Question 1

The selling price of a table is Rs 2808 and the profit percentage on the table is 17 percent. What is the cost price of the table?

Accepted Answer

Introduction / Context: This question is a standard profit and loss calculation where the selling price and profit percentage are given and we must find the cost price. Understanding the relationship between cost price, selling price, and profit percent is essential for commercial arithmetic and aptitude exams. Given Data / Assumptions: Selling price (SP) of the table = Rs 2808. Profit percentage = 17 percent. Cost price (CP) is unknown and must be found. Profit percent is calculated on cost price. Concept / Approach: Profit percent is defined as (profit / cost price) * 100. Since selling price equals cost price plus profit, we can also write SP = CP * (1 + profit percent / 100). Hence CP = SP divided by (1 + profit percent / 100). Substituting the values from the question gives a direct formula to compute cost price. Step-by-Step Solution: Profit percent = 17 percent, so 1 + profit percent / 100 = 1 + 17/100 = 1.17. We know SP = CP * 1.17. Given SP = Rs 2808, so 2808 = CP * 1.17. Thus CP = 2808 / 1.17. Compute 2808 / 1.17. Multiplying numerator and denominator by 100 gives 280800 / 117. 280800 divided by 117 equals exactly 2400. Therefore cost price of the table is Rs 2400. Verification / Alternative check: We can check by forward calculation. If CP is 2400, then profit at 17 percent is 17/100 * 2400 = 408. Selling price becomes 2400 + 408 = 2808, which matches the given selling price. This confirms that CP = 2400 is correct. Why Other Options Are Wrong: If CP were 2288, profit at 17 percent would be 389, giving SP 2677. For 2300, SP would be 2691. For 2600, SP would be 3042. None of these equal 2808. The option 3285 is much larger and would imply negative profit if SP remains 2808. Only 2400 satisfies the profit percentage and selling price condition exactly. Common Pitfalls: Some learners incorrectly compute CP as SP minus 17 percent of SP instead of CP. Profit percent must always be applied on cost price. Others may confuse profit percent with discount percent and mix up formulas. Using the direct relation SP = CP * (1 + profit percent / 100) helps maintain clarity. Final Answer: The cost price of the table is Rs 2400.

Question 2

Calculate the value of 614 percent of 1600 plus 1212 percent of 800.

Accepted Answer

Introduction / Context: This question is a direct computation involving large percentages. It tests the ability to convert high percentage values into their decimal or fractional equivalent and to work carefully with multiplication. Even though the percentages look large, the method is exactly the same as for smaller percentages. Given Data / Assumptions: First term: 614 percent of 1600. Second term: 1212 percent of 800. We must find the sum of these two terms. All values are positive and expressed in the same unit. Concept / Approach: To compute P percent of a number N, use the formula P/100 * N. So 614 percent of 1600 is (614/100) * 1600, and 1212 percent of 800 is (1212/100) * 800. We evaluate each expression separately and then add the results. Using fraction simplification makes the arithmetic cleaner. Step-by-Step Solution: Compute 614 percent of 1600: 614 percent of 1600 = (614 / 100) * 1600. Simplify: 1600 / 100 = 16, so this becomes 614 * 16. Compute 614 * 16 = 614 * 10 + 614 * 6 = 6140 + 3684 = 9824. Now compute 1212 percent of 800: 1212 percent of 800 = (1212 / 100) * 800. Simplify: 800 / 100 = 8, so this becomes 1212 * 8. Compute 1212 * 8 = 9696. Now add both contributions: 9824 + 9696. Sum = 19520. Therefore the required value is 19520. Verification / Alternative check: As a check, we can factor out 16 from both terms using a different grouping. Write 1600 as 16 * 100 and 800 as 16 * 50. Then 614 percent of 1600 is 6.14 * 1600 and 1212 percent of 800 is 12.12 * 800. Expressing 6.14 * 1600 as 614 * 16 and 12.12 * 800 as 1212 * 8 recovers the same intermediate numbers. Repeating the sums confirms that the total is 19520. Any change in arrangement of multiplication gives the same final result. Why Other Options Are Wrong: The options 15600, 17840, 21600, and 18400 are all plausible looking large numbers but do not match the exact arithmetic. A quick check of 9824 plus 9696 clearly yields 19520. Any other sum is due to either a miscalculated product or an incorrect handling of percentage conversion. Common Pitfalls: Learners sometimes treat 614 percent as 6.14 instead of 6.14 as a multiplier, or drop the extra factor of 100 by mistake. Another pitfall is adding percentages before multiplying without checking that the bases are the same. Systematically converting each percentage to a fraction and computing step by step avoids these errors. Final Answer: The expression 614 percent of 1600 plus 1212 percent of 800 evaluates to 19520.

Question 3

A man spends 15 percent of his income. If his expenditure is Rs 75, what is his total income in rupees?

Accepted Answer

Introduction / Context: This simple percentage problem connects a known expenditure with an unknown total income through a given percentage. It is a direct application of reverse percentage and is very common in profit and loss and basic arithmetic sections. Given Data / Assumptions: Let total income be I. Man spends 15 percent of his income. Expenditure is given as Rs 75. We must find I. Concept / Approach: If a percentage of a quantity is known, we can write an equation relating them. Here 15 percent of income equals 75. So 15/100 * I = 75. Solving this equation for I gives the total income. This is a straightforward reverse percentage calculation. Step-by-Step Solution: We know 15 percent of I = 75. Write 15 percent as 15 / 100. Thus (15 / 100) * I = 75. This simplifies to 0.15I = 75. Divide both sides by 0.15. I = 75 / 0.15. Compute 75 / 0.15 = 75 * (1 / 0.15). Since 0.15 = 15 / 100, 1 / 0.15 = 100 / 15 = 20/3. Thus I = 75 * 20/3 = 75 * 20 / 3. Compute 75 / 3 = 25, so I = 25 * 20 = 500. Therefore the total income is Rs 500. Verification / Alternative check: Check by forward calculation. Fifteen percent of 500 is 15/100 * 500 = 75. This matches the stated expenditure. Hence the reverse percentage calculation is correct and consistent with the data. Why Other Options Are Wrong: If income were 400, 15 percent of 400 would be 60. For 300, expenditure would be 45. For 750, expenditure would be 112.5. For 600, expenditure would be 90. None of these equal 75. Only income of 500 gives 75 as 15 percent of income. Common Pitfalls: Sometimes students take 15 percent of 75 instead of viewing 75 as 15 percent of income. Others mistakenly subtract 15 from 75 rather than working with percentages. Translating the language into the correct equation before calculating prevents such errors. Final Answer: The man's total income is Rs 500.

Question 4

In a class of 50 students, the average marks are 70 percent. The average of the first 25 students is 60 percent and the average of the next 24 students is 80 percent. What percentage of marks did the last student obtain?

