Question 1

When 35 is subtracted from a number, the result is 80 percent of the original number. What is four-fifths of that original number?

Accepted Answer

Introduction / Context: This problem tests the relationship between a number and a percentage of itself when a fixed value is subtracted. We are told that subtracting 35 from an unknown number gives 80 percent of that number. Once the original number is found using algebra, we are asked to compute four-fifths of it. This style of question is very common in aptitude exams. Given Data / Assumptions: Let the original number be N. When 35 is subtracted from N, the result equals 80 percent of N. We must find four-fifths (4/5) of the original number N. All values are real numbers, and we expect an integer answer from the options. Concept / Approach: The key concept is that 80 percent of a number is 0.8 times that number. The condition can be expressed as an equation involving N. From that equation, we solve for N. Once N is known, calculating four-fifths of N is straightforward. It is often easier to work with decimal 0.8 or the fraction 4/5 as required, keeping arithmetic simple. Step-by-Step Solution: Step 1: Let the original number be N.Step 2: The condition is that N minus 35 equals 80 percent of N. In equation form, N - 35 = 0.8N.Step 3: Rearrange the equation by bringing 0.8N to the left: N - 0.8N - 35 = 0, which gives 0.2N - 35 = 0.Step 4: Solve for N: 0.2N = 35, so N = 35 / 0.2.Step 5: Since 0.2 equals 1/5, dividing by 0.2 is the same as multiplying by 5. Therefore N = 35 * 5 = 175.Step 6: Find four-fifths of N: (4/5) * 175 = 4 * 35 = 140. Verification / Alternative check: We can verify by substituting N = 175 back into the original condition. Subtracting 35 gives 175 - 35 = 140. Now compute 80 percent of 175: 0.8 * 175 = 140. Since both sides give 140, the equation holds. Next, four-fifths of 175 is indeed (4 * 175) / 5 = 700 / 5 = 140. Everything is consistent, confirming that 140 is correct. Why Other Options Are Wrong: The value 175 is the original number, not four-fifths of it. The value 135 is less than 140 and does not satisfy the condition when used as four-fifths of the original. The value 95 is much too small and would not match the percentage relationship. The value 210 exceeds the original number 175, which is impossible for four-fifths of N. Only 140 correctly represents four-fifths of the computed original number. Common Pitfalls: Some students mistakenly set up the equation as N - 35 = 0.8 * 35 instead of 0.8N. Others misinterpret 80 percent as 8 or 0.08, which leads to incorrect calculations. Forgetting that 0.2 equals 1/5 can also complicate the arithmetic. Working carefully with the decimal representations and rearranging the equation step by step helps avoid these errors. Final Answer: Four-fifths of the original number is 140, so the correct option is 140.

Question 2

In a group of 600 students who take tests in both physics and chemistry, 35 percent fail in physics and 45 percent fail in chemistry. If 40 percent of those who pass in chemistry also pass in physics, how many students fail in both subjects?

Accepted Answer

Introduction / Context: This is a Venn diagram or set theory style question involving two subjects, physics and chemistry. We are given percentages of failures in each subject and additional information about those who pass in one subject and also pass in the other. The goal is to find how many students fail in both subjects simultaneously. This type of question regularly appears in aptitude and entrance exams. Given Data / Assumptions: Total number of students = 600. 35 percent fail in physics. 45 percent fail in chemistry. Therefore 65 percent pass in physics and 55 percent pass in chemistry. Forty percent of those who pass in chemistry also pass in physics. We must find the number of students who fail in both physics and chemistry. Concept / Approach: We can treat the sets as follows: P is the set of students who fail physics, C is the set of students who fail chemistry. Their complements are students who pass. We know the sizes of P and C from the given percentages. The key extra information relates to students who pass both subjects, because it tells us that 40 percent of those who pass chemistry also pass physics. Once we find the number who pass both, we can work backwards to figure out how many are left to fail both subjects. Step-by-Step Solution: Step 1: Number failing physics = 35 percent of 600 = 0.35 * 600 = 210.Step 2: Number failing chemistry = 45 percent of 600 = 0.45 * 600 = 270.Step 3: Number passing chemistry = 600 - 270 = 330.Step 4: Forty percent of those who pass chemistry also pass physics, so students passing both subjects = 0.40 * 330 = 132.Step 5: Let x be the number who fail both subjects. Then failing only physics is 210 - x and failing only chemistry is 270 - x.Step 6: Total students can be expressed as 600 = (pass both) + (fail only physics) + (fail only chemistry) + (fail both) = 132 + (210 - x) + (270 - x) + x.Step 7: Simplify the expression: 132 + 210 + 270 - x = 612 - x. Set 612 - x = 600, giving x = 12. Verification / Alternative check: We can verify by explicitly listing category sizes. Failing both subjects is 12. Failing only physics is 210 - 12 = 198. Failing only chemistry is 270 - 12 = 258. Passing both is 132. Summing these, 12 + 198 + 258 + 132 = 600, matching the total. Also, passing chemistry totals 132 + 198 = 330, and 40 percent of 330 is 132, which confirms the condition about passing both subjects. Everything is consistent. Why Other Options Are Wrong: A value of 60 or 138 or 162 or 180 for those who fail both would break at least one condition. For example, if 60 failed both, then passing chemistry and physics numbers would not match the 40 percent condition. Careful algebra shows that only x = 12 satisfies the equations that come from the given percentages and the relation between passes in the two subjects. Therefore, the other numerical options do not fit the data. Common Pitfalls: Many students mix up failing and passing sets or misinterpret the phrase 40 percent of those who pass in chemistry also pass in physics. Another common mistake is to try to use inclusion exclusion directly on the failing sets without incorporating the extra condition about passes. Drawing a Venn diagram or using variables for each region and writing equations is a reliable way to avoid confusion. Final Answer: The number of students who fail in both physics and chemistry is 12, so the correct option is 12.

