which we then express as a percentage. Step-by-Step Solution: Step 1: Let the total number of students be 5k, where 3k are boys and 2k are girls, because the ratio is 3 : 2. Step 2: Number of scholarship boys = 20% of 3k = (20 / 100) * 3k = 0.6k. Step 3: Number of scholarship girls = 25% of 2k = (25 / 100) * 2k = 0.5k. Step 4: Total scholarship students = 0.6k + 0.5k = 1.1k. Step 5: Total students = 5k, so the fraction with scholarships = 1.1k / 5k = 1.1 / 5 = 0.22. Step 6: Therefore, the fraction without scholarships = 1 - 0.22 = 0.78, which is 78%. Verification / Alternative check: Assume k = 100 for easy numbers. Then total students = 500. Boys = 300, girls = 200. Scholarship boys = 20% of 300 = 60. Scholarship girls = 25% of 200 = 50. Total scholarship students = 110. Non scholarship students = 500 - 110 = 390. Percentage of non scholarship students = (390 / 500) * 100 = 78%. This numerical approach confirms the algebraic result. Why Other Options Are Wrong: 56% and 70%: These values underestimate the non scholarship percentage and come from miscalculations or ignoring the ratio base. 80%: Slightly higher than the correct value; this can occur if one mistakenly averages the complementary percentages incorrectly. 62%: Has no support in the correct ratio and percentage setup and is a clear miscalculation. Common Pitfalls: Many learners mistakenly take a simple average of 20% and 25% to get total scholarship percentage, ignoring the fact that the groups (boys and girls) are not equal in size. Others may incorrectly assume the total students are 100 and break the ratio incorrectly. Always convert ratios into actual parts of a common multiple and then apply the given percentages logically. Final Answer: 78% of the students in the school are not scholarship holders.

Question 18

A student scores 22 marks more in French than in German. Her German marks are 28% of the sum of her French and German marks. What are her marks in French?

Accepted Answer

Introduction / Context: This problem is a classic example of using percentages and linear equations with two related subjects. The marks in French and German are connected by both a difference condition and a percentage condition. Solving such questions enhances algebraic thinking and is common in aptitude and school level exams. Given Data / Assumptions: Let German marks be G and French marks be F. The student scores 22 marks more in French than in German, so F = G + 22. German marks are 28% of the sum of French and German marks, so G = 28% of (F + G). We must find the value of F, the French marks. Concept / Approach: We translate both conditions into algebraic equations. One equation comes from the difference F = G + 22. The second equation comes from the percentage statement G = 0.28 * (F + G). We then substitute the expression for F from the first equation into the second equation, solve for G, and finally compute F using F = G + 22. This two equation system is straightforward once written properly. Step-by-Step Solution: Step 1: From the difference condition, write F = G + 22. Step 2: From the percentage condition, write G = 0.28 * (F + G). Step 3: Substitute F from Step 1 into Step 2: G = 0.28 * ((G + 22) + G) = 0.28 * (2G + 22). Step 4: Expand the right side: G = 0.28 * 2G + 0.28 * 22 = 0.56G + 6.16. Step 5: Bring terms with G together: G - 0.56G = 6.16, which gives 0.44G = 6.16. Step 6: Solve for G: G = 6.16 / 0.44 = 14. Step 7: Use F = G + 22, so F = 14 + 22 = 36. Verification / Alternative check: Check both conditions with F = 36 and G = 14. The difference condition: French minus German = 36 - 14 = 22, which is correct. The percentage condition: F + G = 36 + 14 = 50. German marks as a percentage of total = 14 / 50 * 100 = 28%, which matches the statement. Both checks confirm the solution. Why Other Options Are Wrong: 14: This is the value of German marks, not French marks. 18: Leads to F + G values and differences that do not satisfy the given equations. 42: F = 42 would not yield German marks that are exactly 28% of the total when combined with the difference condition. 28: This again fails one or both of the given relationships when substituted. Common Pitfalls: Learners sometimes reverse the percentage condition, treating French as 28% of the total instead of German. Others may forget to substitute correctly or mismanage the algebra when combining the two equations. Another frequent error is rounding too early; here the arithmetic yields exact integers if the steps are done carefully. Final Answer: The student scored 36 marks in French.

Question 19

After a 31% deduction on an electricity bill, an amount of Rs. 1794 is still payable. What was the original bill amount before the deduction?