Accepted Answer

Introduction / Context: This question is about averages and total sums. The overall average of the class is given, along with separate averages for two groups of students. We must use this information to deduce the marks of a single remaining student. This type of problem shows how averages can be manipulated to find missing values. Given Data / Assumptions: Total number of students = 50. Average marks of entire class = 70 percent. Average of first 25 students = 60 percent. Average of next 24 students = 80 percent. Marks of the last (50th) student are unknown. Concept / Approach: Average is defined as total sum divided by number of observations. Thus total marks of the class equal 50 multiplied by 70. Similarly, we can compute total marks of the first 25 students and the next 24 students separately. Subtracting these subtotals from the grand total gives the marks of the last student. Finally, we can interpret that value as a percentage since all averages are given in percent format. Step-by-Step Solution: Total marks of all 50 students = 50 * 70 = 3500 (in percentage points units). Total marks of first 25 students = 25 * 60 = 1500. Total marks of next 24 students = 24 * 80 = 1920. Combined marks of first 49 students = 1500 + 1920 = 3420. Let marks of 50th student be M. Then 3420 + M = 3500. So M = 3500 - 3420 = 80. Thus the last student scored 80 percent. Verification / Alternative check: Recalculate the overall average to confirm. Adding the marks of first 49 students which are 3420 and the last student which is 80 gives 3500. Dividing by 50 returns 70 which matches the given class average. This confirms the calculation is consistent. Why Other Options Are Wrong: If the last student had 90 percent, total marks would be 3420 + 90 = 3510 and average would be 3510 / 50 = 70.2, not 70. If marks were 60 percent, total would be 3480 and average 69.6. Marks of 70 percent would give average 69.8. A value of 75 percent would also produce an incorrect overall average. Only 80 percent maintains the class average at exactly 70 percent. Common Pitfalls: Some learners mistakenly average the three given percentages directly instead of using total sums weighted by student counts. Another error is to divide by 49 instead of 50 when recomputing averages. It is crucial to remember that averages must be handled through totals, not by naive averaging of averages. Final Answer: The last student of the class obtained 80 percent marks.

Question 5

A number is decreased by 10 percent and the resulting value is then decreased again by 20 percent. What is the overall percentage decrease from the original number to the final number?

Accepted Answer

Introduction / Context: This question involves successive percentage changes. Many learners incorrectly add or subtract percentages directly. The key idea is that each percentage change acts on a new base, not the original number. We must multiply the fractional multipliers to compute the net effect on the original number. Given Data / Assumptions: First change: decrease by 10 percent. Second change: decrease by 20 percent applied to the new value. We need the overall percentage decrease from the original number to the final value. Let the original number be N. Concept / Approach: A decrease of p percent corresponds to multiplying by (1 - p/100). Therefore, a 10 percent decrease multiplies the number by 0.9 and a 20 percent decrease multiplies by 0.8. Successive changes are combined by multiplying their multipliers: 0.9 * 0.8. The final multiplier shows what fraction of the original remains. The overall percentage decrease is then 100 minus this remaining percentage. Step-by-Step Solution: Let original number be N. After a 10 percent decrease, new value is N * (1 - 10/100) = N * 0.9. After a further 20 percent decrease, second new value = (N * 0.9) * (1 - 20/100) = N * 0.9 * 0.8. Compute 0.9 * 0.8 = 0.72. So final value is 0.72N. This means 72 percent of the original number remains. Overall percentage decrease = 100 percent - 72 percent = 28 percent. Verification / Alternative check: Use a concrete number to check. Let N = 100. After 10 percent decrease, value is 90. After 20 percent decrease on 90, value is 90 * 0.8 = 72. Overall drop from 100 to 72 is 28 units, which is 28 percent of 100. This numeric example confirms the result. Why Other Options Are Wrong: Simply adding the percentages 10 and 20 would give 30 percent, which ignores the fact that the second decrease is on a smaller base. Twenty five percent or 26 percent or 27 percent do not match the computed multiplier 0.72. Only a 28 percent decrease corresponds to the final value being 72 percent of the original. Common Pitfalls: The most common mistake is to assume that successive percentage changes can be added or subtracted directly. Another error is to apply the second percentage to the original instead of the intermediate value. Using multipliers for each step and then combining them helps avoid such errors and gives an accurate net effect. Final Answer: The overall percentage decrease from the original number to the final number is 28 percent.

Question 6

An article is sold for Rs 950 after allowing a discount of 5 percent on the marked price. What is the marked price of the article?

Accepted Answer

Introduction / Context: This is a straightforward discount problem where the selling price after a given percentage discount is known and the marked price needs to be determined. It reinforces the concept that the selling price with discount is a fixed percentage of the marked price and that we can reverse this relationship algebraically. Given Data / Assumptions: Selling price after discount = Rs 950. Discount rate = 5 percent. Marked price is unknown. Discount is applied on marked price only. Concept / Approach: If discount is 5 percent, then the customer pays 95 percent of the marked price. That means selling price equals marked price multiplied by 0.95. Therefore, marked price equals selling price divided by 0.95. This formula can be applied directly using the given numbers. Step-by-Step Solution: Let marked price be M. Selling price S = M * (1 - 5/100) = 0.95M. We are given S = 950. So 0.95M = 950. Therefore M = 950 / 0.95. Compute 950 / 0.95 = 950 * (1 / 0.95). 0.95 is 95/100, so 1 / 0.95 = 100 / 95 = 20 / 19. Thus M = 950 * 20 / 19. 950 / 19 = 50, so M = 50 * 20 = 1000. Hence the marked price is Rs 1000. Verification / Alternative check: Check by forward calculation. If marked price is 1000, 5 percent discount equals 5/100 * 1000 = 50. So selling price becomes 1000 - 50 = 950. This exactly matches the given selling price, confirming that the marked price is correct. Why Other Options Are Wrong: For a marked price of 960, 5 percent discount would be 48, giving a selling price of 912. For 955, selling price would be about 907.25. For 945, selling price would be 897.75. A marked price of 1050 would lead to selling price 997.5. None of these equal 950. Only 1000 produces the correct discounted selling price. Common Pitfalls: A common error is to add 5 percent of 950 instead of viewing 950 as 95 percent of the marked price. Another mistake is to subtract 5 rupees rather than 5 percent. Carefully expressing the relationship S = 0.95M and solving algebraically avoids these misconceptions. Final Answer: The marked price of the article is Rs 1000.

Question 7

The price of rice has increased by 60 percent. By what percentage must the new price be reduced so that the original price is restored?