Question 3

A shopkeeper increases the price of a product by 25 percent and, as a result, a customer buys only 70 percent of the earlier quantity. What is the net percentage change in the customer expenditure on that product?

Accepted Answer

Introduction / Context: This question examines combined percentage changes in price and quantity and their effect on total expenditure. Expenditure is the product of price per unit and quantity purchased. When the price goes up and the quantity purchased goes down, we must determine the overall impact using multiplicative reasoning rather than simply adding or subtracting percentages. Given Data / Assumptions: The price per unit of a product increases by 25 percent. The customer now buys only 70 percent of the original quantity. Expenditure equals price per unit multiplied by quantity purchased. We compare the new expenditure with the original expenditure. Concept / Approach: If a quantity is increased by 25 percent, its new value is 1.25 times the original. If another quantity is reduced to 70 percent, its new value is 0.70 times the original. The new expenditure will be 1.25 multiplied by 0.70 times the old expenditure. The factor 1.25 * 0.70 gives the overall multiplicative effect on expenditure. Comparing this to 1 tells us whether expenditure has increased or decreased and by what percentage. Step-by-Step Solution: Step 1: Let the original price per unit be P and the original quantity be Q. Then original expenditure E = P * Q.Step 2: After the 25 percent price increase, the new price is 1.25P.Step 3: After the reduction in quantity, the new quantity is 0.70Q.Step 4: New expenditure E_new = 1.25P * 0.70Q = 0.875PQ.Step 5: Since original expenditure was PQ, the ratio E_new / E = 0.875.Step 6: A factor of 0.875 means the new expenditure is 87.5 percent of the original, so the reduction is 100 percent minus 87.5 percent = 12.5 percent decrease. Verification / Alternative check: Use simple numbers to verify. Assume the original price is Rs. 100 per unit and the original quantity is 10 units, giving original expenditure of Rs. 1000. After the price increase, the price becomes Rs. 125. After the quantity reduction, the customer buys 70 percent of 10, which is 7 units. The new expenditure is 125 * 7 = Rs. 875. This is 125 less than 1000. The difference of 125 out of 1000 is 12.5 percent, confirming our calculation. Why Other Options Are Wrong: A 5 percent or 10 percent decrease would correspond to new expenditure equal to 95 percent or 90 percent of the original, not 87.5 percent. No change in expenditure would require a net factor of exactly 1, which is not the case. A 12.5 percent increase would correspond to a factor of 1.125, opposite to our result. Only a 12.5 percent decrease is consistent with the factor 0.875 derived from the combined changes. Common Pitfalls: Many students simply subtract 25 percent and 30 percent (from 100 percent to 70 percent) and assume a 5 percent or similar net change, which is incorrect because the changes affect different factors (price and quantity) and must be handled multiplicatively. Another common mistake is to apply the percentage change to the wrong base or forget to interpret 70 percent as 0.70 in decimal form. Final Answer: The customer expenditure decreases and becomes 87.5 percent of the original, which is a 12.5% decrease, so the correct option is 12.5% decrease.

Question 4

A number X is mistakenly divided by 10 instead of being multiplied by 10. What is the percentage error in the result, measured relative to the correct value?

