Question 1

A student has to secure 40 percent marks to pass an examination. He obtains 67 marks and fails by 13 marks. What are the maximum marks for the exam?

Accepted Answer

Introduction / Context: This question links passing percentage, actual marks obtained, and the shortfall in marks to determine the maximum marks of the examination. It illustrates a standard technique in percentage problems where the passing score is expressed as a percentage of total marks and also as a specific number of marks. Given Data / Assumptions: - Let the maximum marks be M. - Passing percentage = 40 percent of M. - Student scores 67 marks. - He fails by 13 marks, meaning he is 13 marks short of the passing marks. - Therefore, passing marks = 67 + 13 = 80 marks. Concept / Approach: Passing marks can be expressed in two ways: as 40 percent of the maximum marks and as 80 marks from the shortfall information. Equating these two expressions allows us to solve for the maximum marks M. This is a typical direct proportion equation where we find the unknown base corresponding to a known percentage and value. Step-by-Step Solution: Step 1: From the statement "fails by 13 marks," we know passing marks = 67 + 13 = 80.Step 2: Passing marks are also 40 percent of the maximum marks M.Step 3: Write the equation: 40 percent of M = 80.Step 4: Convert 40 percent to decimal form: 40 percent = 0.40.Step 5: So 0.40 * M = 80.Step 6: Solve for M: M = 80 / 0.40.Step 7: Compute M = 80 / 0.40 = 200. Verification / Alternative check: Check by recomputing the passing marks from the found maximum. If M = 200, then 40 percent of 200 = 0.40 * 200 = 80 marks. The student scored 67 marks, which is indeed 13 marks less than 80. This confirms that maximum marks of 200 are consistent with the information. Why Other Options Are Wrong: - 300 and 240 would give passing marks of 120 and 96 respectively at 40 percent, which do not differ from 67 by exactly 13 marks. - 150 would give passing marks of 60, but the student already scored 67, so he would be passing not failing. Common Pitfalls: Some students incorrectly assume 67 is 40 percent of the maximum, ignoring the "fails by 13 marks" detail. Others subtract 13 from 67 instead of adding, misinterpreting the direction of the shortfall. Always carefully translate "fails by" or "passes by" into how far the candidate's score is from the required passing marks, and then set up a correct equation. Final Answer: The maximum marks for the examination are 200.

Question 2

In a sale there is a 30 percent discount on the marked price of 2,500 rupees, but an item is actually sold for only 1,400 rupees. What additional discount percentage, beyond the 30 percent sale discount, did the customer effectively receive?

Accepted Answer

Introduction / Context: This problem explores the idea of an extra discount applied after a sale discount. The marked price, sale discount, and final selling price are all given, and you must compute the additional discount percentage that explains the further reduction. This type of multi step discount calculation is common in real life promotions and exam questions. Given Data / Assumptions: - Marked price (MP) of the item = 2,500 rupees. - Advertised sale discount = 30 percent on the marked price. - Actual selling price (SP final) = 1,400 rupees. - First, compute the sale price after the 30 percent discount. - Then find what extra discount was given from that sale price down to 1,400 rupees, expressed as a percentage of the sale price. Concept / Approach: The solution consists of two phases: initial sale discount and additional discount. First calculate the price after the 30 percent sale, which is 70 percent of the marked price. Then treat the further reduction from that price to 1,400 rupees as a new discount and compute its percentage relative to the sale price. The base for the additional discount percent is the sale price, not the marked price. Step-by-Step Solution: Step 1: After a 30 percent discount on 2,500 rupees, the customer should pay 70 percent of the marked price.Step 2: 70 percent of 2,500 = 0.70 * 2,500 = 1,750 rupees.Step 3: However, the item is actually sold for 1,400 rupees.Step 4: Extra discount amount beyond the 30 percent sale = 1,750 - 1,400 = 350 rupees.Step 5: Additional discount percentage = (Extra discount / Sale price) * 100.Step 6: Substitute values: (350 / 1,750) * 100.Step 7: 350 / 1,750 = 1 / 5 = 0.20, so additional discount percentage = 0.20 * 100 = 20 percent. Verification / Alternative check: Check in one combined view. The marked price is 2,500. A 30 percent discount reduces it to 1,750. An additional 20 percent discount on 1,750 is 0.20 * 1,750 = 350, which brings the price down to 1,750 - 350 = 1,400 rupees. This matches the given final selling price, confirming that the extra discount is indeed 20 percent. Why Other Options Are Wrong: - 10 percent or 15 percent additional discount would not reduce 1,750 down to 1,400; they would leave a higher final selling price. - 25 percent extra discount would reduce 1,750 by 437.5 rupees, giving a selling price of 1,312.5 rupees, which is too low compared to the given 1,400 rupees. Common Pitfalls: One common mistake is to compute the additional discount percentage using the marked price as the base instead of the already reduced sale price. Another is to directly compare 2,500 and 1,400 and say the total discount is 44 percent and then try to subtract 30 percent to claim 14 percent extra. Successive discounts are multiplicative, so the extra discount must be computed on the already discounted value, not on the original marked price. Final Answer: The customer effectively received an additional 20 percent discount beyond the 30 percent sale discount.

Question 3

Pranita scores 30 marks more in Mathematics than in Science, and her Mathematics marks are 60 percent of the sum of her Mathematics and Science marks. What are her Science marks?