Accepted Answer

Introduction / Context: This question focuses on successive percentage changes, specifically an increase followed by a decrease. It is important to note that a 60 percent increase cannot be simply reversed by a 60 percent decrease, because the bases of these percentages are different. The goal is to find the exact percentage reduction needed to restore the original price of rice. Given Data / Assumptions: Original price of rice = P (some positive amount). Price is first increased by 60 percent. Let the new price be N. We must find the percentage decrease from N that brings the price back to P. Concept / Approach: A 60 percent increase means the new price is P * (1 + 60/100) = 1.6P. Suppose the required reduction percentage is x percent. Then the reduced price is N * (1 - x/100). We need N * (1 - x/100) to equal P. Substituting N = 1.6P gives an equation in x, which we can solve to find the required percentage decrease. Step-by-Step Solution: First increase: N = P * (1 + 60/100) = P * 1.6. Let required reduction percentage be x percent. After reduction, price becomes N * (1 - x/100). This final price must equal original price P. So N * (1 - x/100) = P. Substitute N = 1.6P: 1.6P * (1 - x/100) = P. Divide both sides by P (P is non zero): 1.6 * (1 - x/100) = 1. So 1 - x/100 = 1 / 1.6. Compute 1 / 1.6 = 10 / 16 = 5 / 8 = 0.625. Thus 1 - x/100 = 0.625. So x/100 = 1 - 0.625 = 0.375. Therefore x = 0.375 * 100 = 37.5 percent. Write 37.5 percent as 37 1/2 percent. Verification / Alternative check: Assume original price P = 100 units. After a 60 percent increase, new price N = 160. A reduction of 37.5 percent on 160 equals 37.5/100 * 160 = 60. The price after reduction becomes 160 - 60 = 100, which matches the original price. This numerical example confirms that 37.5 percent is the correct required reduction. Why Other Options Are Wrong: A reduction of 33 1/3 percent on 160 would lower the price by about 53.33, giving 106.67, not 100. A 40 percent reduction would lower 160 by 64, giving 96. A reduction of 45 percent would drop the price to 88. Fifty percent reduction would cut it to 80. None of these restore the original price of 100. Only 37 1/2 percent works exactly. Common Pitfalls: Many learners assume that a 60 percent increase followed by a 60 percent decrease brings the price back to the start, which is incorrect because the decrease is based on the larger price. Another mistake is to subtract percentages directly without considering their different bases. Setting up the equation carefully avoids such misunderstandings. Final Answer: The new price must be reduced by 37 1/2 percent to restore the original price of rice.

Question 8

When an unknown number is increased by 24, the new value becomes 104% of that same original number. Based on this percentage relationship, what is the value of the original number before the increase?

Accepted Answer

Introduction / Context: In this aptitude question we work with a simple percentage relationship between an unknown number and its increased value. The number is increased by a fixed amount and the result is expressed as a percentage of the original number. Such problems test comfort with converting a verbal percentage statement into an algebraic equation and then solving for the unknown. Understanding this type of question is important for many exam topics like profit and loss, interest, and data interpretation where similar percentage relationships appear. Given Data / Assumptions: An unknown original number is increased by 24. The new value after adding 24 is equal to 104% of the original number. We assume all values are real numbers and percentages are applied in the usual arithmetic sense. We need to find the original number before the increase. Concept / Approach: The key concept is that “104% of the original number” means 104 over 100 times the original number. If we call the original number x, then 104% of x is written as 1.04 * x. The statement in the question directly converts to the equation x + 24 = 1.04 * x. Once this equation is formed, solving it is a simple matter of isolating x on one side by subtracting x from both sides and then dividing by the remaining coefficient. This is a straightforward linear equation in one variable. Step-by-Step Solution: Step 1: Let the original number be x. Step 2: After increasing the number by 24, the new value becomes x + 24. Step 3: According to the question, this new value equals 104% of the original number, that is 1.04 * x. Step 4: Set up the equation x + 24 = 1.04 * x. Step 5: Subtract x from both sides to get 24 = 1.04 * x - x. Step 6: Simplify the right side: 1.04 * x - x = 0.04 * x. Step 7: So we have 24 = 0.04 * x. Step 8: Solve for x by dividing both sides by 0.04, giving x = 24 / 0.04. Step 9: Compute 24 / 0.04 = 600, so the original number is 600. Verification / Alternative check: We can verify the answer by substituting x = 600 back into the original statement. Increase 600 by 24 to get 624. Next, find 104% of 600. Calculate 1% of 600 as 6, and then 104% is 104 * 6 = 624. The new value 624 matches exactly, so the algebraic solution is correct. This confirms that the original number must be 600 and there is no contradiction in the given data or the derived result. Why Other Options Are Wrong: If the original number were 300, then adding 24 gives 324, while 104% of 300 is 312, so option 300 is inconsistent. If the original number were 100, then the new value would be 124, but 104% of 100 is only 104. If the original number were 1200, adding 24 gives 1224, but 104% of 1200 equals 1248. None of these match the required relationship, so these options are incorrect. Common Pitfalls: A frequent mistake in such questions is to treat 104% as 1.4 instead of 1.04, which would completely change the equation. Another common error is to add 24 to the percentage value rather than to the original number. Some learners also forget to convert percentages into decimal form before using them in equations. Careful reading of the sentence and stepwise algebraic translation help avoid these issues and lead to the correct answer. Final Answer: The original number, before it was increased by 24, is 600.

Question 9

In an algebraic percentage relation, 20% of a quantity a is equal to b. Based on this relation, b% of 20 is numerically equal to what fraction or percentage of a?

Accepted Answer

Introduction / Context: This question tests the connection between percentage expressions and algebra. Instead of inserting numbers directly, the problem uses variables and symbolic expressions like 20% of a equals b. Many competitive exams include such questions to see whether candidates can translate verbal percentage statements into formulas and then simplify them systematically. Mastery of this type of question helps in simplifying more complicated percentage and ratio problems later on. Given Data / Assumptions: 20% of a is equal to b, written as 20% of a = b. We are asked to compute b% of 20. We must express b% of 20 as some fraction or percentage of a. All percentages are interpreted in their usual arithmetic sense. Concept / Approach: We need to convert percentage statements into algebraic equations using decimal or fraction forms. First, we express 20% of a in algebraic form. Next, we use that relation to express b in terms of a. Once we know b in terms of a, we can compute b% of 20 by substituting this expression and simplifying. The goal is to express the final result as k% of a or as k times a, where k is a numerical constant. Step-by-Step Solution: Step 1: Write 20% of a as an algebraic expression: 20% of a = (20 / 100) * a = 0.2 * a. Step 2: This is given to be equal to b, so we have b = 0.2 * a. Step 3: Now consider b% of 20. By definition, b% of 20 = (b / 100) * 20. Step 4: Substitute b = 0.2 * a into that expression: b% of 20 = (0.2 * a / 100) * 20. Step 5: Simplify the constants: 0.2 * 20 = 4, so the numerator becomes 4 * a. Step 6: We then have b% of 20 = (4 * a) / 100 = 0.04 * a. Step 7: The quantity 0.04 * a is equal to 4% of a. Step 8: Therefore, b% of 20 is 4% of a. Verification / Alternative check: As a quick numerical check, suppose a = 100. Then 20% of 100 is 20, so b = 20. Now b% of 20 means 20% of 20, which equals 4. On the other hand, 4% of a is 4% of 100 which is also 4. The two values match perfectly, confirming that the expression b% of 20 is indeed equal to 4% of a and that no algebraic step has been mishandled in the reasoning. Why Other Options Are Wrong: If we choose 8% of a, that would correspond to 0.08 * a, which is double the correct value. Choosing 40% of a would give 0.4 * a, which is far too large compared to 0.04 * a. Selecting 80% of a would give an even larger 0.8 * a. None of these match the simplified algebraic expression we derived, so they cannot represent b% of 20 under the given relation. Common Pitfalls: A common mistake is to mix up 20% of a and b% of 20 or to treat b% as simply b divided by 100 without applying it to 20. Another frequent error is misplacing the percentage divisor, for example writing 20b instead of 20 * b or 20% * b. Careful stepwise substitution and simplification prevent such mistakes and lead reliably to the correct 4% result. Final Answer: The expression b% of 20 is equal to 4% of a.