Accepted Answer

Introduction / Context: This question involves the concept of percentage error due to a calculation mistake. Instead of multiplying a number by 10, it is divided by 10. We need to compare the incorrect result with the correct result and find how large the error is in percentage terms relative to the correct value. Such questions test awareness of relative error and the difference between very large and very small results. Given Data / Assumptions: The correct operation should be multiplication of X by 10. The mistaken operation is division of X by 10. Percentage error is measured as the difference between correct and obtained results, relative to the correct result, expressed in percent. We consider percentage error in magnitude, so we focus on the size of the error. Concept / Approach: Let the correct value be V_correct and the obtained or incorrect value be V_wrong. Percentage error is usually defined as (V_correct - V_wrong) / V_correct * 100 in magnitude. Here, V_correct equals 10X and V_wrong equals X / 10. By substituting these expressions and simplifying, we find the ratio of the error to the correct value, and from that the percentage error. The sign of the error shows whether the value is under or over the true value, but many exam questions focus on the absolute percentage error. Step-by-Step Solution: Step 1: Correct value: V_correct = 10X.Step 2: Wrong value due to division: V_wrong = X / 10.Step 3: Error in value = V_correct - V_wrong = 10X - (X / 10).Step 4: Simplify 10X - X / 10 by writing 10X as 100X / 10, giving (100X / 10) - (X / 10) = 99X / 10.Step 5: Percentage error (in magnitude) = (error / correct value) * 100 = (99X / 10) / (10X) * 100.Step 6: Simplify the fraction: (99X / 10) / (10X) = 99 / 100 = 0.99.Step 7: Multiply by 100 to get percentage error: 0.99 * 100 = 99 percent. Verification / Alternative check: Use a simple value for X, such as X = 1. The correct value should be 10 * 1 = 10. The wrong value is 1 / 10 = 0.1. The error is 10 - 0.1 = 9.9. Now, percentage error = 9.9 / 10 * 100 = 99 percent. This confirms the algebraic work. If we chose X = 2, we would get correct value 20 and wrong value 0.2, giving error 19.8 and percentage error 19.8 / 20 * 100 = 99 percent again, as expected. Why Other Options Are Wrong: The values plus or minus 100 percent would indicate that the wrong value is zero or twice the correct value, which is not the case. A zero percent error would mean the wrong and correct values are identical, which is clearly not true. A negative 99 percent would indicate direction but exam questions on percentage error usually use the magnitude. The best match with the usual definition is +99 percent, representing a 99 percent error in magnitude. Common Pitfalls: Some learners confuse relative error with absolute error and forget to divide by the correct value. Others may miscalculate 10X minus X / 10 or mishandle the division of fractions, leading to incorrect numerical answers like 90 percent or 100 percent. It is also easy to think that since division by 10 is the opposite of multiplication by 10, the error should be 100 percent, which is not correct. Careful simplification shows that the error is slightly less than the full value, at 99 percent. Final Answer: The result is off by 99% relative to the correct value, so the correct option is +99%.

Question 5

The length of a rectangular plot is increased by 50 percent. To keep its area unchanged, by what percentage should the width of the plot be decreased?

Accepted Answer

Introduction / Context: This question tests understanding of how changing one dimension of a rectangle affects the other dimension when the area is kept constant. When one side is increased by a certain percentage, the other side must change proportionally in the opposite direction so that the product, which represents area, remains unchanged. This type of problem appears often in percentage and mensuration topics. Given Data / Assumptions: Original length of the rectangle is L and original width is W. Original area A = L * W. Length is increased by 50 percent, so new length is 1.5L. Area must remain the same after the change. We must find the required percentage decrease in width. Concept / Approach: Area of a rectangle is the product of its length and width. If the length is multiplied by a factor, then the width must be multiplied by the reciprocal factor for the product to stay equal to the original area. Here the length factor is 1.5. The width factor must be 1 / 1.5. After finding this factor, we convert it to a percentage of the original width and then determine the percentage reduction from 100 percent. Step-by-Step Solution: Step 1: Original area A = L * W.Step 2: After the change, new length L_new = 1.5L.Step 3: Let new width be W_new. Since area is unchanged, L_new * W_new = L * W.Step 4: Substitute L_new = 1.5L: 1.5L * W_new = L * W.Step 5: Divide both sides by 1.5L to get W_new = (L * W) / (1.5L) = W / 1.5.Step 6: Simplify W / 1.5. Since 1.5 = 3/2, W / 1.5 = W * (2/3) = (2/3)W.Step 7: The new width is two-thirds of the old width, which is 66.67 percent of the original. Therefore, the decrease in width is 100 percent minus 66.67 percent = 33.33 percent. Verification / Alternative check: Use simple numbers. Suppose the original rectangle has length 2 units and width 3 units, so area is 2 * 3 = 6 square units. Increase length by 50 percent: new length is 3 units. To keep area at 6, width must be 6 / 3 = 2 units. Since original width was 3, the width has changed from 3 to 2, which is a decrease of 1 out of 3. In percentage terms, that is (1 / 3) * 100 = 33.33 percent decrease. This matches our algebraic result. Why Other Options Are Wrong: A decrease of 29.87 percent or 22.22 percent or 19.5 percent would not produce the reciprocal factor needed for area preservation. For example, a 30 percent decrease would leave width at 70 percent of its original, leading to area 1.5 * 0.70 = 1.05 times the original, which is a 5 percent increase, not unchanged area. Only a reduction to two-thirds of the original width, that is a 33.33 percent decrease, keeps the area constant. Common Pitfalls: One common mistake is to subtract percentages directly, such as assuming that if one side goes up by 50 percent, the other must go down by 50 percent. This ignores the multiplicative nature of area. Another mistake is to invert the fraction incorrectly when calculating W / 1.5. Remember that dividing by 3/2 is the same as multiplying by 2/3, not by 3/2. Final Answer: The width must be decreased by 33.33% to keep the area unchanged, so the correct option is 33.33%.