Accepted Answer

Introduction / Context: This question is a classic example of using percentages in combination with a difference between two quantities. It involves forming and solving a simple linear equation by translating the word statement about marks into algebraic relationships. Such problems appear frequently in exam sections about percentages and ratios. Given Data / Assumptions: - Let Science marks be S. - Mathematics marks are 30 more than Science marks, so Mathematics marks = S + 30. - Mathematics marks are 60 percent of the sum of Mathematics and Science marks. - So S + 30 = 60 percent of (S + S + 30). - We must find S, the Science marks. Concept / Approach: We translate the condition "Mathematics marks are 60 percent of the total of both subjects" into an equation. Percentages are converted to decimals for easier computation. This gives a linear equation in a single variable S. Solving this equation yields Pranita's Science marks, and then Mathematics marks can also be checked if desired. Step-by-Step Solution: Step 1: Let Science marks = S.Step 2: Mathematics marks = S + 30, since she scores 30 more in Mathematics.Step 3: Sum of both subjects = S (Science) + (S + 30) (Mathematics) = 2S + 30.Step 4: Given that Mathematics marks are 60 percent of the total, we write: S + 30 = 0.60 * (2S + 30).Step 5: Expand the right side: 0.60 * (2S + 30) = 1.2S + 18.Step 6: So, the equation becomes S + 30 = 1.2S + 18.Step 7: Rearrange to solve: S - 1.2S = 18 - 30, which gives -0.2S = -12.Step 8: Divide both sides by -0.2: S = -12 / -0.2 = 60. Verification / Alternative check: If Science marks S = 60, then Mathematics marks are S + 30 = 90. The total marks in both subjects are 60 + 90 = 150. Sixty percent of 150 is 0.60 * 150 = 90, which matches the Mathematics marks. This confirms that S = 60 and M = 90 satisfy the given condition completely. Why Other Options Are Wrong: - 90 or 120 as Science marks would produce totals and percentages that do not satisfy the condition that Mathematics marks are 60 percent of the combined total. - 150 as Science marks is impossible when Mathematics is only 30 marks higher, because then Mathematics would be 180 and 60 percent of their sum would not equal 180. Common Pitfalls: A typical mistake is to treat 60 percent as a fraction of only one subject instead of the combined total, or to misunderstand "60 percent of the sum" as some other relationship. Another error is to forget to form the correct equation S + 30 = 0.60 * (2S + 30) and instead equate wrong expressions. Carefully translate each part of the verbal statement before solving. Final Answer: Pranita's Science marks are 60.

Question 4

A watch with marked price 8,400 rupees is sold for 5,040 rupees after two successive discounts. If the first discount is 25 percent, what is the percentage of the second discount?

Accepted Answer

Introduction / Context: This question involves successive discounts and requires finding the second discount rate when the combined effect of two discounts is known. Successive discounts are common in retail pricing and exam problems, and understanding that they are multiplicative rather than additive is essential. Given Data / Assumptions: - Marked price (MP) of the watch = 8,400 rupees. - First discount = 25 percent. - Final selling price (SP) after two discounts = 5,040 rupees. - Let the second discount rate be x (expressed as a decimal, for example 0.2 for 20 percent). - We must find x, and then express it as a percentage to match the answer options (noting that the options here are given as decimals representing the fraction, not the percent symbol itself). Concept / Approach: A 25 percent discount on the marked price means the price becomes 75 percent of the marked price, or 0.75 * MP. Then the second discount of rate x is applied on this reduced price, so the customer finally pays (1 - x) of that reduced amount. Thus, SP = MP * 0.75 * (1 - x). Knowing SP and MP, we can solve for x. Step-by-Step Solution: Step 1: After a 25 percent discount, the price becomes 75 percent of 8,400 rupees.Step 2: Compute 75 percent of 8,400: 0.75 * 8,400 = 6,300 rupees.Step 3: Let the second discount rate be x, so after the second discount the buyer pays (1 - x) of 6,300.Step 4: Final selling price SP = 6,300 * (1 - x) = 5,040 rupees.Step 5: Form the equation: 6,300 * (1 - x) = 5,040.Step 6: Divide both sides by 6,300: 1 - x = 5,040 / 6,300.Step 7: Simplify 5,040 / 6,300 = 0.8.Step 8: So 1 - x = 0.8, which gives x = 1 - 0.8 = 0.2. Verification / Alternative check: If the second discount is 0.2, that is 20 percent, then after first reducing the price to 6,300 rupees, a further 20 percent discount is 0.20 * 6,300 = 1,260 rupees. Subtracting 1,260 from 6,300 gives 5,040 rupees, which matches the given final selling price. This confirms that the second discount rate is 0.2 (20 percent). Why Other Options Are Wrong: - 0.15 (15 percent) and 0.25 (25 percent) would produce different final prices when applied on 6,300 rupees. - 0.3 (30 percent) would reduce the price too much and produce a selling price lower than 5,040 rupees. Common Pitfalls: A common error is to simply add the two discounts as 25 percent plus x and try to match combined percentage directly with SP and MP. However, successive discounts are not additive; they are applied one after another, leading to a multiplicative combined factor. Always express each discount as a factor on the price in sequence and then solve using the given final selling price. Final Answer: The second discount rate is 0.2, which corresponds to 20 percent.

Question 5

A dealer sells an article at a discount of 5 percent on the marked price. The marked price is 12 percent above the cost price, and the article is sold for 532 rupees. What is the cost price of the article?