Question 10

A shopkeeper sells an item for Rs 4200, even though the marked price printed on the item is Rs 4800. Based on this transaction, what percentage discount on the marked price does the shopkeeper offer?

Accepted Answer

Introduction / Context: This question is a standard percentage discount problem from basic profit and loss. The marked price is the printed price on the article, while the selling price is the amount actually paid by the buyer. The goal is to determine how much discount in percentage terms was given relative to the marked price. Such problems appear frequently in entrance exams and daily life situations involving sales and offers in shops or online platforms. Given Data / Assumptions: Marked price of the item = Rs 4800. Selling price of the item = Rs 4200. Discount is calculated on the marked price, not on the cost price. We must find the discount percentage to two decimal places if needed. Concept / Approach: The discount amount is the difference between the marked price and the selling price. Once the monetary discount is known, the discount percentage is computed as (discount / marked price) * 100. This formula directly converts the reduction relative to the marked price into a percentage measure. The problem does not require knowledge of the cost price or profit, only the relationship between marked price and selling price. Step-by-Step Solution: Step 1: Marked price (MP) = Rs 4800. Step 2: Selling price (SP) = Rs 4200. Step 3: Discount amount = MP - SP = 4800 - 4200 = Rs 600. Step 4: Use the formula for discount percentage: discount percent = (discount amount / MP) * 100. Step 5: Substitute the values: discount percent = (600 / 4800) * 100. Step 6: Simplify the fraction 600 / 4800 = 1 / 8. Step 7: Therefore discount percent = (1 / 8) * 100 = 12.5. Step 8: So the shopkeeper is giving a discount of 12.5 percent on the marked price. Verification / Alternative check: We can verify by reversing the calculation. If the discount is 12.5% on Rs 4800, then the discount amount should be (12.5 / 100) * 4800. Now 12.5 / 100 is 0.125 and 0.125 * 4800 = 600. Subtracting 600 from 4800 gives a selling price of Rs 4200, which matches the given selling price exactly. This confirms that our computed discount percentage is consistent with the data in the problem. Why Other Options Are Wrong: If the discount were 14.28%, the reduction would be approximately 0.1428 * 4800 which is about 686, not 600. A 10% discount would reduce the price by 480, leading to a selling price of 4320, which is not correct. A 15% discount would reduce the price by 720, giving a selling price of 4080. Since only 12.5% reproduces the exact given selling price of Rs 4200, the other options are incorrect. Common Pitfalls: Many learners mistakenly compute the discount percentage using selling price in the denominator instead of marked price, which gives the wrong percentage. Another common error is to round intermediate steps too early or mis-handle decimal values. Working carefully with the formula and keeping track of which price is the base for the percentage avoids these mistakes and leads to the correct 12.5% discount rate. Final Answer: The discount offered on the marked price of Rs 4800 is 12.5%.

Question 11

A trader buys 800 kilograms of tomatoes for a total cost of Rs 7200. During transportation 10% of the tomatoes are damaged and cannot be sold. At what selling price per kilogram should the trader sell the remaining tomatoes to earn a profit of 30% o…

Accepted Answer

Introduction / Context: This problem combines the ideas of percentage loss of quantity with required selling price to achieve a target profit. The trader buys a certain mass of tomatoes, but a percentage of them are spoiled in transit, leaving fewer kilograms available for sale. Even though some tomatoes are wasted, the trader still wants to achieve a planned profit on the original investment. This type of question is very common in profit and loss sections of aptitude exams and reflects how wastage affects pricing decisions in real business situations. Given Data / Assumptions: Total quantity purchased = 800 kilograms of tomatoes. Total cost price for 800 kilograms = Rs 7200. Percentage of tomatoes damaged = 10% of the total quantity. Target profit on total cost = 30%. Damaged tomatoes cannot be sold and generate no revenue. We need the selling price per kilogram of the remaining good tomatoes. Concept / Approach: First, calculate the trader total cost price. Then compute the selling price needed to secure a 30% profit on that cost. Next, determine the quantity of tomatoes that remain after 10% are damaged. Finally, divide the required total selling price by the number of kilograms available for sale to obtain the selling price per kilogram. The key idea is that profit is based on the original cost, not on the cost of only the undamaged quantity, so wastage forces a higher per kilogram selling price. Step-by-Step Solution: Step 1: Total cost price (CP) for 800 kg = Rs 7200. Step 2: Required profit = 30% of CP = 30 / 100 * 7200 = 0.3 * 7200 = Rs 2160. Step 3: Required total selling price (SP total) = CP + profit = 7200 + 2160 = Rs 9360. Step 4: Tomatoes damaged = 10% of 800 kg = 10 / 100 * 800 = 80 kg. Step 5: Good tomatoes available for sale = 800 kg - 80 kg = 720 kg. Step 6: Selling price per kg = SP total / good quantity = 9360 / 720. Step 7: Compute 9360 / 720 = 13. Step 8: Therefore the trader should sell the remaining tomatoes at Rs 13 per kilogram. Verification / Alternative check: As a check, multiply the selling price per kilogram by the saleable quantity. At Rs 13 per kilogram for 720 kilograms, total revenue is 13 * 720 = Rs 9360. Subtracting the original cost of Rs 7200 from this revenue gives a profit of Rs 2160. The profit percentage is 2160 / 7200 * 100 = 30%, which matches the required profit rate. This confirms that Rs 13 per kilogram is the correct selling price under the given conditions of wastage and profit requirement. Why Other Options Are Wrong: If the price were Rs 9 per kilogram, revenue would be 9 * 720 = Rs 6480, which is less than the cost and leads to a loss. At Rs 10 per kilogram, revenue would be 7200, meaning zero profit. At Rs 12 per kilogram, revenue would be 8640, giving a profit of only 1440, which is 20% of 7200, not 30%. Therefore only Rs 13 per kilogram gives the exact 30% profit, so the other options do not satisfy the problem requirement. Common Pitfalls: A typical error is to compute the selling price per kilogram based on the original total quantity of 800 kilograms instead of the reduced 720 kilograms. Another mistake is to treat the 10% damaged quantity as a price discount rather than loss of goods. Candidates also sometimes calculate profit percentage on the selling price rather than on the cost price. Careful attention to definitions of cost price, selling price, and profit, along with the effect of wastage on available quantity, helps avoid these issues. Final Answer: The trader must sell the good tomatoes at Rs 13 per kilogram to earn a 30% profit.