Question 6

A girl reads two-fifths of a book on the first day, 34 percent of it on the second day, and the remaining pages over the next two days, reading an equal number of pages on each of those days. If she reads 52 pages on the last day, how many pages doe…

Accepted Answer

Introduction / Context: This problem combines fractions and percentages of a whole quantity, here the total number of pages in a book. The reading progress is spread over four days with different proportions on different days. The goal is to find the total number of pages using the information about the final day reading. Such questions are frequently used to test comfort with fractional parts and equations. Given Data / Assumptions: The girl reads 2/5 of the book on the first day. She reads 34 percent of the book on the second day. She reads the remaining pages over the next two days, in equal amounts each day. On the fourth (last) day, she reads 52 pages. We must find the total number of pages in the book. Concept / Approach: We let the total number of pages be N. Fractions of N represent pages read on each day. By adding the fractions for the first two days, we can find the fraction left for the last two days. Since the last two days have equal numbers of pages and the last day is given as 52, we can find the remaining fraction of N and thus compute N. This is a straightforward linear equation in N involving basic percentage and fraction operations. Step-by-Step Solution: Step 1: Let total number of pages be N.Step 2: On the first day she reads 2/5 of N, which is 0.4N.Step 3: On the second day she reads 34 percent of N, which is 0.34N.Step 4: Together, pages read on the first two days are 0.4N + 0.34N = 0.74N.Step 5: Remaining fraction of the book after two days is 1 - 0.74 = 0.26. So remaining pages are 0.26N.Step 6: These remaining 0.26N pages are read over the next two days in equal amounts, so each of the last two days has (0.26N) / 2 = 0.13N pages.Step 7: We are told that on the last day she reads 52 pages, so 0.13N = 52.Step 8: Solve for N: N = 52 / 0.13.Step 9: Since 0.13 equals 13 / 100, dividing by 0.13 is multiplying by 100 / 13, giving N = 52 * (100 / 13) = 4 * 100 = 400. Verification / Alternative check: Check the distribution with N = 400 pages. On day one, she reads 2/5 of 400, which is 160 pages. On day two, she reads 34 percent of 400, which is 0.34 * 400 = 136 pages. Total after two days is 160 + 136 = 296 pages. Remaining pages are 400 - 296 = 104 pages for the last two days. If she reads equal amounts on days three and four, each day has 104 / 2 = 52 pages, which matches the given last day reading. So N = 400 is correct and consistent. Why Other Options Are Wrong: If the book had 376 or 382 or 356 or 420 pages, the calculations for first two days and remaining pages would not produce 52 pages on the last day when split equally across the last two days. For example, with N = 376, the remaining fraction 0.26N would not be exactly 104 pages and half of it would not be exactly 52. Only N = 400 satisfies all the conditions in the problem. Common Pitfalls: Some students mistakenly treat 34 percent as 34 pages instead of 34 percent of N. Others may add fractions incorrectly or forget to divide the remaining pages equally between the last two days. It is also easy to make arithmetic mistakes when working with decimals like 0.74 and 0.26. Converting everything carefully and checking each step helps prevent such errors. Final Answer: The book contains 400 pages, so the correct option is 400.

