Question 1

On a television of brand A, the discount offered is 25%, while on a television of brand B the discount offered is 40%. After discount, the price of brand B television is Rs 2250 higher than the discounted price of brand A television. If the marked p…

Accepted Answer

Introduction / Context: This problem compares the discounted prices of two products that have different marked prices and different discount rates. We know the marked price of one brand and the difference between the final discounted prices, and we are asked to find the marked price of the other brand. Such questions appear frequently in discount and pricing sections of aptitude exams and they encourage careful algebraic formulation based on percentage reductions and price differences. Given Data / Assumptions: Brand A television has a discount of 25% on its marked price. Brand B television has a discount of 40% on its marked price. Marked price of brand B television = Rs 35,000. After discount, price of brand B is Rs 2250 more than the discounted price of brand A. We need to find the marked price of brand A, denoted by M. Concept / Approach: We first compute the discounted price of brand B using its marked price and discount rate. Then we express the discounted price of brand A in terms of its marked price M and its 25% discount. The question states that the discounted price of B is Rs 2250 greater than that of A, which leads to a linear equation involving M. Solving this equation yields the required marked price of brand A. The important idea is to represent both discounted prices algebraically and relate them using the given difference. Step-by-Step Solution: Step 1: Marked price of brand B = Rs 35000. Step 2: Discount on brand B = 40%, so the customer pays 60% of the marked price. Step 3: Discounted price of brand B = 0.60 * 35000 = Rs 21000. Step 4: Let marked price of brand A be M. Step 5: Discount on brand A = 25%, so the customer pays 75% of its marked price. Step 6: Discounted price of brand A = 0.75 * M. Step 7: Given that price of B after discount is Rs 2250 higher than price of A after discount, so 21000 = 0.75 * M + 2250. Step 8: Subtract 2250 from both sides: 21000 - 2250 = 0.75 * M. Step 9: Compute 21000 - 2250 = 18750, so 0.75 * M = 18750. Step 10: Solve for M: M = 18750 / 0.75 = 25000. Verification / Alternative check: With M = 25000, the discounted price of brand A is 75% of 25000, which is 0.75 * 25000 = 18750. For brand B, we already found the discounted price is 21000. The difference between them is 21000 - 18750 = 2250, which matches the given condition. This confirms that the marked price of brand A must indeed be Rs 25000 and that the linear equation was set up correctly based on the description in the question. Why Other Options Are Wrong: If the marked price of brand A were Rs 18750, the discounted price at 25% off would be 14062.50, and the difference to 21000 would not equal 2250. A marked price of Rs 21000 for A would give a discounted price of 15750, still not satisfying the required difference. A marked price of Rs 17850 would also produce a discounted value far from the one needed. Only a marked price of Rs 25000 yields a discounted price that is exactly Rs 2250 less than the discounted price of brand B, as required. Common Pitfalls: Some learners mistakenly add 2250 to the marked price of brand B or misuse the percentage, failing to recognize that the difference is between discounted prices, not between marked prices. Others may confuse which brand has the higher discounted price. It is crucial to carefully read that brand B price after discount is 2250 greater than brand A price after discount, and then build the equation accordingly. Writing down the intermediate expressions clearly for both brands helps avoid such confusion. Final Answer: The marked price of brand A television is Rs 25000.

Question 2

A total of Rs 10,200 is to be divided among three people A, B, and C so that A receives 2/3 of what B receives and B receives 1/4 of what C receives. How many rupees more does C receive than A?

Accepted Answer

Introduction / Context: This question is a classic ratio and proportion problem presented in words. The shares of three people A, B, and C are linked through fractional relationships rather than directly stated ratios. From these relationships and the total amount to be distributed, we must determine the individual shares and then compare two of them. Such problems frequently appear in partnership, division of income, and allocation topics in aptitude tests. Given Data / Assumptions: Total amount to be divided among A, B, and C = Rs 10200. A receives 2/3 of what B receives. B receives 1/4 of what C receives, so C receives four times what B receives. We need to find how much more C receives than A. All amounts are non negative and the entire sum is distributed among A, B, and C. Concept / Approach: We translate the verbal fractional relationships into algebraic equations. By letting B share be a variable, we can express A and C shares in terms of that same variable. Then we use the equation A + B + C = 10200 to solve for the variable. Once we know B share, we can compute A and C shares and finally determine the difference C minus A. This method turns a word problem into a straightforward algebraic system. Step-by-Step Solution: Step 1: Let B share be x rupees. Step 2: A receives 2/3 of B share, so A share = (2 / 3) * x. Step 3: B receives 1/4 of what C receives, so C share = 4 * x. Step 4: Total amount distributed is A + B + C = 10200. Step 5: Substitute the expressions: (2 / 3) * x + x + 4 * x = 10200. Step 6: Combine like terms. First sum the coefficients of x: (2 / 3) + 1 + 4 = (2 / 3) + 5. Step 7: Write 5 as 15 / 3, so combined coefficient is (2 / 3) + (15 / 3) = 17 / 3. Step 8: Therefore (17 / 3) * x = 10200. Step 9: Solve for x: x = 10200 * 3 / 17 = 1800. Step 10: So B share = Rs 1800. Then A share = (2 / 3) * 1800 = Rs 1200, and C share = 4 * 1800 = Rs 7200. Step 11: Difference between C and A shares = 7200 - 1200 = Rs 6000. Verification / Alternative check: Check that the three shares add up to the total and respect the conditions. Sum A, B, and C shares: 1200 + 1800 + 7200 = 10200, which matches the total given. Also A receives 2/3 of B share since 2 / 3 of 1800 is 1200, and B receives 1/4 of C share since 1 / 4 of 7200 is 1800. Both conditions are satisfied exactly, so the algebraic solution is consistent and the difference of Rs 6000 between C and A is correct. Why Other Options Are Wrong: A difference of Rs 7200 would imply extremely unbalanced shares that would violate the given fractional relationships. A difference of Rs 1800 or Rs 1200 is too small and would not match the computed values from the equations. When the relationships and total are applied correctly, only a difference of Rs 6000 is possible, and the other values are incompatible with the constraints of the problem. Common Pitfalls: One common mistake is reversing the fraction relationship, for example interpreting “A gets 2/3 of what B gets” as the opposite or misreading “B gets 1/4 of what C gets” as C gets 1/4 of B. Another issue is trying to convert the word description directly into a ratio without carefully tracing who depends on whom. Introducing a variable for one person share and writing all other shares in terms of that variable is the safest and clearest method. Final Answer: C receives Rs 6000 more than A.

Question 3

If 2% of a quantity a is equal to b, then b% of 10 is numerically equal to which of the following expressions in terms of a?