Accepted Answer

Introduction / Context: This problem links cost price, marked price, discount percentage, and final selling price. It is a typical profit and loss question where you must move backward from selling price through discount and marked price to find the cost price. Understanding these chained relationships is essential for exam problems about pricing. Given Data / Assumptions: - Let cost price (CP) be C rupees. - Marked price (MP) is 12 percent above CP, so MP = C * (1 + 0.12) = 1.12 * C. - Discount given = 5 percent on MP. - So selling price (SP) is 95 percent of MP, that is 0.95 * MP. - The actual selling price is given as 532 rupees. - We must find the cost price C. Concept / Approach: The marked price is a fixed percentage above cost price, and discount is a percentage of the marked price. We express SP in terms of CP using both relationships and then set it equal to the given selling price. This produces a direct equation in C. Solving that equation yields the cost price. Step-by-Step Solution: Step 1: Marked price MP = 1.12 * C.Step 2: A 5 percent discount on MP means the customer pays 95 percent of MP.Step 3: Therefore, selling price SP = 0.95 * MP = 0.95 * 1.12 * C.Step 4: Multiply 0.95 and 1.12: 0.95 * 1.12 = 1.064.Step 5: So SP = 1.064 * C.Step 6: Given SP = 532 rupees, we have 1.064 * C = 532.Step 7: Solve for C: C = 532 / 1.064.Step 8: Compute 532 / 1.064 = 500 rupees. Verification / Alternative check: Check by moving forward. If CP = 500 rupees, then MP = 1.12 * 500 = 560 rupees. A 5 percent discount on 560 rupees is 0.05 * 560 = 28 rupees. So SP = 560 - 28 = 532 rupees, matching the given selling price. This confirms that cost price equals 500 rupees. Why Other Options Are Wrong: - 525, 505, and 520 rupees do not produce a marked price and discounted selling price that equal 532 when the same percentage relationships are applied. Common Pitfalls: Some students mistakenly apply 12 percent on the selling price instead of on the cost price, or treat the 5 percent discount as applied on cost price instead of on marked price. Another common error is to add the percentages directly without considering that one is a markup and the other a discount. Always write an explicit expression for SP in terms of CP and then solve systematically. Final Answer: The cost price of the article is 500 rupees.

Question 6

A boy is asked to subtract the sum of 1/4 and 1/5 from unity and express the answer in decimals. He gives the answer as 0.45. What is the percentage error in his answer?

Accepted Answer

Introduction / Context: This question tests your ability to work with fractions, decimals, and percentage error. The student is supposed to subtract the sum of two fractions from 1 and convert the result into decimal form, but he mistakenly reports the intermediate sum instead. You must compute the correct value and then determine the error relative to that value. Given Data / Assumptions: - Required computation: 1 - (1/4 + 1/5). - Boy's answer in decimal form: 0.45. - We must find the correct value of the expression. - Then we must calculate percentage error = (Absolute error / True value) * 100 percent. Concept / Approach: First add the fractions 1/4 and 1/5 by finding a common denominator, then subtract this sum from unity (1). Then convert the result into decimals. The boy's answer is compared with the correct answer to find the absolute difference. Finally, the percentage error is calculated by dividing the absolute error by the true value and multiplying by 100. Step-by-Step Solution: Step 1: Compute the sum 1/4 + 1/5.Step 2: Common denominator of 4 and 5 is 20, so 1/4 = 5/20 and 1/5 = 4/20.Step 3: Sum = 5/20 + 4/20 = 9/20.Step 4: Required expression is 1 - 9/20.Step 5: Write 1 as 20/20, so 1 - 9/20 = 20/20 - 9/20 = 11/20.Step 6: Convert 11/20 to decimal: 11 divided by 20 = 0.55.Step 7: True value of the expression is 0.55, while the boy's answer is 0.45.Step 8: Absolute error = |0.55 - 0.45| = 0.10.Step 9: Percentage error = (0.10 / 0.55) * 100 percent.Step 10: 0.10 / 0.55 = 10 / 55 = 2 / 11.Step 11: So percentage error = (2 / 11) * 100 percent = 200 / 11 percent. Verification / Alternative check: To confirm, approximate 200 / 11 percent as a decimal: 200 / 11 is about 18.18 percent. This is a reasonable size for an error of 0.10 when the true value is 0.55, because 10 is roughly 18 percent of 55. The approximate mental estimation matches our exact calculation, which increases confidence in the result. Why Other Options Are Wrong: - (100/11) percent, about 9.09 percent, would correspond to an error of about 0.05 on a true value of 0.55, not 0.10. - 50 percent is far too large and would imply an error equal to half the true value. - 10 percent would correspond to 0.055 error, which is much smaller than the actual 0.10 difference. Common Pitfalls: Many students forget that percentage error is based on the true value, not on the wrong value. Others mis-handle the fraction addition or accidentally subtract 1/4 - 1/5 instead of adding them. It is also easy to confuse 0.45 and 0.55 when converting fractions to decimals. Working methodically and checking the arithmetic helps avoid these mistakes. Final Answer: The percentage error in the boy's answer is 200 / 11 percent.