Question 7

A farmer divides his herd of k cows among his four sons so that the first son gets one-half of the herd, the second son gets one-fourth, the third son gets one-fifth and the fourth son gets 9 cows. What is the value of k, the total number of cows?

Accepted Answer

Introduction / Context: This question is based on fractional division of a whole quantity among several people. The farmer divides his herd in fractional shares plus a fixed number of cows. The key idea is that the sum of all those portions must equal the entire herd. This is a classic algebra problem involving fractions and a single unknown total. Given Data / Assumptions: Total number of cows is k. First son gets one-half of the herd, that is (1/2)k cows. Second son gets one-fourth of the herd, that is (1/4)k cows. Third son gets one-fifth of the herd, that is (1/5)k cows. Fourth son gets 9 cows. The entire herd is distributed among the four sons. Concept / Approach: We interpret the division of cows as an equation where the sum of all the portions equals k. The first three portions are written as fractions of k, and the last portion is a fixed number. Summing the fractions gives a combined fractional multiple of k, and adding 9 cows yields k. Solving this equation reveals the total number of cows. Manipulating fractional coefficients is the central skill here. Step-by-Step Solution: Step 1: Express the distribution as an equation: (1/2)k + (1/4)k + (1/5)k + 9 = k.Step 2: Find a common denominator for the fractions 1/2, 1/4 and 1/5. The least common multiple of 2, 4 and 5 is 20.Step 3: Rewrite the fractions with denominator 20. Then 1/2 = 10/20, 1/4 = 5/20, 1/5 = 4/20.Step 4: Add these fractions: (10/20 + 5/20 + 4/20)k = (19/20)k.Step 5: The equation becomes (19/20)k + 9 = k.Step 6: Subtract (19/20)k from both sides to get 9 = k - (19/20)k = (1/20)k.Step 7: Solve for k: (1/20)k = 9 implies k = 9 * 20 = 180. Verification / Alternative check: Check the distribution for k = 180. First son gets 1/2 of 180 = 90 cows. Second son gets 1/4 of 180 = 45 cows. Third son gets 1/5 of 180 = 36 cows. Fourth son gets 9 cows. Sum them: 90 + 45 + 36 + 9 = 180 cows. This matches the total herd and confirms that k = 180 satisfies the conditions. Why Other Options Are Wrong: If k were 160, then 1/2, 1/4 and 1/5 portions plus 9 would not sum to 160. For k = 120 or 140 or 200, similar calculations show that the combined fractional shares plus 9 do not equal the total. Only k = 180 makes the equation (1/2 + 1/4 + 1/5)k + 9 = k true, because the combined fractional part is exactly 19/20 of k, leaving 1/20k equal to 9. Common Pitfalls: A common error is to add fractions incorrectly or to misunderstand that the fractions are of the same total k. Some students may treat the 9 cows as part of a fraction or forget to include it in the equation. Miscalculating the common denominator or adding 10/20, 5/20 and 4/20 incorrectly can also lead to wrong answers. Careful fraction arithmetic and checking with substitution can prevent these mistakes. Final Answer: The total number of cows in the herd is 180, so the correct option is 180.

Question 8

What is the effective percentage discount when an offer says "Buy 6 and get 1 free" on identical items?