Accepted Answer

Introduction / Context: This question again tests the ability to convert symbolic percentage relations into algebra and to simplify them into an expression in terms of a single variable. We are told how b relates to a, and then asked to compute b% of a numerical quantity, expressing the result purely in terms of a. Such symbolic percentage problems help in building strong foundations for handling more complex algebraic percentage scenarios in exams and real life applications. Given Data / Assumptions: Two percent of a is equal to b, that is 2% of a = b. We need to find b% of 10. The final expression must be written using a only. All percentage operations follow usual arithmetic rules. Concept / Approach: The main approach is to write the given percentage relation as a formula. From 2% of a = b, we find b in terms of a. Then we interpret b% of 10 as (b / 100) multiplied by 10. Substituting for b leads to a numerical coefficient times a. Finally, we express this coefficient in the form shown in the answer choices, which use phrases like “20% of a/100” to represent the fraction of a. Step-by-Step Solution: Step 1: Express 2% of a. We have 2% of a = (2 / 100) * a = 0.02 * a. Step 2: Given that 2% of a equals b, we get b = 0.02 * a. Step 3: Now compute b% of 10. By definition, b% of 10 = (b / 100) * 10. Step 4: Substitute b = 0.02 * a into the expression: b% of 10 = (0.02 * a / 100) * 10. Step 5: Combine constants. First compute 0.02 * 10 = 0.2. Step 6: So b% of 10 = 0.2 * a / 100. Step 7: This is the same as 20% of a divided by 100, because 20% of a is (20 / 100) * a = 0.2 * a. Step 8: Therefore b% of 10 equals 20% of a / 100. Verification / Alternative check: To check numerically, choose a convenient value such as a = 1000. Then 2% of 1000 is 20, so b = 20. Now b% of 10 means 20% of 10, which equals 2. Next evaluate 20% of a / 100 for a = 1000. First find 20% of a: 20% of 1000 is 200. Then divide by 100 to get 200 / 100 = 2. The numeric result matches exactly, confirming that the expression 20% of a / 100 is equivalent to b% of 10. Why Other Options Are Wrong: Option a, 200% of a, equals 2 * a, which is far larger than the tiny fraction we obtained. Option c, 20% of a / 10, simplifies to 0.2 * a / 10 = 0.02 * a, which is ten times too large. Option d, 200% of a / 10, equals 2 * a / 10 = 0.2 * a, which is also much larger than the correct expression. Therefore only “20% of a/100” correctly represents the value of b% of 10 in terms of a. Common Pitfalls: It is easy to confuse percent and decimal forms or to forget to divide by 100 when converting percentages. Another typical error is to misread 2% of a = b as b% of a = 2, completely changing the relationship. To stay accurate, always write percentage expressions as fractions or decimals explicitly and perform substitutions step by step, checking the units and magnitudes at each stage. Final Answer: The value of b% of 10 is equal to 20% of a/100.

Question 4

A shop offers two successive discounts of 40% on the marked price of an article. These two consecutive discounts together are equivalent to a single discount of what percentage on the original marked price?

Accepted Answer

Introduction / Context: This question focuses on the concept of successive discounts, which are very common in shopping and sales scenarios. When two discounts are applied one after another, the net discount is not simply the sum of the two percentages. Instead, each discount applies to the price resulting from the previous discount. Understanding how to compute the combined effect is essential in profit and loss, commercial maths, and real life decision making about offers and sales. Given Data / Assumptions: The shop offers a first discount of 40% on the marked price. Then a second discount of 40% is applied on the already reduced price. We want to find the single equivalent discount percentage that would produce the same final price when applied directly to the original marked price. Marked price is assumed to be some positive value, which we can denote by M. Concept / Approach: Successive discounts are represented with multiplicative factors. A discount of 40% leaves 60% of the price, which corresponds to multiplying the price by 0.60. Two such discounts in a row multiply to 0.60 * 0.60. The result is a combined multiplier that tells us what fraction of the marked price the customer ultimately pays. The equivalent single discount is then 100% minus this final percentage paid. This method is systematic and avoids errors that occur when percentages are simply added. Step-by-Step Solution: Step 1: Let the marked price be M. Step 2: After the first discount of 40%, the customer pays 60% of M, which is 0.60 * M. Step 3: After the second discount of 40% on the reduced price, the customer pays 60% of the new price. Step 4: Therefore final price = 0.60 * (0.60 * M) = 0.60 * 0.60 * M. Step 5: Multiply 0.60 by 0.60 to get 0.36. Step 6: So the final price is 0.36 * M, which means the customer pays 36% of the marked price. Step 7: The equivalent single discount is 100% minus 36% = 64%. Step 8: Hence two successive discounts of 40% are equal to one discount of 64%. Verification / Alternative check: Choose a convenient marked price, for example M = Rs 100. First discount of 40% reduces the price to 60, since 40% of 100 is 40 and 100 minus 40 is 60. A second discount of 40% on 60 reduces it by 24 to 36. So the final price after two discounts is Rs 36. If a single discount were applied to 100 to produce the same final price, that discount would be 100 - 36 = 64. This confirms the algebraic result and shows that the combined discount rate is indeed 64%. Why Other Options Are Wrong: Option a, 80%, comes from the incorrect idea of simply adding 40% and 40%, which does not account for the reduced base after the first discount. Option b, 96%, would correspond to paying only 4% of the price, which is far lower than the actual 36%. Option d, 72%, suggests paying 28% of the price, which is also inconsistent with the computed final price of 36%. Only 64% accurately reflects the combined effect of two successive 40% discounts. Common Pitfalls: The most common error is to assume that two discounts of x% each add up to a total discount of 2x%. This ignores that the second discount is applied to a lower price. Another mistake is failing to convert percentages to decimal multipliers before multiplying. Always remember that with successive percentage changes you work with factors of the form (1 minus discount rate) repeatedly, and then convert the final factor back into an equivalent percentage. Final Answer: Two successive discounts of 40% are equivalent to a single discount of 64% on the marked price.

Question 5

A shopkeeper marks up his wares by 125% over cost price and then offers a discount of 25% on this marked price. If the cost price of an article is Rs 640, what will be the final selling price (in rupees) after applying both the markup and the discou…

Accepted Answer

Introduction / Context: This question is another example of combining a markup with a discount. The trader first increases the price by a large percentage over the cost and later reduces that higher price by a discount before selling to the customer. The net effect is a certain profit percentage on the original cost price. Problems like these are standard in profit and loss sections because they model how retailers use marked prices and discounts to manage profits while making offers appear attractive. Given Data / Assumptions: Cost price (CP) of the article = Rs 640. Markup on cost price = 125%. Discount on marked price = 25%. We must find the final selling price after both steps. No taxes or additional fees are mentioned, so we ignore them. Concept / Approach: A markup of 125% means the marked price is the cost price plus 125% of the cost price, which is 2.25 times the cost. A discount of 25% means that the customer pays 75% of the marked price. Thus, we can use a multiplier of 2.25 for the markup and then 0.75 for the discount. The final price is the product of the cost price and these two multipliers. This multiplicative viewpoint captures the combined effect of successive percentage changes accurately. Step-by-Step Solution: Step 1: Cost price (CP) = Rs 640. Step 2: Markup rate = 125% on cost. Markup factor = 1 + 125 / 100 = 2.25. Step 3: Marked price (MP) = CP * 2.25 = 640 * 2.25. Step 4: Compute 640 * 2.25. This is 640 * (9 / 4) = (640 / 4) * 9 = 160 * 9 = 1440. Step 5: Discount rate = 25% on the marked price. After discount, the customer pays 75% of MP, so factor = 0.75. Step 6: Selling price (SP) = MP * 0.75 = 1440 * 0.75. Step 7: Compute 1440 * 0.75 = 1440 * (3 / 4) = 1080. Step 8: Therefore, the final selling price is Rs 1080. Verification / Alternative check: We can compute the net effect on the cost price directly. The combined multiplier is 2.25 (markup) times 0.75 (discount). Multiplying 2.25 by 0.75 gives 1.6875. Thus the final selling price is 1.6875 times the cost price. Applying this to the cost price, SP = 1.6875 * 640 = 1080. This confirms our earlier calculation and shows that the net result is a profit of 68.75% on the original cost price, which is significant even after offering a 25% discount on the marked price. Why Other Options Are Wrong: A selling price of Rs 1000 would correspond to a lower net multiplier and thus a smaller profit percentage than implied by the given markup and discount. A price of Rs 920 is even lower and would represent only a modest margin above cost. A price of Rs 860 is barely more than the cost of 640 plus a small extra, which does not align with the large markup followed by a moderate discount. Only Rs 1080 fits the correct calculation for both steps combined. Common Pitfalls: Some students may subtract the percentages directly, for example taking 125% minus 25% to get 100%, and then incorrectly concluding that the selling price equals twice the cost price. Others may apply the discount to the cost price rather than to the marked price. To handle such problems safely, always compute the marked price from the cost price with the markup factor, then apply the discount factor to the marked price only, keeping track of each step clearly. Final Answer: The selling price of the article after a 125% markup and a 25% discount is Rs 1080.