Question 12

What is the numerical value of 10% of 150% of 400, when the percentages are applied in sequence to the number 400?

Accepted Answer

Introduction / Context: This question checks understanding of how to handle successive percentages applied to a base number. The phrase “10% of 150% of 400” means that we first calculate 150% of 400 and then take 10% of that result. Problems like this are important in many quantitative topics, including compound percentage situations, multi stage discounts, and interest calculations. Correct interpretation of the order of operations is crucial for arriving at the right answer. Given Data / Assumptions: Base number = 400. We first compute 150% of 400. Then we compute 10% of the result obtained in the first step. All percentages are applied in the standard arithmetic way. Concept / Approach: Percentages can always be converted into fraction or decimal form. One effective approach is to write 150% as 150 / 100 and 10% as 10 / 100. Then apply these step by step to the base number. Alternatively we can combine the percentage multipliers into a single factor before applying them to the base. Both methods give the same final result if executed correctly. This problem does not involve any tricky rounding or hidden information, it is purely about correct sequence and arithmetic. Step-by-Step Solution: Step 1: First find 150% of 400. Step 2: 150% of 400 = (150 / 100) * 400. Step 3: Simplify (150 / 100) * 400 = 1.5 * 400 = 600. Step 4: Now we need 10% of this result, which is 10% of 600. Step 5: 10% of 600 = (10 / 100) * 600. Step 6: Simplify (10 / 100) * 600 = 0.1 * 600 = 60. Step 7: Therefore the value of 10% of 150% of 400 is 60. Step 8: We can also combine the calculation: overall factor = (10 / 100) * (150 / 100) = 1500 / 10000 = 0.15, and 0.15 * 400 = 60. Verification / Alternative check: We have verified by two approaches. The first approach applies percentages stepwise, and the second approach multiplies the percentage factors before applying them to 400. In both ways the final result is 60. There is no ambiguity about order because the phrase clearly states “10% of 150% of 400,” which means 10% of the quantity that is 150% of 400. If we mistakenly took 150% of 10% of 400 instead, we would compute a different value, but that would not follow the wording given. Why Other Options Are Wrong: If the answer were 600, that would correspond to 150% of 400 without taking the final 10%. The value 50 does not arise from any natural miscalculation here. The value 500 would suggest replacing 150% by 125% or similar error. Only 60 matches the correct computation of 10% of 600. Thus, among the options provided, 60 is the only correct result that fits the stepwise percentage operations stated in the problem. Common Pitfalls: A common mistake is to misread “10% of 150% of 400” as simply 160% of 400 or as 10% plus 150% of 400. Another frequent error is to treat both percentages as added instead of multiplied. Learners also sometimes forget that the outer percentage operates on the intermediate result, not on the original number again. Writing everything explicitly as fractions or decimals helps maintain clarity and prevents such errors. Final Answer: The correct value of 10% of 150% of 400 is 60.

Question 13

A shopkeeper marks up the cost price of his goods by 60% and then offers a discount of 25% on the marked price. If the cost price of an article is Rs 1600, what will be the final selling price (in rupees) after applying both the markup and the disco…

Accepted Answer

Introduction / Context: This question involves both markup and discount, a very common pattern in profit and loss problems. First the trader increases the price above cost by a given percentage to determine the marked price. Later, to attract customers, a percentage discount is applied to that marked price. The net effect on the selling price depends on both percentages and cannot be obtained by simply adding or subtracting them. Understanding how to handle such successive percentage changes is essential for solving real life pricing and sales questions. Given Data / Assumptions: Cost price (CP) of the article = Rs 1600. Markup rate on cost price = 60%. Discount rate on marked price = 25%. We need to find the final selling price after both steps. All prices and percentages are applied in the normal arithmetic way. Concept / Approach: The strategy is to proceed in two stages. First compute the marked price by increasing the cost price by 60%. Then compute the selling price by reducing the marked price by 25%. Mathematically this is done by multiplying the cost price by (1 plus markup rate expressed as a decimal) and then multiplying the resulting marked price by (1 minus discount rate expressed as a decimal). This avoids any confusion and shows clearly how successive percentage changes combine through multiplication rather than simple addition or subtraction. Step-by-Step Solution: Step 1: Cost price (CP) = Rs 1600. Step 2: Markup rate = 60%, so factor for markup = 1 + 60 / 100 = 1.6. Step 3: Marked price (MP) = CP * 1.6 = 1600 * 1.6 = Rs 2560. Step 4: Discount rate on marked price = 25%, so discount factor = 1 - 25 / 100 = 0.75. Step 5: Selling price (SP) = MP * 0.75 = 2560 * 0.75. Step 6: Calculate 2560 * 0.75. This is the same as 2560 * 3 / 4 = 1920. Step 7: Therefore the final selling price after markup and discount is Rs 1920. Verification / Alternative check: We may also combine both percentage effects into one factor. The net multiplier on cost price is (1 + 0.60) * (1 - 0.25) = 1.6 * 0.75. Multiply these to get 1.6 * 0.75 = 1.20. Thus the effective effect on cost is a 20% increase overall, and SP = 1.20 * 1600 = 1920. This cross check confirms that the detailed stepwise approach and the combined factor approach give the same answer, so the computation is consistent. Why Other Options Are Wrong: If the selling price were Rs 2000, that would correspond to a different effective net increase on cost price, not exactly 20%. A value of Rs 2120 implies an even larger overall percentage, which does not match a 60% markup followed by a 25% discount. A price of Rs 2200 is higher still and does not satisfy the computed multiplier of 1.20. Only Rs 1920 is consistent with a 60% increase followed by a 25% reduction on the marked amount. Common Pitfalls: A common mistake is to subtract the discount rate from the markup rate directly, for example saying 60% minus 25% equals 35% and applying that to the cost, which is incorrect because the discount applies to the increased marked price, not the original cost. Others may misapply the discount to the cost price instead of the marked price. Always remember that each percentage change acts on the current value at that stage, and successive changes combine multiplicatively, not by simple addition or subtraction. Final Answer: The final selling price of the article is Rs 1920.

Question 14

At a 30% discount, the selling price of an article is Rs 1050. If instead the shopkeeper had offered a discount of 15% on the same marked price, what would the new selling price (in rupees) have been?