Question 7

Two baskets together contain 640 oranges. If one fifth of the oranges in the first basket are transferred to the second basket and then the numbers of oranges in the two baskets become equal, how many oranges were there in the first basket originall…

Accepted Answer

Introduction / Context: This is a word problem involving simple algebra and ratios. It describes a transfer of oranges between two baskets and states that after moving a fraction of the first basket's contents, both baskets end up with the same number of oranges. The total number of oranges is fixed. You must set up and solve equations to find the original number in the first basket. Given Data / Assumptions: - Total number of oranges in both baskets together = 640. - Let the number of oranges in the first basket initially be x. - Then the second basket initially has 640 - x oranges. - One fifth of the oranges in the first basket are transferred to the second basket. - After the transfer, both baskets contain the same number of oranges. Concept / Approach: The key idea is conservation of total oranges and equality of the final counts. When one fifth of x is moved from the first basket to the second, the first basket is left with four fifths of x, and the second basket gains that one fifth of x. Setting these final quantities equal produces an equation that can be solved for x. Once x is known, it directly gives the original number in the first basket. Step-by-Step Solution: Step 1: Let the initial number of oranges in the first basket be x.Step 2: Then the initial number in the second basket is 640 - x.Step 3: One fifth of the first basket's oranges is x / 5.Step 4: After transferring x / 5 from the first to the second basket, the first basket has x - x / 5 = (4x / 5) oranges.Step 5: The second basket now has (640 - x) + x / 5 oranges.Step 6: After the transfer, the two baskets have equal numbers of oranges, so set 4x / 5 = (640 - x) + x / 5.Step 7: Multiply every term by 5 to clear the denominator: 4x = 5(640 - x) + x.Step 8: Expand: 4x = 3,200 - 5x + x = 3,200 - 4x.Step 9: Add 4x to both sides: 8x = 3,200.Step 10: Solve for x: x = 3,200 / 8 = 400. Verification / Alternative check: If the first basket originally had 400 oranges, the second had 640 - 400 = 240 oranges. One fifth of the first basket is 400 / 5 = 80. After moving 80 oranges, the first basket has 400 - 80 = 320, and the second basket has 240 + 80 = 320. Both baskets now have 320 oranges, which confirms that x = 400 is consistent with the conditions. Why Other Options Are Wrong: - 800 and 600 exceed or misfit the total of 640 or fail the equality condition when checked with the transfer rule. - 300 does not satisfy both the total 640 and the final equality condition; testing it will show unequal final counts in the baskets. Common Pitfalls: Some learners forget that the second basket gains exactly the amount the first basket loses, leading to incorrect equations. Others may incorrectly assume that one fifth is taken from the total instead of from the first basket only. Always define variables clearly and translate the transfer step precisely into algebraic expressions before solving. Final Answer: The first basket originally contained 400 oranges.

Question 8

A shopkeeper offers a 15% discount on all plastic toys, and gives an additional 4% discount on the reduced price to customers who pay in cash. For a toy with a marked price of Rs 200, how much (in Rs) will a customer actually pay if the payment is m…

Accepted Answer

Introduction / Context: This question is about successive percentage discounts and how they affect the final selling price that a customer has to pay. Such problems are very common in competitive exams under the profit, loss and discount chapter, and they test whether the student understands that multiple discounts are applied one after another on the reduced price, and not added directly as simple percentages. Given Data / Assumptions: The marked price of the plastic toy is Rs 200. The shopkeeper gives a first discount of 15% on the marked price. An additional discount of 4% is given on the already reduced price to customers who pay in cash. We assume there are no taxes or extra charges. Concept / Approach: To solve such questions, we use the percentage reduction formula step by step. A discount of d% on a price P means the new price is P * (1 - d/100). If two discounts are given successively, we apply the first discount, compute the reduced price, and then apply the second discount on that reduced price. It is important not to simply add the percentages (15% + 4% = 19%), because that would ignore the compounding effect of the discounts on different bases. Step-by-Step Solution: Step 1: Marked price of the toy = Rs 200. Step 2: First discount = 15% of 200 = 0.15 * 200 = Rs 30. Step 3: Price after first discount = 200 - 30 = Rs 170. Step 4: Second discount = 4% of 170 = 0.04 * 170 = Rs 6.8. Step 5: Final price after both discounts = 170 - 6.8 = Rs 163.2. Step 6: Therefore, the customer pays Rs 163.2 when paying in cash. Verification / Alternative check: Instead of subtracting discount amounts, we can work with multiplying factors. The first discount of 15% means the price becomes 85% of the original: 200 * 0.85 = 170. Then a 4% discount makes the price 96% of 170: 170 * 0.96 = 163.2. This matches our earlier calculation, so the answer is consistent and verified. Why Other Options Are Wrong: 133.7: This is far lower than the correct price and could come from incorrectly applying a much higher total discount. 129.8: This also represents an excessive discount, possibly from mistakenly subtracting both percentages directly from 200 and then applying further errors. 153.3: This might come from applying only one discount or an incorrect order of operations. 160.0: This is close but incorrect, possibly from rounding or approximating the discounts rather than calculating accurately. Common Pitfalls: Students sometimes simply add 15% and 4% to say the total discount is 19% and then compute 19% of 200. That would give 200 * 0.81 = 162, which does not match the correct answer. The main mistake is ignoring that the second discount is on the already reduced price, not on the original marked price. Another common error is to round intermediate values aggressively, which can slightly change the final result in sensitive questions. Final Answer: The customer will have to pay Rs 163.2 for the toy when paying in cash after both discounts are applied.