Question 6

The difference between the cost price and the selling price of an article is Rs 221, and the profit percentage on cost price is 17%. What is the selling price (in rupees) of the article?

Accepted Answer

Introduction / Context: This question is a direct application of the relationship between cost price, profit, and selling price. Knowing the profit percentage and the monetary profit allows us to find the cost price, from which we can compute the selling price. Such questions are fundamental in the profit and loss chapter of quantitative aptitude and help build intuition about how percentage profit relates to actual amounts. Given Data / Assumptions: Difference between selling price (SP) and cost price (CP) is Rs 221. This difference represents profit, because the profit percentage is positive. Profit percentage on cost price = 17%. We must find the selling price SP. All amounts and percentages follow standard definitions of profit and cost. Concept / Approach: Profit is defined as SP minus CP. Profit percentage is profit divided by cost price multiplied by 100. Here, we know the profit amount and the profit percent, so we can set up the equation 17% of CP = 221 and solve for CP. After finding CP, we add the profit to obtain SP. This stepwise method uses the basic formulas of profit and loss and avoids confusion between percentage profit on cost and on selling price. Step-by-Step Solution: Step 1: Let cost price be CP. Step 2: Profit = SP - CP. Given that this difference is Rs 221. Step 3: Profit percentage is 17% of CP, so profit = 17 / 100 * CP. Step 4: According to the problem, 17 / 100 * CP = 221. Step 5: Solve for CP: CP = 221 * 100 / 17. Step 6: Compute 221 * 100 / 17. Since 221 / 17 = 13, CP = 13 * 100 = 1300. Step 7: Selling price SP = CP + profit = 1300 + 221 = 1521. Step 8: Therefore the selling price of the article is Rs 1521. Verification / Alternative check: Check the profit percentage using the computed values. Profit = SP - CP = 1521 - 1300 = 221. Profit percentage on cost is 221 / 1300 * 100. Compute 221 / 1300 = 0.17, and multiplying by 100 gives 17%, which matches the given profit rate. This confirms that CP and SP have been calculated correctly and that the selling price is indeed Rs 1521. Why Other Options Are Wrong: If SP were Rs 1079, then profit would be negative relative to any reasonable cost, which contradicts the given profit percentage. For SP = Rs 1300, the profit would be zero, not Rs 221. If SP were Rs 1724, then the profit would be 1724 minus CP, and it would not equal 221 when the profit percentage is fixed at 17%. Only the SP value of Rs 1521 leads to a profit of Rs 221 and a profit percentage of exactly 17% on the cost price. Common Pitfalls: One error is to treat 221 as 17% of the selling price instead of the cost price. This leads to a different equation and an incorrect answer. Another mistake is to forget that profit percentage uses cost price in the denominator in most standard questions unless otherwise specified. To avoid confusion, always write the formula profit percent = profit / cost price * 100 and substitute the known values carefully. Final Answer: The selling price of the article is Rs 1521.

Question 7

The marked price of an article is Rs 3600 and the actual selling price is Rs 3132. What is the discount percentage offered on this article relative to its marked price?

Accepted Answer

Introduction / Context: This question is a straightforward discount calculation problem. The marked price is the displayed price on the item, while the selling price is the amount the customer actually pays after discount. The aim is to determine the discount percentage based on these two values. This kind of calculation is very common in everyday shopping scenarios as well as in competitive examinations under the profit and loss and discount topics. Given Data / Assumptions: Marked price (MP) of the article = Rs 3600. Selling price (SP) after discount = Rs 3132. Discount is the difference between marked price and selling price. Discount percentage is calculated on the marked price. We must find the discount percentage to two decimal places if necessary. Concept / Approach: The discount amount is MP minus SP. Once we know the discount amount, we divide it by the marked price and multiply by 100 to convert it into a percentage. The formula is discount percent = (discount / marked price) * 100. This direct formula avoids confusion and is standard in all discount calculations where marked price and selling price are known. Step-by-Step Solution: Step 1: Marked price MP = Rs 3600. Step 2: Selling price SP = Rs 3132. Step 3: Discount amount = MP - SP = 3600 - 3132. Step 4: Compute 3600 - 3132 = 468. Step 5: Use the formula discount percent = (discount / MP) * 100. Step 6: Substitute values: discount percent = (468 / 3600) * 100. Step 7: Simplify the fraction 468 / 3600. Divide numerator and denominator by 36 to get 13 / 100. Step 8: Therefore discount percent = (13 / 100) * 100 = 13%. Step 9: So the discount offered on the article is 13% of the marked price. Verification / Alternative check: To verify, compute 13% of the marked price and subtract from the marked price. Thirteen percent of 3600 is (13 / 100) * 3600 = 468. Subtracting 468 from 3600 gives 3600 - 468 = 3132, which matches the given selling price. This confirms that the discount percentage is correctly calculated and that the values are internally consistent with the data in the question. Why Other Options Are Wrong: A discount of 12% on 3600 would be 0.12 * 3600 = 432, giving a selling price of 3168, not 3132. A discount of 17.21% would reduce the price by a much larger amount than 468. A discount of 14.94% would also lead to a selling price different from 3132 when applied to 3600. Only a 13% discount produces exactly the given selling price of Rs 3132, so the other options cannot be correct. Common Pitfalls: One common mistake is to calculate discount percentage using the selling price as the base instead of the marked price, which leads to a different numerical value. Another error is mis subtracting the selling price from the marked price, especially under exam pressure. To avoid these errors, always write out the steps explicitly: compute the discount amount first, then divide by marked price, and finally multiply by 100 to obtain the percentage. Final Answer: The discount percentage offered on the article is 13% of the marked price.

Question 8

A shopkeeper marks an item at Rs. 1250 but finally sells it for Rs. 1000. Based on these values of marked price and selling price, what percentage discount is he effectively offering on the marked price?