Accepted Answer

Introduction / Context: This is a percentage discount question disguised as a promotional offer. The phrase "Buy 6 and get 1 free" means the customer receives 7 items but pays for only 6. To find the effective percentage discount, we compare the price that would have been paid for all 7 items at full price with the reduced price paid under the offer. These kinds of problems are common in profit and loss or percentage sections of aptitude tests. Given Data / Assumptions: All items are identical and have the same marked price. Under the offer, the customer pays for 6 items and gets 1 item free, receiving 7 items in total. The normal situation without discount would be paying full price for all 7 items. We must compute the percentage discount relative to the total full price. Concept / Approach: Let the price of one item be P. Without any offer, 7 items would cost 7P. With the offer, the customer receives 7 items but pays only 6P. The discount in rupees is the difference between 7P and 6P, which is P. The percentage discount is the discount amount divided by the original full price (7P) multiplied by 100. The price P cancels out in the ratio, which means the discount percentage is independent of the actual price per item. Step-by-Step Solution: Step 1: Let the price of one item be P.Step 2: Without any offer, the cost of 7 items = 7P.Step 3: Under the offer "Buy 6 and get 1 free," the customer pays for 6 items and gets 7 items in total, so the amount paid = 6P.Step 4: Discount in rupees = original full cost - offer cost = 7P - 6P = P.Step 5: Percentage discount = (Discount / original full cost) * 100 = (P / 7P) * 100.Step 6: Simplify (P / 7P) * 100 to (1 / 7) * 100 ≈ 14.285 percent. Verification / Alternative check: Take a simple price, say P = Rs. 70. Then 7 items at full price would cost 7 * 70 = Rs. 490. Under the offer, the customer pays 6 * 70 = Rs. 420. The discount is 490 - 420 = Rs. 70. The percentage discount is 70 / 490 * 100 = 1 / 7 * 100 ≈ 14.285 percent. This matches the earlier algebraic calculation. The result does not depend on the particular value chosen for P. Why Other Options Are Wrong: The values 85.78 percent and 58.48 percent and 19.25 percent and 25 percent do not correspond to (1/7) * 100. For example, a discount of 25 percent would mean paying only 75 percent of the full price, which here would correspond to paying for 5.25 items instead of 6, which is not the offer. Only 14.285 percent matches the ratio of 1 free item out of 7 received. Common Pitfalls: Many students mistakenly divide by 6 instead of 7 or treat the discount as 1/6 of the price rather than 1/7 of the full cost of 7 items. Others confuse the number of items received with the number of items paid for, leading to incorrect ratios. Keeping track of the baseline for percentage calculation, which is the full cost of 7 items, is essential. Final Answer: The effective percentage discount in a "Buy 6 and get 1 free" offer is 14.285%, so the correct option is 14.285%.

Question 9

A house owner is told that painting his house will require 45 kg of paint allowing for 6 percent wastage. If paint is available only in 4 kg tins, how many tins are required for painting the house?

Accepted Answer

Introduction / Context: This problem is about adjusting a required quantity for wastage and then translating that adjusted requirement into discrete package sizes. Painters often allow for a percentage of wastage when estimating materials. The question checks whether you can handle percentage increase and then compute how many whole tins must be purchased to satisfy that requirement, since fractional tins cannot be bought. Given Data / Assumptions: Net paint required for actual painting work is 45 kg, allowing for 6 percent wastage. This statement means that after wastage, 45 kg remains available for application. Paint is sold only in tins of 4 kg each. We must buy enough tins so that the usable paint after wastage is at least 45 kg. Concept / Approach: If 6 percent of the paint will be wasted, then only 94 percent (100 percent minus 6 percent) of the purchased paint will actually be used. Let the total purchased paint be P kg. Then 94 percent of P must equal 45 kg. From this equation we solve for P, then divide by 4 to find how many 4 kg tins are required. Since we cannot buy a fraction of a tin, we round up to the next whole number. Step-by-Step Solution: Step 1: Let total paint purchased be P kg.Step 2: Wastage is 6 percent, so usable paint is 94 percent of P, which is 0.94P.Step 3: According to the problem, the usable paint must be 45 kg, so 0.94P = 45.Step 4: Solve for P: P = 45 / 0.94.Step 5: Numerically, 45 / 0.94 is approximately 47.872 kg.Step 6: Paint tins are 4 kg each, so number of tins required = P / 4 ≈ 47.872 / 4 ≈ 11.968.Step 7: Since we cannot buy a fraction of a tin, we must buy 12 tins to meet the requirement. Verification / Alternative check: Check with 12 tins. Twelve tins provide 12 * 4 = 48 kg of paint. Wastage is 6 percent of 48 kg, which is 0.06 * 48 = 2.88 kg. The usable paint is 48 - 2.88 = 45.12 kg, which is slightly more than the required 45 kg. With 11 tins, total paint would be 44 kg, and even with zero wastage this would be less than 45 kg. Therefore 12 tins are the minimum that satisfy the requirement with wastage. Why Other Options Are Wrong: Eleven tins give only 44 kg of paint, which even without wastage is insufficient. Ten tins provide 40 kg, which is even further from the requirement. Thirteen or fourteen tins provide more paint than necessary and would cover the requirement but are not the least number needed. The question asks for the number of tins required, which implies the smallest integer that meets the need, so 12 is correct. Common Pitfalls: Some students misinterpret the phrase allowing 6 percent wasting and assume that 45 kg already includes wastage, leading them to calculate 94 percent of 45 instead of the other way around. Others may forget to round up the number of tins and instead choose 11 based on the approximate division result. In real situations, insufficient paint would be a problem, so always round up when dealing with package counts. Final Answer: The house owner must purchase 12 tins of paint, so the correct option is 12.

Question 10

What is 30 percent of Rs. 500?