Question 9

A photographer allows a 10% discount on the advertised marked price of a camera. If the camera costs him Rs 600 and he wants to earn a profit of 20% on his cost price, what marked price (in Rs) should he print on the camera so that after the discoun…

Accepted Answer

Introduction / Context: This question checks understanding of the relationship between cost price, marked price, discount and desired profit. It is a classic profit and loss situation where the seller offers a discount but still wants to achieve a specific profit percentage. Students must be able to work backwards from the required profit to the necessary marked price. Given Data / Assumptions: Cost price of the camera = Rs 600. Desired profit = 20% on cost price. Discount allowed on marked price = 10%. We assume no taxes or additional charges. Concept / Approach: First, we compute the selling price needed to achieve a 20% profit on the cost price. Profit percent is always calculated on cost price unless stated otherwise. Then, since the camera will be sold after allowing a 10% discount on the marked price, we express selling price as 90% of the marked price. From this equation we can solve for the required marked price. Understanding that discount is applied on the marked price, not on cost price, is crucial. Step-by-Step Solution: Step 1: Cost price (CP) = Rs 600. Step 2: Desired profit = 20% of CP = 0.20 * 600 = Rs 120. Step 3: Required selling price (SP) = CP + profit = 600 + 120 = Rs 720. Step 4: Let the marked price be M. After a 10% discount, SP = 90% of M = 0.90 * M. Step 5: Set 0.90 * M = 720 and solve for M. Step 6: M = 720 / 0.90 = 800. Step 7: Therefore, the photographer must mark the camera at Rs 800. Verification / Alternative check: We can verify quickly: 10% of 800 is 80, so discounted price = 800 - 80 = 720. This is exactly the selling price that gives a 20% profit over the cost price of 600. Hence the marked price of Rs 800 is correct. Why Other Options Are Wrong: 650: Even without discount, this price would give a profit of only 50 over 600, which is less than 20%. 700: After 10% discount, selling price would be 630, which is just 5% profit on 600. 850: After 10% discount, selling price would be 765, which is more than the required 20% profit. 900: After 10% discount, selling price becomes 810, far greater than the targeted profit margin. Common Pitfalls: A common mistake is to calculate the 20% profit on the marked price instead of the cost price. Another frequent error is to forget that the 10% discount is on the marked price and to subtract 10% from the cost price instead. Students also sometimes try to add or subtract percentages without translating them into actual amounts, which leads to incorrect results. Final Answer: The camera should be marked at Rs 800 so that, after a 10% discount, the photographer still earns a 20% profit on his cost price.

Question 10

A dinner set has a marked price of Rs 1500. A customer buys it after receiving two successive discounts: first a discount of 15% on the marked price and then an additional discount on the reduced price. If the customer finally pays Rs 1173, what was…

Accepted Answer

Introduction / Context: This problem focuses on successive percentage discounts and how to find an unknown discount rate when the final selling price is known. It is a standard question in the percentage and discount chapter and tests algebraic manipulation along with a clear understanding that every discount is applied on the current price, not the original marked price. Given Data / Assumptions: Marked price of the dinner set = Rs 1500. First discount = 15% on the marked price. Second discount = unknown percentage on the already reduced price. Final amount paid by the customer = Rs 1173. We assume no additional charges or taxes. Concept / Approach: The key idea is that the first discount reduces the marked price to a new intermediate price. The second discount is then applied on this intermediate price. We first compute the price after the first discount. Then we express the final price in terms of the unknown second discount and equate it to the given amount. Solving this linear equation gives the discount rate. We should remember that successive discounts cannot simply be added because their bases are different. Step-by-Step Solution: Step 1: Marked price (MP) = Rs 1500. Step 2: First discount = 15% of MP = 0.15 * 1500 = Rs 225. Step 3: Price after first discount = 1500 - 225 = Rs 1275. Step 4: Let the second discount rate be d% on Rs 1275. Step 5: Final price after second discount = 1275 * (1 - d/100) = Rs 1173. Step 6: Form the equation 1275 * (1 - d/100) = 1173. Step 7: Divide both sides by 1275 to get 1 - d/100 = 1173 / 1275. Step 8: 1173 / 1275 = 0.92, so 1 - d/100 = 0.92. Step 9: d/100 = 1 - 0.92 = 0.08, so d = 8. Step 10: Therefore, the second discount rate is 8%. Verification / Alternative check: We can verify by forward calculation. After the first 15% discount, the price is 1500 * 0.85 = 1275. Applying an 8% discount gives 1275 * 0.92 = 1173. This exactly matches the given final price, confirming that 8% is correct. Why Other Options Are Wrong: 15%: This would give a much lower final price than 1173 because the total effect of two 15% discounts is too large. 7%: Using 7% gives a final price of 1275 * 0.93 = 1186.25, not 1173. 9%: Using 9% gives a final price of 1275 * 0.91 = 1160.25, which is also incorrect. 10%: This would give 1275 * 0.90 = 1147.5, lower than the actual amount paid. Common Pitfalls: Many learners assume that the two discounts simply add up and try to guess the second discount from a total discount percentage. Others mistakenly apply the second discount on the original marked price instead of the already reduced price. Errors in forming or solving the equation are also common. Carefully tracking each step and consistently working with the correct base value helps avoid these mistakes. Final Answer: The rate of the second discount was 8% on the already reduced price.

Question 11

A businessman imported laptops worth Rs 210000, mobile phones worth Rs 100000 and television sets worth Rs 150000. He had to pay import duties at special rates of 10% on laptops, 8% on phones and 5% on television sets. What is the total duty (in Rs)…