Accepted Answer

Introduction / Context: Discount questions are a core part of percentage based aptitude problems. Here, the shopkeeper has a clearly stated marked price and a lower selling price. The difference between these two values represents the absolute discount, and converting this difference into a percentage of the marked price gives the discount percentage, which is exactly what most competitive exams ask you to calculate. Given Data / Assumptions: Marked price (MP) of the item = Rs. 1250. Selling price (SP) of the item = Rs. 1000. Discount amount = MP - SP. Discount percentage is always calculated on the marked price, not on the selling price. All prices are in rupees and represent exact values. Concept / Approach: The key idea is that percentage discount = (discount amount / marked price) * 100. So we first compute the discount in rupees by subtracting the selling price from the marked price. Then we divide this discount by the marked price to see what fraction of the original price is being reduced. Finally, we multiply that fraction by 100 to express it as a percentage. This simple three step method works for all direct discount questions. Step-by-Step Solution: Step 1: Compute the discount amount: Discount = MP - SP = 1250 - 1000 = Rs. 250. Step 2: Write the formula for discount percentage: Discount% = (Discount / MP) * 100. Step 3: Substitute the values: Discount% = (250 / 1250) * 100. Step 4: Simplify the fraction: 250 / 1250 = 1 / 5. Step 5: Compute: (1 / 5) * 100 = 20. Step 6: Therefore, the discount percentage offered is 20 percent. Verification / Alternative check: An alternative way is to think proportionally. If the discount is 20 percent, then the customer pays 80 percent of the marked price. Calculate 80 percent of Rs. 1250: (80 / 100) * 1250 = 0.8 * 1250 = Rs. 1000. This matches the given selling price, confirming that the discount rate we found is correct. Why Other Options Are Wrong: 25 percent: A 25 percent discount on Rs. 1250 would be 0.25 * 1250 = Rs. 312.50, giving a selling price of Rs. 937.50, not Rs. 1000. 33.3 percent: Around one third off would reduce the price far below Rs. 1000, making it too large a discount. 250 percent: A discount cannot exceed 100 percent in normal situations, so 250 percent is meaningless here. 15 percent: A 15 percent discount would be 0.15 * 1250 = Rs. 187.50, giving a selling price of Rs. 1062.50, not Rs. 1000. Common Pitfalls: Common mistakes include dividing the discount by the selling price instead of the marked price, or confusing the absolute discount (in rupees) with the percentage discount. Some learners also reverse the numbers and compute 1000 / 1250 * 100 directly, thinking that gives the discount, whereas it actually gives the percentage of the marked price that is paid. Always remember: discount percentage is based on the marked price. Final Answer: The shopkeeper is offering a 20 percent discount on the marked price.

Question 9

A shopkeeper marks an item at Rs. 1200 but sells it for Rs. 960. Using these values of marked price and selling price, what percentage discount is he offering on the marked price?

Accepted Answer

Introduction / Context: This question again tests your understanding of how to convert a reduction in price into a discount percentage. Such problems are extremely common in shop and market based word problems, where a customer is given a reduction on the marked price. Being able to quickly compute the discount percent from marked and selling prices is an essential exam skill. Given Data / Assumptions: Marked price (MP) of the item = Rs. 1200. Selling price (SP) of the item = Rs. 960. Discount amount = MP - SP. Discount percentage is taken with respect to the marked price. All rupee values are exact and there are no additional taxes or charges mentioned. Concept / Approach: To find the discount percentage, we use the formula: Discount% = (Discount / Marked Price) * 100. So, first calculate the discount as the difference between marked and selling prices. Then divide this discount by the marked price to get the fraction of the original price that has been reduced. Finally, multiply by 100 to express this fraction as a percentage. This direct approach avoids confusion and works for any marked and selling prices. Step-by-Step Solution: Step 1: Find the discount amount: Discount = MP - SP = 1200 - 960 = Rs. 240. Step 2: Use the formula: Discount% = (Discount / MP) * 100. Step 3: Substitute the numbers: Discount% = (240 / 1200) * 100. Step 4: Simplify the fraction: 240 / 1200 = 24 / 120 = 1 / 5. Step 5: Compute (1 / 5) * 100 = 20. Step 6: Hence, the discount offered is 20 percent. Verification / Alternative check: If the discount is 20 percent, then the customer pays 80 percent of the marked price. Calculate 80 percent of Rs. 1200: (80 / 100) * 1200 = 0.8 * 1200 = Rs. 960. This value matches the given selling price, so our computed discount percentage is fully consistent with the problem data. Why Other Options Are Wrong: 25 percent: 25 percent of 1200 is 300, so the selling price would be 900, not 960. 12 percent: 12 percent of 1200 is 144, giving a selling price of 1056, which does not match 960. 28 percent: 28 percent of 1200 is 336, which would reduce the price to 864, not 960. 18 percent: 18 percent of 1200 is 216, giving a selling price of 984, not 960. Common Pitfalls: A frequent mistake is to divide the discount by the selling price instead of by the marked price, which gives a different and incorrect percentage. Another error occurs when students subtract the selling price from the discount or mix up the numbers. Writing the formula clearly and substituting values carefully helps avoid such confusion. Final Answer: The shopkeeper is offering a 20 percent discount on the marked price.

Question 10

A shop offers a 20% discount on an item. In addition, the customer applies a promo code and receives 5% cashback on the amount actually paid after the discount. What is the effective overall discount on the original marked price?

Accepted Answer

Introduction / Context: Modern shopping frequently combines multiple offers such as discounts and cashback. Exam questions use such scenarios to test your understanding of successive percentage changes and to distinguish between a simple discount and an effective overall reduction in what the customer finally spends. Here, you must carefully combine a 20% discount and a 5% cashback to find the true effective discount on the original price. Given Data / Assumptions: Let the original marked price of the item be M rupees. A flat 20% discount is applied first on M. The customer then gets 5% cashback on the amount actually paid after this discount. We must calculate the effective discount as a percentage of the original price M. Cashback is treated as money returned to the customer after payment, reducing the net amount spent. Concept / Approach: First, we compute the amount paid after the 20% discount. Then we calculate the cashback as 5% of that paid amount. The effective net amount spent is the discounted amount minus the cashback. Finally, the effective discount percentage is (original price - net amount spent) / original price * 100. This is different from simply adding discounts, because cashback is applied on a reduced base and acts after payment. Step-by-Step Solution: Step 1: After a 20% discount, the customer pays 80% of M, which is 0.80M. Step 2: Cashback is 5% of the amount paid, so cashback = 5% of 0.80M = 0.05 * 0.80M = 0.04M. Step 3: Net amount actually spent by the customer = amount paid - cashback = 0.80M - 0.04M = 0.76M. Step 4: So effectively, the customer is paying 76% of the original price. Step 5: Effective discount fraction = 1 - 0.76 = 0.24. Step 6: Effective discount percentage = 0.24 * 100 = 24 percent. Verification / Alternative check: Assume a concrete value, say M = Rs. 100. After a 20% discount, the customer pays Rs. 80. Cashback is 5% of 80, which is Rs. 4. Net spending = 80 - 4 = Rs. 76. Compared to the original Rs. 100, the effective reduction is 100 - 76 = Rs. 24, which is 24 percent of the original price. This numerical check confirms the algebraic reasoning. Why Other Options Are Wrong: 25.2 percent: This would come from incorrectly adding 20% and 5% of 80 directly as if both were discounts on M, which is not how the offer works. 25 percent: A simple sum 20% + 5% ignores the fact that cashback is calculated on the reduced price, not on the original price. 6 percent: This misinterprets 5% cashback as just 1% more than a 5% discount; it ignores the main 20% reduction entirely. 23 percent: This is a rounding or approximation error; the exact calculation clearly shows 24 percent. Common Pitfalls: Students often simply add 20% and 5% and answer 25 percent, assuming both are equivalent discounts on the original price. Others may treat cashback as a regular discount before payment and multiply wrong bases. Always pay attention to the order and base of each percentage: the first discount is on M, the cashback is on the discounted payment, and the final effective discount is compared back to M. Final Answer: The effective overall discount on the original marked price is 24 percent.