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Introduction / Context: This question tests understanding of how the selling price changes when the discount rate on the same marked price is altered. First we know the selling price when a 30% discount is offered. From that we infer the marked price. Then we recalculate the selling price using a different discount of 15% on the same marked price. It is a standard exercise in profit and loss and discount topics, and it helps students practice moving backwards from selling price to marked price and then forwards again with a new discount. Given Data / Assumptions: When the discount rate is 30%, the selling price is Rs 1050. The discount is on the marked price of the article. The marked price remains the same in both cases. We want the selling price when the discount rate is 15% on that same marked price. No additional taxes or charges are involved. Concept / Approach: The discount percentage indicates how much of the marked price is removed. If the discount is 30%, the selling price is 70% of the marked price. Therefore we can write the given selling price as 70% of the marked price and solve for the marked price. After finding the marked price, we then compute 85% of it (since a 15% discount means the customer pays 85% of the marked price) to obtain the new selling price. This two stage approach is systematic and avoids guesswork. Step-by-Step Solution: Step 1: Let the marked price be M. Step 2: A discount of 30% means the customer pays 70% of M, that is 0.70 * M. Step 3: Given that at 30% discount, the selling price is Rs 1050, so 0.70 * M = 1050. Step 4: Solve for M: M = 1050 / 0.70. Step 5: 1050 / 0.70 is equal to 1050 * (10 / 7) = 1500, so the marked price is Rs 1500. Step 6: Now consider a discount of 15%. Then the customer pays 85% of the marked price, or 0.85 * M. Step 7: New selling price = 0.85 * 1500 = 1275. Step 8: Therefore, with a 15% discount, the article would sell for Rs 1275. Verification / Alternative check: As a quick verification, we can check that a 30% discount on Rs 1500 indeed gives the original selling price. Thirty percent of 1500 is 0.30 * 1500 = 450. Subtracting this from 1500 yields 1500 - 450 = 1050, which matches the given selling price at 30% discount. Similarly, 15% of 1500 is 225. Subtracting this from 1500 gives 1275, which is consistent with our computed new selling price. Both checks agree with the data, confirming the solution. Why Other Options Are Wrong: If we choose 1200, that would correspond to paying 80% of the marked price, effectively a 20% discount, not 15%. A selling price of 1175 does not match any simple percentage of 1500 and is therefore inconsistent with the given discount rate. A price of 1100 is even lower and would reflect a discount higher than 26%, not 15%. Only 1275 corresponds exactly to a 15% discount on 1500, so the other options are not correct. Common Pitfalls: A common error is to apply the new discount rate directly to the old selling price rather than to the marked price. Another mistake is to subtract the difference between discount percentages from the old selling price, which is not correct because the base value for the percentage remains the marked price. The safest method is always to recover the marked price first from the initial data and then apply the new discount properly to that same marked price. Final Answer: The selling price with a 15% discount on the same marked price is Rs 1275.

Question 15

If 50% of a quantity a is equal to b, then b% of 40 is numerically equal to which of the following expressions in terms of a?

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Introduction / Context: This algebraic percentage question asks you to relate a symbolic percentage expression back to the original variable a. The relation between a and b is given by a simple percentage, and you have to use that relation to evaluate b% of a numerical quantity. Questions like this strengthen understanding of how percentages interact with variables and help improve algebraic manipulation skills that are important across many quantitative topics. Given Data / Assumptions: Fifty percent of a is equal to b, written as 50% of a = b. We are asked to find b% of 40. The final expression must be written in terms of a. All percentages are used in a standard arithmetic sense. Concept / Approach: First we express 50% of a in algebraic form to obtain b in terms of a. Once we know b as a multiple of a, we can compute b% of 40 by interpreting b% as b divided by 100 times 40. Substituting the expression for b and simplifying leads to a constant coefficient times a. That constant can then be compared with the options, which are given as numerical values indicating the required fraction of a. Step-by-Step Solution: Step 1: Express 50% of a. We have 50% of a = (50 / 100) * a = 0.5 * a. Step 2: According to the question, this equals b, so b = 0.5 * a. Step 3: Now we need b% of 40. By definition, b% of 40 = (b / 100) * 40. Step 4: Substitute b = 0.5 * a into the expression: b% of 40 = (0.5 * a / 100) * 40. Step 5: Simplify the constants. First compute 0.5 * 40 = 20. Step 6: So we get b% of 40 = (20 * a) / 100. Step 7: Reduce (20 * a) / 100 to a simpler fraction: (20 / 100) * a = 0.2 * a. Step 8: Therefore, b% of 40 is equal to 0.2 of a. Verification / Alternative check: To verify, choose a convenient value for a. Let a = 100. Then 50% of 100 is 50, so b = 50. Now b% of 40 is 50% of 40, which equals 20. On the other hand, 0.2 of a is 0.2 * 100 = 20. The two values match exactly, confirming that b% of 40 is correctly expressed as 0.2 * a, and 0.2 is the coefficient we need from the options. Why Other Options Are Wrong: If we choose 0.25 of a, that would correspond to 25% of a, which is larger than the correct 0.2 * a. The value 0.16 of a would correspond to 16% of a, which is smaller than the correct amount. The value 2 * a is far too large and does not come from any realistic interpretation of the given relationships. Since only 0.2 of a matches the algebraic simplification, the other options cannot be correct. Common Pitfalls: A common confusion is mixing up b and b% and treating them as the same thing. Another error is failing to divide by 100 when converting percentage expressions into multipliers. Some learners also mistakenly apply 50% to the number 40 instead of correctly following the sequence given in the question. Writing out each step carefully, with explicit fractions for percentages, helps avoid these mistakes and ensures the correct result. Final Answer: The expression b% of 40 is equal to 0.2 of a.

Question 16

A certain number is first increased by 20%. To return from this increased value back to the original number, by what percentage must the increased number be reduced?

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Introduction / Context: This question explores the idea that a percentage increase and a percentage decrease of the same numerical rate do not cancel each other out. When a quantity is increased by a certain percentage, the base value changes, so the percentage decrease required to return to the original value is different. This is a classic concept in percentage arithmetic, very common in aptitude exams, and it demonstrates why successive percentage changes must be handled carefully using multiplication rather than simple addition or subtraction. Given Data / Assumptions: An original number is increased by 20%. We then want to reduce the increased number by some percentage so that we recover the original number. We assume the percentage decrease is calculated on the increased value, not the original value. The task is to find this required percentage decrease. Concept / Approach: If the original number is x, a 20% increase gives a new value of x * 1.20. To return from this value to x, we need to apply a reduction factor such that x = (1.20 * x) * (1 - r), where r is the required reduction rate expressed as a decimal. Solving this equation for r yields the percentage decrease needed. This method highlights that the increase and decrease are based on different bases, which is why the rates are not equal even though they seem symmetrical at first glance. Step-by-Step Solution: Step 1: Let the original number be x. Step 2: After a 20% increase, the new value is x * (1 + 20 / 100) = x * 1.20. Step 3: Let the required reduction rate be r (in decimal form) applied to the increased value. Step 4: To return to the original number, we need x = 1.20 * x * (1 - r). Step 5: Divide both sides by x (x is nonzero), giving 1 = 1.20 * (1 - r). Step 6: Solve for (1 - r): (1 - r) = 1 / 1.20. Step 7: Compute 1 / 1.20 = 1 / (6 / 5) = 5 / 6. Step 8: So 1 - r = 5 / 6, which means r = 1 - 5 / 6 = 1 / 6. Step 9: Convert r to a percentage: r = 1 / 6 which is 16 2/3%. Verification / Alternative check: Take a concrete example. Let the original number be 100. A 20% increase gives 120. Now we ask what percentage decrease on 120 will bring us back to 100. The required reduction is 120 - 100 = 20. The decrease as a percentage of 120 is 20 / 120 * 100 = 16.666..., which is 16 2/3%. This numeric check matches the algebraic derivation and confirms that the correct reduction rate is 16 2/3%, not 20%. Why Other Options Are Wrong: A reduction of 20% on 120 would give 96, not 100, so 20% is incorrect. A 21% reduction is even larger and would lead to 120 * 0.79 = 94.8, which is too low. A reduction of 14 1/3% would lead to 120 * (1 - 14 1/3 / 100) and also not reach 100. Only 16 2/3% produces the exact original number when applied to the increased value, so the other options do not satisfy the equality. Common Pitfalls: Many learners mistakenly assume that a 20% decrease will reverse a 20% increase, but this ignores the fact that the base for the decrease is larger than the base for the increase. This misunderstanding leads to incorrect answers in many percentage and profit and loss questions. The safe approach is always to define a variable for the original value, write out the multiplicative factors, and solve the resulting equation instead of relying on intuition. Final Answer: To return to the original number after a 20% increase, the new number must be reduced by 16 2/3%.