Accepted Answer

Introduction / Context: This problem is a straightforward application of percentage calculation on different parts of a total amount. It involves computing percentage duties on separate categories of imported goods and then adding them to get the total duty. It checks basic arithmetic and the ability to handle multiple percentages correctly. Given Data / Assumptions: Value of laptops imported = Rs 210000, duty rate = 10%. Value of mobile phones imported = Rs 100000, duty rate = 8%. Value of television sets imported = Rs 150000, duty rate = 5%. Total duty is the sum of duties on each category. Concept / Approach: The duty on an item is calculated as (duty rate / 100) * value of that item. Since different categories have different rates, we calculate each duty separately and then add the results. There is no compounding or successive percentage here, only simple percentage on fixed base values. This is a common type of problem in profit and loss and taxation concepts. Step-by-Step Solution: Step 1: Duty on laptops = 10% of 210000 = 0.10 * 210000 = Rs 21000. Step 2: Duty on mobile phones = 8% of 100000 = 0.08 * 100000 = Rs 8000. Step 3: Duty on television sets = 5% of 150000 = 0.05 * 150000 = Rs 7500. Step 4: Total duty = 21000 + 8000 + 7500. Step 5: Total duty = Rs 36500. Verification / Alternative check: As a quick check, we can confirm that each percentage is applied to the correct base. Laptops have the highest value and highest duty rate, giving the largest duty component. Adding 21000 and 8000 gives 29000, and 29000 + 7500 gives 36500. The numbers are consistent and easy to verify manually. Why Other Options Are Wrong: 37000: This is slightly higher than the correct total and suggests that one of the individual duties may have been rounded up or miscalculated. 37250: This value does not match the sum of any plausible combination of the given percentage duties. 37500: This could come from mistakenly applying 10% on all three categories, which would be wrong. 36000: This is lower than the correct total, possibly from miscalculating one of the smaller duty components. Common Pitfalls: Students may incorrectly apply a single average percentage to the total value, or mix up which rate applies to which category. Others may mistakenly add percentages before applying them. Careful reading and separate calculations for each category help prevent these errors. Using clear intermediate steps is important when dealing with multiple components. Final Answer: The businessman had to pay a total import duty of Rs 36500 on all the items combined.

Question 12

A man spends 7.5% of his money first, and then spends 75% of the remaining amount. After these two expenditures he is left with Rs 370. How much money did he originally have?

Accepted Answer

Introduction / Context: This question involves successive percentage reductions of a total amount of money. It is typical of percentage and income expenditure questions, where part of the money is spent in stages and the final remaining balance is known. The task is to work backwards to find the original amount before any spending took place. Given Data / Assumptions: The person initially has an unknown amount of money, say M. He spends 7.5% of M first. He then spends 75% of the remaining amount after the first spending. He is left with Rs 370 after both spendings. Concept / Approach: We treat each spending as a percentage reduction applied successively. After spending 7.5% of M, he retains 92.5% of M. Then he spends 75% of that remaining amount, so he retains only 25% of the remaining amount. Overall, the final money left is a certain fraction of the original M. Once we express that fraction, we equate it to Rs 370 and solve for M using simple algebra. This is a good example of how successive percentage changes multiply rather than add. Step-by-Step Solution: Step 1: Let the original money be M. Step 2: First spending = 7.5% of M = 0.075 * M. Step 3: Money left after first spending = M - 0.075M = 0.925M. Step 4: Second spending = 75% of 0.925M = 0.75 * 0.925M = 0.69375M. Step 5: Money left after second spending = 0.925M - 0.69375M = 0.23125M. Step 6: According to the question, 0.23125M = 370. Step 7: So M = 370 / 0.23125 = 1600. Step 8: Therefore, the man originally had Rs 1600. Verification / Alternative check: We can check by forward calculation. Start with M = 1600. First spending = 7.5% of 1600 = 0.075 * 1600 = 120. Remaining = 1600 - 120 = 1480. Second spending = 75% of 1480 = 0.75 * 1480 = 1110. Remaining = 1480 - 1110 = 370. This matches the given remaining amount, so the calculation is correct. Why Other Options Are Wrong: 1200: If M were 1200, the final remainder after the same steps would not be 370 but a smaller amount. 1500: This would also result in a different remaining amount after two spendings. 1400: Applying the same process to 1400 does not end with 370. 1800: With 1800, the remaining balance after both reductions would be higher than 370. Common Pitfalls: Students sometimes subtract percentages incorrectly by adding 7.5% and 75% as if the man spent 82.5% of his money in one shot. That ignores the fact that 75% is taken from the remaining amount, not from the original. Another common mistake is to forget to convert percentages into decimals before multiplication. Writing each step with clear fractional or decimal values helps avoid these errors. Final Answer: The man originally had Rs 1600 before he started spending.

Question 13

Two successive discounts of 25% each are given on the marked price of an article. A single discount equivalent to these two successive discounts must be equal to what percentage?

Accepted Answer

Introduction / Context: This problem is about converting two successive percentage discounts into one equivalent single discount. It tests the understanding that successive percentage changes are multiplicative in effect and cannot be combined by simple addition. Such questions appear frequently in competitive exams within the percentage and discount chapter. Given Data / Assumptions: There are two discounts applied successively, each of 25%. We want to find a single discount rate that gives the same final price. No information about the actual marked price is needed because the result is percentage based. Concept / Approach: If a discount of d% is given, the price becomes (1 - d/100) times the original. For successive discounts d1% and d2%, the combined reduction factor is (1 - d1/100) * (1 - d2/100). To find the equivalent single discount D%, we set (1 - D/100) equal to that product and solve for D. In this question both discounts are 25%, so the calculation simplifies nicely. Step-by-Step Solution: Step 1: First discount of 25% leaves 75% of the price, so factor = 0.75. Step 2: Second discount of 25% again leaves 75% of the current price, so second factor = 0.75. Step 3: Combined factor after two discounts = 0.75 * 0.75 = 0.5625. Step 4: This means the customer finally pays 56.25% of the original price. Step 5: Therefore, the total effective discount = 100% - 56.25% = 43.75%. Step 6: So the single equivalent discount is 43.75%. Verification / Alternative check: Take a convenient marked price, say Rs 100. After the first 25% discount, price becomes 100 - 25 = 75. After the second 25% discount, price becomes 75 - 18.75 = 56.25. So the loss in price is 100 - 56.25 = 43.75. This confirms the computed single discount of 43.75%. Why Other Options Are Wrong: 56.25: This is the final percentage of price paid, not the percentage discount. 50: Adding 25% and 25% directly would give 50%, but that ignores the multiplicative nature of successive discounts. 45: This is an approximation, not the exact value. 40: This is lower than the correct discount and does not match the actual effect. Common Pitfalls: The most common mistake is to simply add the percentages and claim that two 25% discounts equal a 50% discount, which is incorrect. Another error is to take the average of percentages. The correct technique is always to convert percentages to decimal factors, multiply them, and then convert back. Using a trial marked price of 100 is a very helpful method to visualise and verify results quickly. Final Answer: Two successive discounts of 25% each are equivalent to a single discount of 43.75% on the original price.