Accepted Answer

Introduction / Context: This question illustrates how to reverse a percentage deduction to find the original amount. It uses a real life situation of an electricity bill that has had a certain percentage deducted, possibly as a rebate or subsidy, leaving a final payable amount. Being comfortable with reversing percentages is a valuable skill for many financial and billing problems. Given Data / Assumptions: The original electricity bill is unknown and is to be found. There is a deduction of 31% on the original bill. After this deduction, the payable amount is Rs. 1794. All amounts are in rupees and positive. Concept / Approach: A deduction of 31% means that the customer pays 69% of the original bill, because 100% - 31% = 69%. Let the original bill be B. Then, 69% of B equals 1794. This gives a simple linear equation: 0.69 * B = 1794. Solving this equation yields the value of B. This is a direct reverse percentage calculation. Step-by-Step Solution: Step 1: Let the original bill amount be B rupees. Step 2: A 31% deduction means the customer pays 69% of B, so 69% of B = 1794. Step 3: Write this mathematically: (69 / 100) * B = 1794. Step 4: Convert to decimal: 0.69 * B = 1794. Step 5: Solve for B by dividing both sides by 0.69: B = 1794 / 0.69. Step 6: Compute B = 2600, so the original bill was Rs. 2600. Verification / Alternative check: Check by recalculating the deduction from the original bill of Rs. 2600. Deduction at 31% = (31 / 100) * 2600 = 806. Remaining payable amount = 2600 - 806 = 1794, which matches the given value. This confirms that our reverse percentage calculation is correct. Why Other Options Are Wrong: Rs. 1369 and Rs. 1405: These are much lower than 1794 and cannot yield a 69% value of 1794. Rs. 2636: If 69% of B were 1794, B would be slightly higher than 2600 only if the percentage were slightly lower than 69; this value does not fit the equation exactly. Rs. 2200: 69% of 2200 is 1518, not 1794, so it is clearly incorrect. Common Pitfalls: Some students mistakenly treat 31% as the amount paid instead of the deduction, which would lead them to set 0.31B = 1794. Others subtract 31 from 1794 or attempt to compute the difference without setting a proper equation. The safest way is to convert the verbal description into a clear percentage of the original amount and then solve. Final Answer: The original electricity bill amount was Rs. 2600.

Question 20

An article has a marked price of Rs. 1500 and is sold for Rs. 1250. What discount percentage is offered on the marked price?

Accepted Answer

Introduction / Context: This question focuses on calculating discount percentage when the marked price and selling price of an article are known. This type of problem is commonly found in commercial arithmetic and tests the ability to relate absolute rupee differences to percentage reductions. Given Data / Assumptions: Marked price (MP) of the article = Rs. 1500. Selling price (SP) of the article = Rs. 1250. Discount amount = MP minus SP. We need to find the discount percentage with respect to the marked price. Concept / Approach: The discount percent is defined as (discount amount / marked price) * 100. First compute the discount amount as the difference between the marked price and the selling price. Then divide this difference by the marked price to obtain the fraction of discount, and finally convert it into a percentage by multiplying by 100. This straightforward method is essential for solving shop and selling price related questions. Step-by-Step Solution: Step 1: Compute the discount amount: Discount = MP - SP = 1500 - 1250 = Rs. 250. Step 2: Use the formula for discount percentage: Discount% = (Discount / MP) * 100. Step 3: Substitute the values: Discount% = (250 / 1500) * 100. Step 4: Simplify the fraction: 250 / 1500 = 1 / 6. Step 5: Multiply by 100: Discount% = (1 / 6) * 100 = 16.666...%, usually written as 16.67%. Verification / Alternative check: To cross check, compute 16.67% of the marked price 1500. Approximately, 16.67% of 1500 is 1500 * 0.1667 which is close to 250. Subtracting 250 from 1500 yields 1250, which matches the selling price. This confirms that the discount rate of 16.67% is consistent with the given data. Why Other Options Are Wrong: 10%: 10% of 1500 is 150, not 250; selling price would be 1350, not 1250. 20%: 20% of 1500 is 300, which would make the selling price 1200, not 1250. 25%: 25% of 1500 is 375, also inconsistent with the given selling price. 12.5%: 12.5% of 1500 is 187.5, which is not the actual discount amount of 250. Common Pitfalls: A typical mistake is to divide the discount by the selling price instead of the marked price, which leads to the wrong percentage. Another error is rounding too early in calculations and not recognizing that 1 divided by 6 is exactly 16.666...%. Always base the discount percentage on the original marked price. Final Answer: The discount offered is 16.67% of the marked price.

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