Question 11

In a shop, a trader has 1500 kg of toor dal in stock. If he sells 4.5% of this toor dal during the day, what quantity (in kilograms) of toor dal is sold?

Accepted Answer

Introduction / Context: This problem tests a very common application of percentages to quantities, in this case kilograms of toor dal. You are asked to find what 4.5% of a given weight is. Such calculations appear frequently in questions on inventory, stock, agriculture, and business, and mastering them builds a strong base for more complex percentage applications. Given Data / Assumptions: Total stock of toor dal = 1500 kg. Percentage sold = 4.5% of the total stock. The remaining stock is not required; only the sold quantity is asked. We assume all measurements are in kilograms and represent exact values. Concept / Approach: To find a percentage of a quantity, we use the basic formula: Percentage of a quantity = (percentage / 100) * quantity. Here, the percentage is 4.5 and the quantity is 1500 kg. We convert 4.5% to a decimal or fraction and then multiply by 1500. Breaking the calculation into smaller steps (like finding 1% or 0.5%) makes mental math easier and reduces errors. Step-by-Step Solution: Step 1: Express 4.5% as a fraction over 100: 4.5% = 4.5 / 100. Step 2: Quantity sold = (4.5 / 100) * 1500. Step 3: Compute 4.5 * 1500 first: 4.5 * 1500 = 4.5 * (15 * 100) = (4.5 * 15) * 100. Step 4: 4.5 * 15 = 67.5, so 4.5 * 1500 = 67.5 * 100 = 6750. Step 5: Now divide by 100: 6750 / 100 = 67.5 kg. Step 6: Therefore, the trader sells 67.5 kg of toor dal. Verification / Alternative check: You can also use the idea of 1%. One percent of 1500 kg is 15 kg. Then 0.5% is half of 1%, which is 7.5 kg. So 4.5% = 4% + 0.5%. Four percent of 1500 is 4 * 15 = 60 kg, and 0.5% is 7.5 kg. Adding them: 60 + 7.5 = 67.5 kg. This mental math approach confirms the earlier result exactly. Why Other Options Are Wrong: 64.5 kg: Slightly less than the correct value; this can arise from miscomputing 4.3% or a minor arithmetic slip. 63.5 kg: Clearly lower than 4.5% of 1500 and not supported by correct percentage calculation. 70 kg: Slightly more than 4.5%; corresponds to about 4.67% of 1500, not 4.5%. 60 kg: This is exactly 4% of 1500, not 4.5%, so it underestimates the sold quantity. Common Pitfalls: A common error is to confuse 4.5% with 45% and mistakenly compute a much larger value. Another pitfall is rounding too early or mishandling the decimal, for example treating 4.5 as 4.05. Always write the percentage clearly as percentage / 100 and take care when multiplying with decimals. Breaking down into 1% and 0.5% chunks also helps avoid mistakes. Final Answer: The quantity of toor dal sold is 67.5 kg.

Question 12

What is 15% of 34? Calculate the value of fifteen percent of the number thirty four, expressing your answer as a decimal.

Accepted Answer

Introduction / Context: Finding a given percentage of a number is one of the most basic yet frequently tested skills in quantitative aptitude. This question asks you to compute 15% of 34, which is a straightforward application of the percentage formula. Practising such small calculations builds confidence and speed for more complicated problems involving percentages and ratios. Given Data / Assumptions: The base number is 34. The required percentage is 15% of this number. We need the exact decimal value of 15% of 34. All calculations are in real numbers and there is no rounding instruction, so we keep the natural decimal result. Concept / Approach: The standard formula is: Percentage of a number = (percentage / 100) * number. Here, we must compute (15 / 100) * 34. You can do this either by converting 15% to the decimal 0.15 and multiplying by 34, or by first multiplying 15 * 34 and then dividing by 100. Both methods give the same result when done carefully, so choose whichever you find easier. Step-by-Step Solution: Step 1: Express 15% as a fraction over 100: 15% = 15 / 100. Step 2: Compute 15% of 34 as (15 / 100) * 34. Step 3: Multiply the numerator: 15 * 34 = (15 * 30) + (15 * 4) = 450 + 60 = 510. Step 4: Now divide by 100: 510 / 100 = 5.10. Step 5: 5.10 can be written as 5.1 without changing its value. Step 6: Therefore, 15% of 34 is 5.1. Verification / Alternative check: Another approach is to break 15% into 10% and 5%. Ten percent of 34 is 3.4 (since 10% is one tenth). Five percent is half of 10%, so it is 1.7. Adding them: 3.4 + 1.7 = 5.1. This mental breakdown confirms our earlier calculation and is a fast technique useful in exams. Why Other Options Are Wrong: 5: Slightly less than the correct value; this may come from rounding 5.1 down or using approximations instead of exact arithmetic. 5.2: Slightly greater than the correct result; it could come from incorrect multiplication or miswriting 5.1 as 5.2. 4.9: This is even further from the true answer and has no basis in the correct calculation of 15% of 34. 4.5: This corresponds to a smaller percentage than 15% and clearly does not match 510 / 100. Common Pitfalls: Some learners mistakenly divide 34 by 15 instead of multiplying 34 by 15% or 15 / 100. Others may forget to divide by 100, leaving the numerator 510 as the final answer. Another error is misplacing the decimal point when dividing by 100. To avoid such mistakes, always write the fraction explicitly and carefully move the decimal point two places when dividing by 100. Final Answer: 15% of 34 is 5.1.

Question 13

In a school there are 200 students in total. If one-fifth (1/5) of the students are boys, how many students in the school are girls?