Question 14

Two labourers A and B are together paid a total amount of Rs 650 per day. Labourer A is paid 160% of the amount paid to labourer B. How much (in Rs) is labourer B paid per day?

Accepted Answer

Introduction / Context: This question involves percentage comparison between two quantities and total sum decomposition. It is a typical example from ratio and percentage topics, where one worker is paid a certain percent of the others wage, and the total payment is known. The idea is to express both payments in terms of one variable and then solve a simple equation. Given Data / Assumptions: Total daily payment to A and B together = Rs 650. Payment to A is 160% of payment to B. We need to find the daily wage of B. Concept / Approach: If we let B's daily wage be x, then A's daily wage becomes 160% of x, that is 1.6x. The total wage per day for both is x + 1.6x = 2.6x, and this sum is given as Rs 650. Solving for x gives the wage of B. The problem is essentially a ratio problem where the effective ratio of A to B is 1.6 : 1, or 16 : 10, which simplifies to 8 : 5. Step-by-Step Solution: Step 1: Let daily wage of B be x. Step 2: Payment to A is 160% of x, so wage of A = 1.6x. Step 3: Total daily payment = x + 1.6x = 2.6x. Step 4: According to the question, 2.6x = 650. Step 5: So x = 650 / 2.6. Step 6: Compute x = 250. Step 7: Therefore, B is paid Rs 250 per day. Verification / Alternative check: Using the result x = 250, wage of B is 250 and wage of A is 160% of 250 = 1.6 * 250 = 400. The total becomes 250 + 400 = 650, which matches the given total. This confirms that the calculation is correct. Why Other Options Are Wrong: 400: This is actually the wage of A, not B. 350: If B were paid 350, then A would get 1.6 * 350 = 560 and the total would be 910, not 650. 450: This value would lead to a total greater than 650 when A's wage is calculated. 300: With 300 for B, A would get 480 and the total 780, which is higher than 650. Common Pitfalls: Students may confuse 160% more with 160% of and treat it as A = B + 1.6B, which would be 260% of B instead of 160%. Here the wording clearly means A gets 160% of B's wage, that is 1.6 times B's wage. Another common issue is arithmetic errors in dividing 650 by 2.6. Converting 2.6 into a fraction like 26/10 can make the division easier. Final Answer: Labourer B is paid Rs 250 per day.

Question 15

On a machine there is 10% trade discount on the marked price of Rs 2,50,000. But the machine is sold at Rs 2,16,000 after giving a cash discount. How much is this cash discount (in %)?

Accepted Answer

4

Question 16

A trader marks up his goods by 120% and offers 30% discount. What will be the selling price (in Rs) if the cost price is Rs 750?

Accepted Answer

1155

Question 17

0.08% of 120% of 50,000 is equal to __________.

Accepted Answer

48

Question 18

When a number is increased by 24, it becomes 115% of its original value. What is the original number?

Accepted Answer

Introduction / Context: This problem combines a fixed numerical increase with a percentage description of the new value. Such questions check a student's ability to translate percentage statements into algebraic equations and then solve for the original number. The idea is that the final value is a certain percent of the initial value, and the difference between them is given. Given Data / Assumptions: Let the original number be N. When 24 is added to N, the result becomes 115% of N. We need to find N. Concept / Approach: If the final value is 115% of the original number, then the final value is 1.15 * N. The question states that this final value is also equal to N + 24. Therefore, we set up an equation N + 24 = 1.15N and solve for N. This is a linear equation with one variable and can be solved by simple rearrangement. Step-by-Step Solution: Step 1: Let the original number be N. Step 2: After increasing N by 24, we get N + 24. Step 3: According to the problem, N + 24 = 115% of N. Step 4: Write 115% of N as 1.15N. Step 5: So the equation becomes N + 24 = 1.15N. Step 6: Bring N terms on one side: 24 = 1.15N - N = 0.15N. Step 7: Therefore N = 24 / 0.15. Step 8: Compute N = 160. Step 9: So the original number is 160. Verification / Alternative check: We can verify by substituting N = 160 back into the condition. N + 24 = 160 + 24 = 184. Now check 115% of 160: 1.15 * 160 = 184. The values match exactly, so N = 160 is correct. Why Other Options Are Wrong: 250: 250 + 24 = 274, but 115% of 250 is 287.5, which does not match. 100: 100 + 24 = 124, but 115% of 100 is 115. 200: 200 + 24 = 224, while 115% of 200 is 230. 180: 180 + 24 = 204, but 115% of 180 is 207. Common Pitfalls: One common error is misinterpreting 115% as 1.15 plus N instead of 1.15 times N. Another frequent mistake is solving the equation incorrectly by subtracting the wrong terms or dividing by 15 instead of 0.15. Working carefully with decimal multipliers and checking the result by substitution helps avoid these mistakes. Final Answer: The original number is 160.