Accepted Answer

Introduction / Context: This is a straightforward percentage calculation question where we need to find a given percent of a specified amount of money. These types of questions form the foundation of more complex percentage and profit and loss problems, so it is important to be comfortable with them. Given Data / Assumptions: We are given an amount of Rs. 500. We need to find 30 percent of this amount. All calculations are in rupees. Concept / Approach: To find 30 percent of a number, we convert the percentage to a fraction or decimal and then multiply by the number. Thirty percent equals 30 divided by 100, which can be simplified to 3 divided by 10, or 0.3. Multiplying Rs. 500 by 0.3 will give the required value. This is basic percentage multiplication. Step-by-Step Solution: Step 1: Convert 30 percent to decimal form: 30 percent = 30 / 100 = 0.3.Step 2: Multiply the amount by this decimal: 0.3 * 500.Step 3: Compute 0.3 * 500. This is equal to 3 * 50 = 150.Step 4: Therefore, 30 percent of Rs. 500 is Rs. 150. Verification / Alternative check: We can view 30 percent as three tenths. One tenth of Rs. 500 is Rs. 50. Three tenths would be 3 * Rs. 50 = Rs. 150. This alternative method confirms the result without needing decimal multiplication. Both procedures yield the same answer, reinforcing that 150 is correct. Why Other Options Are Wrong: Rs. 180 would be 36 percent of 500, not 30 percent. Rs. 120 is only 24 percent of 500. Rs. 240 corresponds to 48 percent of 500. Rs. 100 is just 20 percent of 500. None of these match 30 percent. Only Rs. 150 is exactly 30 percent of Rs. 500. Common Pitfalls: Errors usually come from incorrect conversion of the percentage to decimal form, such as using 30 instead of 0.3, or from simple multiplication mistakes. Another common issue is misreading the question and computing 500 percent of 30 instead of 30 percent of 500. Careful reading and correct placement of the percentage are essential. Final Answer: The value of 30 percent of Rs. 500 is Rs. 150, so the correct option is Rs. 150.

Question 11

A shopkeeper charges sales tax of x percent on the first Rs. 2000 of a bill and y percent on the remaining amount. A customer pays a total tax of Rs. 320 on goods worth Rs. 6000 and a total tax of Rs. 680 on goods worth Rs. 12,000. What is the value…

Accepted Answer

Introduction / Context: This question involves a piecewise or tiered tax system where different tax rates apply to different parts of the bill amount. We are told how much tax is paid for two different purchase values. Using this information, we must find the difference between the two tax rates x and y. It combines percentage calculation with solving simultaneous linear equations. Given Data / Assumptions: For any bill, the first Rs. 2000 is taxed at x percent. The amount above Rs. 2000 is taxed at y percent. On goods worth Rs. 6000, the total tax paid is Rs. 320. On goods worth Rs. 12,000, the total tax paid is Rs. 680. We must find x - y. Concept / Approach: The tax on any bill can be written as the sum of two parts: tax on the first Rs. 2000 plus tax on the remaining amount. For a bill of Rs. 6000, the remaining amount is Rs. 4000. For a bill of Rs. 12,000, the remaining amount is Rs. 10,000. Writing equations for the total tax in each scenario in terms of x and y leads to two linear equations. Solving these equations simultaneously yields values of x and y and thus x - y. Step-by-Step Solution: Step 1: For a bill of Rs. 6000, tax on first Rs. 2000 is (x / 100) * 2000. Tax on remaining Rs. 4000 is (y / 100) * 4000.Step 2: Total tax for the Rs. 6000 bill is Rs. 320, so (x / 100) * 2000 + (y / 100) * 4000 = 320.Step 3: Multiply both sides by 100 to simplify: 2000x + 4000y = 32000. Divide entire equation by 100 to get 20x + 40y = 320.Step 4: For a bill of Rs. 12,000, tax on first Rs. 2000 is (x / 100) * 2000 and tax on remaining Rs. 10,000 is (y / 100) * 10,000.Step 5: Total tax for the Rs. 12,000 bill is Rs. 680, so (x / 100) * 2000 + (y / 100) * 10000 = 680.Step 6: Multiply both sides by 100: 2000x + 10000y = 68000. Divide by 100 to get 20x + 100y = 680.Step 7: Now we have the system: 20x + 40y = 320 and 20x + 100y = 680.Step 8: Subtract the first equation from the second: (20x + 100y) - (20x + 40y) = 680 - 320, giving 60y = 360.Step 9: Solve for y: y = 360 / 60 = 6.Step 10: Substitute y = 6 into 20x + 40y = 320: 20x + 40 * 6 = 320, so 20x + 240 = 320, thus 20x = 80 and x = 4.Step 11: Therefore x - y = 4 - 6 = -2. Verification / Alternative check: Verify using the found rates x = 4 percent and y = 6 percent. For Rs. 6000: tax on first Rs. 2000 is 4 percent of 2000 = 80. Tax on remaining Rs. 4000 is 6 percent of 4000 = 240. Total tax is 80 + 240 = 320, which matches the given amount. For Rs. 12,000: tax on first Rs. 2000 is again 80, and on Rs. 10,000 at 6 percent is 600. Total tax is 80 + 600 = 680, which matches the second given condition. So the values are correct. Why Other Options Are Wrong: If x - y were 0, then both rates would be equal, which does not satisfy the two different tax totals. Values -4, 5 or 2 do not result from the system of equations. Checking with those differences would lead to inconsistent tax amounts for one or both bills. Only x - y = -2 fits all the provided data and is supported by direct substitution. Common Pitfalls: Some students misinterpret the two slab rates and apply the higher rate to the entire bill instead of only the amount above Rs. 2000. Others may make algebraic errors while simplifying or subtracting the equations. Using clear stepwise manipulation and checking both scenarios with the found rates helps avoid these mistakes. Final Answer: The difference between the two tax rates is x - y = -2, so the correct option is -2.