Question 17

A village loses 12% of its goats in a flood and then 5% of the remaining goats die due to disease. If 8360 goats are still alive after both losses, what was the original number of goats in the village before the flood?

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Introduction / Context: This question deals with successive percentage decreases applied to a population, in this case goats in a village. First a certain percentage of animals are lost in a natural disaster, and then another percentage of the survivors die due to disease. We know the final count and are asked to work backward to the original number. Problems of this type appear under percentage, population growth and decay, and compound change topics, and they develop skill in reversing multi step percentage processes. Given Data / Assumptions: First loss: 12% of the original goats die in a flood. Second loss: 5% of the remaining goats die due to disease. Number of goats left after both losses = 8360. We need to find the original number of goats before the flood. There are no other gains or losses besides the two mentioned events. Concept / Approach: Successive percentage decreases can be represented by multiplication factors applied to the original quantity. If the village initially has x goats, then after a 12% loss, the number becomes x * (1 - 12 / 100) = x * 0.88. After this, a further loss of 5% occurs, which reduces the number by a factor of (1 - 5 / 100) = 0.95, giving x * 0.88 * 0.95. We know this final value equals 8360. So we solve the equation x * 0.88 * 0.95 = 8360 to find x, the original population. Step-by-Step Solution: Step 1: Let the original number of goats be x. Step 2: After the flood, 12% die, so 88% remain. Remaining after flood = 0.88 * x. Step 3: Of these remaining goats, 5% die due to disease, so 95% survive this second event. Step 4: Number of goats after disease = 0.95 * (0.88 * x) = 0.88 * 0.95 * x. Step 5: According to the problem, this final number is 8360, so 0.88 * 0.95 * x = 8360. Step 6: Compute the combined multiplier: 0.88 * 0.95 = 0.836. Step 7: So the equation becomes 0.836 * x = 8360. Step 8: Solve for x: x = 8360 / 0.836. Step 9: 8360 / 0.836 simplifies to 10000, so the original number of goats is 10000. Verification / Alternative check: Check the answer by applying the given losses to 10000 goats. First loss of 12% means 12 / 100 * 10000 = 1200 goats die, leaving 10000 - 1200 = 8800 goats. Second loss of 5% of 8800 means 5 / 100 * 8800 = 440 goats die, leaving 8800 - 440 = 8360 goats. This matches the number stated in the question, confirming that our backward calculation is correct and that 10000 goats is indeed the original population before the flood. Why Other Options Are Wrong: If the original population were 1000 goats, even with small percentage losses, the final count could never be as high as 8360. A value of 8360 as the original population would lead to a lower final number after the two losses, not the same value. An original population of 1,00,000 goats would result in a final population ten times larger than required. Only 10000 goats leads to exactly 8360 goats after the given successive losses, so the other options are incompatible with the problem data. Common Pitfalls: A common mistake is to subtract 12% and 5% directly and treat the total loss as 17% of the original, which ignores that the second loss applies to a reduced base. Another error is to try to work additively instead of multiplicatively, leading to an incorrect equation. Some learners also reverse the process incorrectly, for example by adding 12% and 5% to the final number. Always represent each stage as a multiplier and work systematically either forward or backward. Final Answer: The village originally had 10000 goats before the flood and disease losses.

Question 18

A candidate scores 72% in one examination paper with a maximum of 900 marks and 80% in another paper with a maximum of 700 marks. If the overall result is based on the combined percentage across both papers, what is the candidate combined percentage…

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Introduction / Context: This question focuses on finding a combined percentage when a student appears in two different papers with different maximum marks. Rather than simply averaging the two percentage scores, we must use a weighted average based on the maximum marks in each paper. This situation is very common in school and competitive exams where subjects carry different weight, so understanding how to calculate the correct overall percentage is important for accurate result interpretation. Given Data / Assumptions: First paper maximum marks = 900. Candidate scores 72% in the first paper. Second paper maximum marks = 700. Candidate scores 80% in the second paper. The final result is based on total marks obtained out of total maximum marks. We need the overall percentage scored across both papers combined. Concept / Approach: The key concept is weighted average. The candidate total marks are the sum of marks obtained in each paper. The total maximum marks are the sum of the two papers maximums. The combined percentage is then (total obtained marks / total maximum marks) * 100. We do not simply average 72% and 80%, because each percentage is calculated on a different base. Instead we convert each percentage to actual marks, add them, and divide by the combined maximum. Step-by-Step Solution: Step 1: Compute marks in the first paper: 72% of 900 = (72 / 100) * 900. Step 2: Calculate (72 / 100) * 900 = 0.72 * 900 = 648 marks. Step 3: Compute marks in the second paper: 80% of 700 = (80 / 100) * 700. Step 4: Calculate (80 / 100) * 700 = 0.80 * 700 = 560 marks. Step 5: Total marks obtained = 648 + 560 = 1208. Step 6: Total maximum marks = 900 + 700 = 1600. Step 7: Combined percentage = (total obtained / total maximum) * 100. Step 8: Combined percentage = (1208 / 1600) * 100. Step 9: Compute 1208 / 1600 = 0.755, so combined percentage = 75.5%. Verification / Alternative check: As a rough check, note that both percentages are above 70%, and the higher percentage (80%) is on the paper with fewer maximum marks. So the combined percentage should be between 72% and 80%, but closer to 72% because the 900 mark paper carries more weight. The result 75.5% lies between these values and is somewhat closer to 72% than to 80%, which makes intuitive sense. This confirms that the computed value is reasonable and consistent with the distribution of maximum marks. Why Other Options Are Wrong: A combined percentage of 76%, 76.5%, or 77% would correspond to higher total marks than 1208. Since the actual total is fixed once we calculate marks from each paper, these values cannot occur. For example a 76% combined score would require 0.76 * 1600 = 1216 marks, which is greater than 1208. Similarly 77% would require 1232 marks. Therefore only 75.5% exactly matches the candidate actual performance in both papers. Common Pitfalls: A frequent error is to average the two percentages directly, that is compute (72 + 80) / 2 = 76%. This ignores the different maximum marks and leads to an incorrect answer. Another mistake is to miscalculate one of the individual percentages in terms of marks. To avoid these problems, always convert each percentage to actual marks first, then sum them and compute one overall percentage from the totals. Final Answer: The candidate combined percentage score across both papers is 75.5%.