Question 19

The price of diesel increases from Rs 45 per litre to Rs 50 per litre. A person wants his total expenditure on diesel to increase by only 5%. By what percentage should he reduce his consumption of diesel?

Accepted Answer

Introduction / Context: This question is about the relationship between price, quantity and total expenditure. When the price per unit increases, a consumer may reduce the quantity consumed to keep total spending under control. The problem asks for the required percentage reduction in consumption so that the total expenditure increases by only a limited percentage, even though the price has gone up more sharply. Given Data / Assumptions: Initial price of diesel = Rs 45 per litre. New price of diesel = Rs 50 per litre. Allowed increase in total expenditure = 5%. We need the percentage reduction in quantity consumed. Initial quantity is assumed to be q litres, and new quantity is q prime litres. Concept / Approach: Total expenditure E equals price per litre multiplied by quantity consumed. Let initial expenditure be E1 and new expenditure be E2. We have E1 = 45 * q. After the price increase, E2 = 50 * q prime, and it is given that E2 = 1.05 * E1 (since expenditure should increase by only 5%). From this equation we find the ratio q prime / q and then compute the percentage reduction in quantity as (1 - q prime / q) * 100%. Step-by-Step Solution: Step 1: Initial expenditure E1 = 45 * q. Step 2: New expenditure E2 = 50 * q prime. Step 3: We require E2 = 1.05 * E1 (5% increase in expenditure). Step 4: So, 50 * q prime = 1.05 * (45 * q) = 47.25 * q. Step 5: Therefore, q prime / q = 47.25 / 50. Step 6: Compute q prime / q = 0.945. Step 7: So the new quantity is 94.5% of the old quantity. Step 8: Percentage reduction in consumption = (1 - 0.945) * 100% = 0.055 * 100% = 5.5%. Verification / Alternative check: Assume an initial quantity, for example q = 100 litres. Initial expenditure = 45 * 100 = Rs 4500. New quantity after 5.5% reduction = 100 - 5.5 = 94.5 litres. New expenditure = 50 * 94.5 = Rs 4725. The percentage increase in expenditure = (4725 - 4500) / 4500 * 100% = 5%. This confirms that a 5.5% reduction in quantity works correctly. Why Other Options Are Wrong: 5: This would lead to a slightly higher increase in expenditure than 5% because the reduction in quantity would be too small. 4: This reduction does not offset the price increase sufficiently. 4.5: This also underestimates the necessary reduction and leads to more than a 5% increase in spending. 6: This overcompensates and leads to less than the allowed 5% increase in expenditure. Common Pitfalls: A common mistake is to think that if price increases by a certain percentage, the quantity must reduce by the same percentage, which is incorrect. Others directly subtract percentages without forming the relationship between the products price * quantity. Always set up the equation for total expenditure before and after the change, and solve for the new quantity ratio carefully. Final Answer: The person should reduce his diesel consumption by 5.5% to limit the expenditure increase to 5%.

Question 20

Giving two successive discounts of 20% on the marked price of an article is equivalent to giving a single discount of what percentage on the original marked price?

Accepted Answer

Introduction / Context: This is another example of combining successive percentage discounts into a single equivalent discount. It reinforces the idea that percentage changes are multiplicative. Instead of adding the percentages, we must find the combined effect on the final price and then convert that back into one effective discount rate. Given Data / Assumptions: First discount = 20% on the marked price. Second discount = 20% on the reduced price after the first discount. We must find the single discount percentage that gives the same final price. The actual marked price does not matter because the result is percentage based. Concept / Approach: A discount of d% leaves (1 - d/100) of the original price. For successive discounts of 20% and 20%, the remaining fraction after both discounts is (0.80) * (0.80). The final fraction of the original price can then be expressed as (1 - D/100), where D is the single equivalent discount. We compute the product, subtract from 1, and obtain D. Step-by-Step Solution: Step 1: After a 20% discount, 80% of the price is left, so the factor is 0.80. Step 2: The second 20% discount again leaves 80% of the current price, with factor 0.80. Step 3: Combined factor after both discounts = 0.80 * 0.80 = 0.64. Step 4: This means the final price is 64% of the original marked price. Step 5: Therefore, total effective discount = 100% - 64% = 36%. Step 6: So a single discount of 36% is equivalent to two successive discounts of 20% each. Verification / Alternative check: Assume a convenient marked price, say Rs 100. After the first 20% discount, the price becomes 80. After the second 20% discount, the price becomes 80 - 16 = 64. Thus the final price is Rs 64, which is 36 less than 100, confirming that the overall discount is 36%. Why Other Options Are Wrong: 40: This is obtained by incorrectly adding the two 20% discounts, which ignores the change of base. 44: This would be the discount if the final fraction was 56%, which is not the case here. 50: This is far too large and bears no relation to the correct product of factors. 32: This indicates a misunderstanding of how the combined discount works, possibly from subtracting 4 from 36. Common Pitfalls: Many students simply add 20% and 20% to claim a 40% overall discount, which is wrong because each 20% is on a different base. Others may compute the product correctly but forget to subtract from 1 to get the discount. Whenever dealing with successive percentage changes, it is best to think in terms of decimal multipliers applied one after another. Final Answer: Two successive discounts of 20% each are equivalent to a single discount of 36% on the original marked price.

Percentage Questions