Accepted Answer

Introduction / Context: This problem combines simple fractions with counting students in a school. Questions like this are very common in aptitude and school level exams because they test whether you can correctly interpret fractional information (like one fifth) and translate it into counts of boys and girls. It also reinforces the idea that the total must be split consistently between the given categories. Given Data / Assumptions: Total number of students in the school = 200. One fifth (1/5) of the students are boys. The remaining students are girls. We assume all students are either boys or girls, with no other categories mentioned. We need to find only the number of girls. Concept / Approach: First, convert the fraction 1/5 into an actual number of boys by multiplying it with the total number of students. Then, subtract the number of boys from the total to get the number of girls. This approach is straightforward: Number of boys = (1/5) * total. Number of girls = total - number of boys. Understanding such fraction based splits is foundational for more complex ratio and percentage problems. Step-by-Step Solution: Step 1: Total students = 200. Step 2: Fraction of students who are boys = 1/5. Step 3: Number of boys = (1/5) * 200. Step 4: Compute 200 / 5 = 40, so there are 40 boys. Step 5: Number of girls = total students - number of boys = 200 - 40. Step 6: Therefore, number of girls = 160. Verification / Alternative check: Check whether the distribution is reasonable. If there are 40 boys and 160 girls, then boys form 40 / 200 = 1/5 of the students, and girls form 160 / 200 = 4/5 of the students. The fractions 1/5 and 4/5 add up to 1, confirming that the entire school population is correctly accounted for and that the calculation is consistent. Why Other Options Are Wrong: 16: This is one fifth of 80, not 200, and is far too small for the given total. 140: Would mean 60 boys (since 200 - 140 = 60), which is 3/10 of the total, not 1/5. 40: This is the number of boys, not the number of girls. 120: Would imply 80 boys (200 - 120), yielding a boy fraction of 80 / 200 = 2/5, not 1/5. Common Pitfalls: A common error is to misread 1/5 as 5 or 20%, or to incorrectly think that 1/5 of 200 is 20. Another mistake is to treat 1/5 as if it were the number of girls instead of boys. Carefully identify which part of the population the fraction refers to and double check by adding the calculated parts to ensure they match the total. Final Answer: The number of girls in the school is 160.

Question 14

A shop offers a promotion on dupattas: if a customer buys 6 dupattas priced at Rs. 1200 each, they receive 3 additional dupattas free. What is the effective discount percentage on each dupatta compared to its marked price?

Accepted Answer

Introduction / Context: Promotional offers such as “buy some, get some free” are very common in real life and in aptitude exams. Although no explicit percentage is mentioned, such offers can be converted into an equivalent discount percentage to compare offers. This question asks you to find the effective discount on each dupatta when 3 pieces are given free on the purchase of 6, all with the same marked price. Given Data / Assumptions: Marked price of one dupatta = Rs. 1200. Customer buys 6 dupattas and pays for all 6 at marked price. Customer receives 3 extra dupattas free. Total dupattas received = 6 paid + 3 free = 9 dupattas. We must find the effective discount percentage on each dupatta relative to its marked price of Rs. 1200. Concept / Approach: The key idea is that the customer pays a certain total amount but receives more items than they pay for. So the effective price per dupatta is the total amount paid divided by the total number of dupattas received. Once we know this effective price per piece, we compare it with the marked price to get the effective discount in rupees, and then convert that discount into a percentage of the marked price. Step-by-Step Solution: Step 1: Total amount paid = price of 6 dupattas = 6 * 1200 = Rs. 7200. Step 2: Total number of dupattas received = 9. Step 3: Effective price per dupatta = total paid / number of dupattas = 7200 / 9. Step 4: Compute 7200 / 9 = 800, so effective price per dupatta is Rs. 800. Step 5: Marked price per dupatta = Rs. 1200, so discount per dupatta = 1200 - 800 = Rs. 400. Step 6: Effective discount percentage = (400 / 1200) * 100 = (1 / 3) * 100 ≈ 33.33 percent. Verification / Alternative check: Think of it as paying for 6 pieces and getting 9, which is effectively paying for 2/3 of the total pieces (since 6 is two thirds of 9). Thus the customer pays 66.67 percent of the total marked value and gets 33.33 percent effectively free as discount. This gives the same discount rate: 100 percent - 66.67 percent ≈ 33.33 percent. Why Other Options Are Wrong: 25 percent: This would mean effective price per piece is 75 percent of 1200, which is 900, not the 800 we computed. 30 percent: Would give an effective price of 70 percent of 1200, which is 840, also not supported by the total paid and received. 12.5 percent: Far too small; this corresponds to paying 87.5 percent of the price, much higher than the actual 66.67 percent. 50 percent: Would imply getting half the value free, which would require a different offer such as buy 1 get 1 free. Common Pitfalls: A common mistake is to treat the free dupattas as a flat percentage discount on the amount paid for the 6 pieces, rather than accounting for the fact that the free items are part of the total quantity received. Another error is to use 3/6 directly as 50 percent without considering the full 9 items. Always base the calculation on the total number of items received versus the total payment. Final Answer: The effective discount on each dupatta is approximately 33.33 percent of the marked price.

Question 15

Each question below compares two quantities.  Quantity I: The length of a rectangle is increased by 20% while its breadth is decreased by 10%. Find the percentage change in the area of the rectangle.  Quantity II: The base of a triangle is increased…

Accepted Answer

Introduction / Context: This is a quantity comparison problem involving percentage changes in geometric dimensions. You must understand how changes in length and breadth or in base and height affect areas of a rectangle and a triangle. The question checks whether you can convert successive percentage changes into multiplicative factors and then compare the net percentage changes in areas. Given Data / Assumptions: Quantity I: Rectangle with length increased by 20% and breadth decreased by 10%. Quantity II: Triangle with base increased by 30% and height decreased by 20%. Original shapes have some initial dimensions; only relative percentage changes matter, not the actual starting sizes. Area of rectangle = length * breadth. Area of triangle = (1/2) * base * height. We must compare the final percentage change in area for both cases. Concept / Approach: When a dimension changes by a percentage, the new dimension is obtained by multiplying the original by a factor. For example, a 20% increase corresponds to multiplying by 1.20, and a 10% decrease corresponds to multiplying by 0.90. For the area, we multiply all relevant dimension factors together. Because each shape’s original area is scaled by a product of these factors, we can find the overall percentage change in area by comparing the new factor to 1 and then convert it to a percentage. Step-by-Step Solution: Step 1: For Quantity I (rectangle), let original length = L and breadth = B. Original area = L * B. Step 2: Length increases by 20%, so new length = 1.20L. Breadth decreases by 10%, so new breadth = 0.90B. Step 3: New area of rectangle = 1.20L * 0.90B = 1.08LB. Step 4: Factor for area change in rectangle = 1.08, meaning an 8% increase in area. Step 5: For Quantity II (triangle), let original base = b and height = h. Original area = (1/2) * b * h. Step 6: Base increases by 30%, so new base = 1.30b. Height decreases by 20%, so new height = 0.80h. Step 7: New area of triangle = (1/2) * 1.30b * 0.80h = (1/2) * 1.04bh. Step 8: Factor for area change in triangle = 1.04, meaning a 4% increase in area. Step 9: Compare: 8% increase (Quantity I) versus 4% increase (Quantity II). So Quantity I > Quantity II. Verification / Alternative check: Assign simple numerical values, for example L = B = 10 for the rectangle, b = h = 10 for the triangle. Rectangle: original area = 100. New length = 12, new breadth = 9, new area = 108, which is 8% more than 100. Triangle: original area = (1/2) * 10 * 10 = 50. New base = 13, new height = 8, new area = (1/2) * 13 * 8 = 52, which is 4% more than 50. The numerical results confirm that Quantity I has a larger percentage increase than Quantity II. Why Other Options Are Wrong: Quantity I = Quantity II: This would require both areas to change by the same percentage, which is not the case (8% vs 4%). Quantity I Quantity II is the accurate relation. Common Pitfalls: One common mistake is to add or subtract percentages linearly without converting them into multiplicative factors, for example, thinking area change is 20% - 10% = 10% for the rectangle. Another error is forgetting that the factor 1/2 in the triangle’s area formula is common to both original and new areas and therefore cancels out. Always treat percentage changes as multipliers and avoid intuitive but incorrect shortcut additions. Final Answer: Quantity I is greater than Quantity II; that is, Quantity I > Quantity II.