Question 19

On a certain date, Pakistan has a success rate of 60% against India in all the One Day International matches played between the two countries. Pakistan then loses the next 30 ODIs in a row to India, after which its overall success rate falls to 30%.…

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Introduction / Context: This problem applies percentage concepts to sports statistics. Pakistan has an initial success rate expressed as a percentage, meaning the proportion of matches won out of those played. After losing several matches in a row, the success rate changes. We need to use this information to determine the total number of matches played. Questions of this type are common in quantitative reasoning, where success rates and changes in performance over time must be modelled algebraically. Given Data / Assumptions: Initially, Pakistan success rate against India in ODIs is 60%. Pakistan then loses the next 30 ODIs consecutively. After these 30 losses, the overall success rate falls to 30%. We assume only wins and losses, with no ties or abandoned matches affecting the statistics. We must find the total number of ODIs played between the two countries after these 30 losses. Concept / Approach: Let the initial number of matches played be N, with Pakistan winning 60% of them. That means the number of wins is 0.60 * N. The team then plays 30 more matches and loses all of them, so the number of wins remains the same while the total number of matches becomes N + 30. The new success rate is given as 30%, which leads to an equation involving N. Solving this equation provides the initial number of matches, and adding 30 gives the total number of ODIs after the losing streak. Step-by-Step Solution: Step 1: Let the initial total number of ODIs between the teams be N. Step 2: Initial success rate for Pakistan is 60%, so wins initially = 0.60 * N. Step 3: Pakistan then loses the next 30 ODIs, so wins do not increase; they remain 0.60 * N. Step 4: Total matches after these 30 ODIs become N + 30. Step 5: After the losing streak, the success rate is 30%, so we have 0.60 * N / (N + 30) = 0.30. Step 6: Multiply both sides by (N + 30) to get 0.60 * N = 0.30 * (N + 30). Step 7: Expand the right-hand side: 0.60 * N = 0.30 * N + 9. Step 8: Subtract 0.30 * N from both sides: 0.30 * N = 9. Step 9: Solve for N: N = 9 / 0.30 = 30. Step 10: Total matches after the extra 30 ODIs = N + 30 = 30 + 30 = 60. Verification / Alternative check: With N = 30 initial matches, Pakistan initially wins 60% of 30, which is 18 matches. After that, Pakistan loses 30 matches in a row, so total matches become 60 and total wins remain 18. The final success rate is 18 / 60 * 100 = 30%. This matches the problem statement precisely, confirming that our calculation of N and the final total number of matches is correct and consistent with the given percentages. Why Other Options Are Wrong: If the total number of matches were 50, then after subtracting the last 30, the initial matches would be only 20, and winning 60% of 20 would give 12 wins. The final success rate would then be 12 / 50 * 100 = 24%, not 30%. For 45 total matches, a similar check fails. If the total number of matches were only 30, that would mean no earlier matches at all, which contradicts the initial 60% success rate. Therefore, 60 is the only value that makes all conditions hold true. Common Pitfalls: Some learners try to average success rates or subtract percentages directly rather than setting up and solving an equation. Others may forget that after 30 losses, the number of wins remains unchanged. Confusing the initial and final total matches can also lead to incorrect algebra. The safest method is to introduce variables, translate each verbal condition into a clear equation, and solve step by step as done here. Final Answer: The total number of ODIs played between the two countries after the 30 consecutive losses is 60.

Question 20

A retailer marks up the cost price of goods by 150% and then offers a discount of 40% on the marked price. If the cost price of an article is Rs 800, what will be the final selling price (in rupees) after applying both the markup and the discount?

Accepted Answer

Introduction / Context: This question examines the combined effect of a large markup followed by a substantial discount. Retailers often increase the marked price well above the cost price and then advertise a discount to make the deal look attractive while still earning profit. Understanding the net effect of such successive percentage changes is important in profit and loss calculations and in interpreting real world pricing strategies in shops and online marketplaces. Given Data / Assumptions: Cost price (CP) of the article = Rs 800. Markup rate on cost price = 150%. Discount rate on marked price = 40%. We need to determine the final selling price after both operations. There are no additional taxes or hidden charges. Concept / Approach: The marked price is obtained by increasing the cost price by the markup percentage. A markup of 150% means that the marked price is the cost price plus 150% of the cost, or 2.5 times the cost price. The selling price is then found by applying the discount percentage to this marked price. Specifically, a 40% discount leaves 60% of the marked price. This can be modelled with multiplicative factors, first 2.5 for the markup and then 0.6 for the discount. Step-by-Step Solution: Step 1: Cost price (CP) = Rs 800. Step 2: Markup rate = 150% on cost, so markup factor = 1 + 150 / 100 = 2.5. Step 3: Marked price (MP) = CP * 2.5 = 800 * 2.5 = Rs 2000. Step 4: Discount rate = 40% on the marked price. Step 5: After a 40% discount, the customer pays 60% of the marked price, so multiplier = 1 - 40 / 100 = 0.60. Step 6: Selling price (SP) = MP * 0.60 = 2000 * 0.60 = Rs 1200. Step 7: Therefore the final selling price is Rs 1200. Verification / Alternative check: We can interpret the net effect directly on the cost price. The overall multiplier is 2.5 (markup) times 0.60 (discount), which gives 2.5 * 0.60 = 1.5. This means that the final selling price is 150% of the cost price, or a 50% profit on cost. Calculating 1.5 * 800 gives 1200, exactly matching the stepwise result. This confirms both that the arithmetic is correct and that the retailer still gains a 50% profit despite the seemingly large discount. Why Other Options Are Wrong: A selling price of Rs 1500 would correspond to a larger net multiplier, giving a higher profit rate than 50%. A price of Rs 1000 would be only 25% above the cost price and does not follow from a 2.5 times markup followed by a 40% discount. A selling price of Rs 2000 would represent the marked price before any discount and ignores the 40% reduction. Only Rs 1200 is consistent with both the stated markup and the discount percentage. Common Pitfalls: One common error is to subtract the percentages directly, for example saying 150% minus 40% equals 110% profit, which is incorrect because the discount applies to the marked price, not to the cost price. Another mistake is to compute 40% of the cost price instead of 40% of the marked price. To avoid these issues, always write explicit multiplication factors for each percentage step and apply them in order to the correct base amount. Final Answer: The final selling price of the article is Rs 1200.

Percentage Questions