Question 16

What value should replace the question mark (?) in the following equation?  45% of 400 + √(?) = 56% of 750 − 40% of 350

Accepted Answer

Introduction / Context: This question combines basic percentage calculations with square roots and an equation. The goal is to find the unknown number under the square root so that the left hand side and right hand side of the equation balance. Such problems test your ability to compute percentages accurately, manipulate equations, and recall the relationship between a square and its square root. Given Data / Assumptions: The equation is 45% of 400 + √(?) = 56% of 750 − 40% of 350. The unknown value under the square root is a non negative real number. All percentages are standard percentages, so 45% = 45 / 100, and so on. The operations follow normal arithmetic rules: calculate percentages first, then apply addition and subtraction. Concept / Approach: First, compute the known percentage expressions on both sides using the formula (percentage / 100) * number. Once you have numerical values, simplify the right hand side to a single number. Then subtract the known term on the left hand side to isolate the square root term. Finally, square both sides (or recognize a perfect square) to find the unknown value. Checking with familiar squares (like 100^2, 99^2, 101^2) helps confirm the answer. Step-by-Step Solution: Step 1: Compute 45% of 400: (45 / 100) * 400 = 0.45 * 400 = 180. Step 2: Compute 56% of 750: (56 / 100) * 750 = 0.56 * 750 = 420. Step 3: Compute 40% of 350: (40 / 100) * 350 = 0.40 * 350 = 140. Step 4: Simplify the right hand side: 56% of 750 − 40% of 350 = 420 − 140 = 280. Step 5: Now the equation becomes: 180 + √(?) = 280. Step 6: Subtract 180 from both sides to isolate the square root term: √(?) = 280 − 180 = 100. Step 7: To remove the square root, square both sides: ? = 100^2 = 10000. Verification / Alternative check: Substitute ? = 10000 back into the original equation. Then √(10000) = 100. The left side becomes 45% of 400 + 100 = 180 + 100 = 280. The right side, as computed earlier, is 56% of 750 − 40% of 350 = 420 − 140 = 280. Both sides match exactly, so ? = 10000 is confirmed as correct. Why Other Options Are Wrong: 1000: √1000 is approximately 31.6, which would make the left side 180 + 31.6 ≈ 211.6, not 280. 10201: √10201 is 101, giving a left side of 180 + 101 = 281, which is slightly larger than 280. 9801: √9801 is 99, giving a left side of 180 + 99 = 279, slightly less than 280. 6400: √6400 is 80, giving a left side of 180 + 80 = 260, again not equal to 280. Common Pitfalls: Common errors include miscalculating one of the percentages, especially 56% of 750 or 40% of 350, or forgetting to subtract properly when isolating the square root term. Another pitfall is squaring too early instead of first simplifying the equation, which can create unnecessary complexity. Finally, always remember that √x denotes the principal non negative square root, so you only consider the positive value when matching it to a perfect square. Final Answer: The missing value is 10000, because √(10000) = 100 balances the equation.

Question 17

The price of an article is reduced (cut) by 3%. By what percentage must this reduced price be increased so that the article returns exactly to its original price?

Accepted Answer

Introduction / Context: This question highlights an important concept in percentages: a decrease of a certain percentage does not require the same percentage increase to return to the original value. Instead, the required increase is slightly larger because it is applied to a smaller base. Understanding this asymmetry is crucial for solving many successive change questions in profit, loss, and pricing. Given Data / Assumptions: The original price of the article is some amount P. The price is first cut by 3%, leaving a reduced price. The reduced price is then increased by some unknown percentage x% to get back to P. We must compute the value of x. All percentage changes are applied multiplicatively to the current price at each step. Concept / Approach: A 3% decrease means the new price is 97% of the original, or 0.97P. Let the required percentage increase on this reduced price be x%. After the increase, the new price becomes 0.97P * (1 + x/100). To restore the original price, this expression must equal P. By forming the equation 0.97P * (1 + x/100) = P and solving for x, we obtain the required percentage increase. Step-by-Step Solution: Step 1: Let original price be P. Step 2: After a 3% reduction, reduced price = P - 0.03P = 0.97P. Step 3: Let the required increase be x%. New price after increase = 0.97P * (1 + x/100). Step 4: To get back to original price, set 0.97P * (1 + x/100) = P. Step 5: Divide both sides by P: 0.97 * (1 + x/100) = 1. Step 6: Divide both sides by 0.97: 1 + x/100 = 1 / 0.97. Step 7: Compute 1 / 0.97 ≈ 1.030927835. Step 8: Therefore, x/100 ≈ 1.030927835 - 1 = 0.030927835. Step 9: Multiply by 100: x ≈ 3.0927835%, which rounds to about 3.09 percent. Verification / Alternative check: Take a simple number for P, say P = 100. After a 3% cut, the price becomes 97. Now increase 97 by 3.09%: 3.09% of 97 ≈ 0.0309 * 97 ≈ 2.9973, and 97 + 2.9973 ≈ 99.9973, which is effectively 100 when rounded. This confirms that an increase of about 3.09 percent restores the original price after a 3 percent cut. Why Other Options Are Wrong: 3 percent: Using 3% again on the reduced price only brings it to 97 * 1.03 = 99.91, slightly below the original. 7.11 percent and 6 percent: These are far larger than needed and overshoot the original price by a noticeable margin. 2.69 percent: Too small; increasing 97 by only 2.69% yields a value below 100. Common Pitfalls: Many students assume that a 3% decrease followed by a 3% increase cancels out, but this is incorrect because the increase is applied to a smaller base. Others try to add or subtract percentages linearly without using multiplicative factors. Always remember to convert percentage changes into factors (like 0.97 or 1.0309) and work with equations when restoring original values. Final Answer: The reduced price must be increased by approximately 3.09 percent to restore the original price.

Question 18

At a discount of 15%, the selling price of a microwave oven is Rs. 34,000. What would be the selling price of the same microwave oven if the discount is changed to 37.5% on the same marked price?

Accepted Answer

Introduction / Context: This question involves working backwards from a discounted selling price to find the marked price, and then applying a different discount to that marked price. It tests your understanding of how discount percentages relate to selling prices, and how to reverse a discount to recover the original marked price. These steps are common in profit and loss and pricing problems. Given Data / Assumptions: At a 15% discount, the selling price (SP1) = Rs. 34,000. Let the marked price (MP) be M. We know SP1 = M after a 15% reduction, so SP1 = 85% of M. We must find the selling price SP2 if the discount is 37.5% on the same marked price M. All prices are in rupees and no extra charges or taxes are mentioned. Concept / Approach: A discount of 15% means the customer pays 85% of the marked price, that is SP1 = 0.85M. We use the given SP1 to solve for M. Once we have M, we apply 37.5% discount to get the new selling price SP2, which is 62.5% of M (because 100% - 37.5% = 62.5%). So, SP2 = 0.625M. Both steps rely on converting percentage discounts into decimal factors. Step-by-Step Solution: Step 1: Represent the first discount: At 15% discount, SP1 = 85% of MP. Step 2: Write the equation: 0.85M = 34,000. Step 3: Solve for M: M = 34,000 / 0.85. Step 4: Compute 34,000 / 0.85 = 40,000. So the marked price M = Rs. 40,000. Step 5: Now consider the new discount: 37.5% discount means the customer pays 62.5% of MP. Step 6: Write SP2 = 62.5% of 40,000 = 0.625 * 40,000. Step 7: Compute 0.625 * 40,000 = 25,000. Step 8: Therefore, at 37.5% discount, the selling price will be Rs. 25,000. Verification / Alternative check: We can confirm the marked price by recalculating the original selling price. Marked price M = Rs. 40,000. At 15% discount, discount amount = 0.15 * 40,000 = 6,000, so SP1 = 40,000 - 6,000 = 34,000, matching the problem statement. Then, at 37.5% discount, discount amount = 0.375 * 40,000 = 15,000, giving SP2 = 40,000 - 15,000 = 25,000, which matches our previous calculation exactly. Why Other Options Are Wrong: Rs. 15,625: This is far less than the price after a 37.5% discount and would correspond to a much bigger reduction. Rs. 17,968.75 and Rs. 29,218.75: These numbers do not correspond to a simple percentage such as 37.5% off Rs. 40,000 and likely arise from partial or incorrect factor calculations. Rs. 30,000: This would correspond to a 25% discount on 40,000, not 37.5%. Common Pitfalls: Students sometimes mistakenly subtract 15% and 37.5% directly from the selling price instead of working with the marked price. Another common error is to assume that 34,000 is 15% of the marked price instead of 85%. Always remember that a 15% discount means you pay 85% of the marked price. Converting percentages to factors like 0.85 and 0.625 keeps the reasoning clear. Final Answer: If the discount is 37.5%, the selling price of the microwave oven will be Rs. 25,000.

Question 19

A student was supposed to multiply a number by 6/5 but instead multiplied it by 5/6. What is the percentage error in the result (taking the value obtained by using 6/5 as the correct value)?

Accepted Answer

Introduction / Context: This question tests error analysis using percentages. A student uses the wrong multiplication factor, so the result obtained is different from the correct result. You are asked to quantify the error as a percentage of the correct value. Such questions are common in aptitude tests and help you understand how small mistakes in factors can create significant percentage errors. Given Data / Assumptions: Let the original number be N. Correct operation: multiply N by 6/5, so correct value = (6/5) * N. Wrong operation: multiply N by 5/6, so wrong value = (5/6) * N. Percentage error is computed with respect to the correct value. We assume N is positive, but the result is independent of the actual value of N. Concept / Approach: Percentage error is defined as (|correct value − wrong value| / correct value) * 100. We can keep N symbolic and compute both correct and wrong values in terms of N. Then we find their difference, divide by the correct value, and finally multiply by 100 to convert to a percentage. Since N cancels out, the answer is a single number independent of the particular value of N. Step-by-Step Solution: Step 1: Correct value = (6/5) * N = 1.2N. Step 2: Wrong value = (5/6) * N ≈ 0.8333N. Step 3: Error in absolute terms = correct value − wrong value = 1.2N − 0.8333N. Step 4: Compute difference: 1.2N − 0.8333N ≈ 0.3667N. Step 5: Percentage error = (error / correct value) * 100 = (0.3667N / 1.2N) * 100. Step 6: Simplify: N cancels, so we have (0.3667 / 1.2) * 100. Step 7: 0.3667 / 1.2 ≈ 0.3056. Step 8: Multiply by 100: percentage error ≈ 30.56 percent. Verification / Alternative check: Choose a convenient number, for example N = 60. Correct value = (6/5) * 60 = 72. Wrong value = (5/6) * 60 = 50. Error = 72 − 50 = 22. Percentage error = (22 / 72) * 100 ≈ 30.555..., which rounds to 30.56 percent. This numerical check agrees with the symbolic calculation and confirms the result. Why Other Options Are Wrong: 44 percent and 22 percent: These are typical guesses arising from mixing the ratio values but do not match the correct ratio of error to true value. 15.28 percent: Roughly half of the correct error; may result from using incorrect denominator in the percentage error formula. 36 percent: Overestimates the error; (36 / 100) * correct value would correspond to a larger difference than actually occurs. Common Pitfalls: Students often mistakenly use wrong value in the denominator when computing percentage error, which changes the result. Another error is to compare the two fractions 6/5 and 5/6 directly without considering that the base for percentage error is the correct value. Always stick to the standard definition: error divided by correct value, then multiplied by 100. Final Answer: The percentage error in the calculation is approximately 30.56 percent.

Question 20

A student was supposed to multiply a number by 5/4 but instead multiplied it by 4/5. What is the percentage error in the result (taking the value obtained by using 5/4 as the correct value)?

Accepted Answer

Introduction / Context: This is another percentage error question where the student uses the wrong multiplication factor. Instead of increasing the number by multiplying with 5/4, the student decreases it by multiplying with 4/5. You are asked to measure the error as a percentage of the correct result. Understanding this helps build strong skills in handling fractional multipliers and relative error. Given Data / Assumptions: Let the original number be N. Correct operation: multiply N by 5/4, so correct value = (5/4) * N. Wrong operation: multiply N by 4/5, so wrong value = (4/5) * N. Percentage error is calculated relative to the correct value. N is positive, but its actual value will cancel out in the ratio. Concept / Approach: Percentage error = (|correct value − wrong value| / correct value) * 100. We first express the correct and wrong results in terms of N. Then we find the absolute difference between them. After that, we divide the difference by the correct value and multiply by 100 to convert the fraction into a percentage. Using exact fractions helps avoid rounding errors until the last step. Step-by-Step Solution: Step 1: Correct value = (5/4) * N = 1.25N. Step 2: Wrong value = (4/5) * N = 0.8N. Step 3: Error in absolute terms = correct value − wrong value = 1.25N − 0.8N = 0.45N. Step 4: Percentage error = (error / correct value) * 100 = (0.45N / 1.25N) * 100. Step 5: Simplify: N cancels, so we get (0.45 / 1.25) * 100. Step 6: 0.45 / 1.25 = 45 / 125 = 9 / 25 = 0.36. Step 7: Multiply by 100: percentage error = 0.36 * 100 = 36 percent. Verification / Alternative check: Take N = 20 for easy numbers. Correct value = (5/4) * 20 = 25. Wrong value = (4/5) * 20 = 16. Error = 25 − 16 = 9. Percentage error = (9 / 25) * 100 = 36 percent. This concrete example matches the symbolic calculation and confirms the result. Why Other Options Are Wrong: 56.25 percent: This would correspond to a larger difference relative to the correct value and does not match the ratio 9/25. 18 percent and 28.13 percent: These are too small; they result from using the wrong denominator (possibly the wrong value) or partial computations. 25 percent: This corresponds to a difference of one quarter of the correct value, which is not the case here. Common Pitfalls: Students sometimes reverse the roles of correct and wrong values when forming the percentage error, leading to a different ratio. Another frequent mistake is to subtract the fractions 5/4 and 4/5 incorrectly or to divide their difference by the wrong base. Keeping everything symbolically in terms of N and applying the standard formula consistently prevents such errors. Final Answer: The percentage error in the calculation is 36 percent.

Percentage Questions

Questions

Practice smarter