Question 12

What is the value of 83 percent of 2350?

Accepted Answer

Introduction / Context: This is a direct percentage calculation involving a non-round percentage, 83 percent, applied to a given number 2350. The question checks whether the student can handle multiplication of a decimal by a multi digit number and interpret the result correctly as a decimal. Given Data / Assumptions: We have the number 2350. We are asked to find 83 percent of this number. All calculations are in ordinary decimal arithmetic. Concept / Approach: To find 83 percent of a quantity, we convert 83 percent to decimal form as 0.83 and then multiply. Alternatively, we can treat 83 percent as 83 / 100 and compute (83 * 2350) / 100. Choosing the easier way of multiplication helps reduce mistakes. Since 2350 ends with two zeros, multiplying by 83 and then dividing by 100 is particularly simple. Step-by-Step Solution: Step 1: Express 83 percent as a fraction: 83 percent = 83 / 100.Step 2: Compute 83 / 100 of 2350 as (83 * 2350) / 100.Step 3: Multiply 2350 by 83. We can do this as 2350 * 80 + 2350 * 3.Step 4: Compute 2350 * 80 = 188000 and 2350 * 3 = 7050.Step 5: Add these results: 188000 + 7050 = 195050.Step 6: Divide by 100: 195050 / 100 = 1950.50. Verification / Alternative check: We can use the decimal form 0.83 directly. Multiply 2350 by 0.83. Note that 0.83 = 83 / 100, so 2350 * 0.83 = 1950.5. Writing this with two decimal places gives 1950.50. This matches the result obtained using the fraction method. You can also approximate by noting that 80 percent of 2350 is 1880, and 3 percent of 2350 is 70.5, which sum to 1950.5, confirming the result. Why Other Options Are Wrong: The value 1889.95 is close to 80 percent of 2350 but not exactly 83 percent. The value 1912.35 is also not equal to 1950.5 and corresponds to a slightly lower percentage. The value 1875.25 is significantly lower and not associated with 83 percent. The value 1925.00 would correspond to about 81.9 percent. Only 1950.50 is exactly 83 percent of 2350. Common Pitfalls: Errors can arise from misplacing the decimal point during multiplication or from incorrectly converting 83 percent to a decimal such as 8.3 or 0.083. Another issue is rounding too early in intermediate steps instead of keeping the exact arithmetic until the final answer. Using the fraction method with division by 100 is a safe way to keep track of decimal places here. Final Answer: The value of 83 percent of 2350 is 1950.50, so the correct option is 1950.50.

Question 13

A student by mistake multiplies a number by 2/5 instead of multiplying it by 5/2. What is the percentage error in the final value obtained?

Accepted Answer

Introduction / Context: This question tests your understanding of percentage error when a wrong multiplier is applied instead of the correct one. Such questions are very common in aptitude exams where you must compare a correct value with an incorrect value obtained due to a calculation mistake. Given Data / Assumptions: • Let the original number be N.• Correct multiplier should be 5/2.• Student wrongly uses 2/5 as the multiplier.• We must find the percentage error in the evaluated result. Concept / Approach: Percentage error is calculated as: Percentage error = (Correct value − Wrong value) / Correct value * 100The sign indicates whether the result is more or less than the correct value. In aptitude questions we usually report the magnitude of the error. Step-by-Step Solution: Step 1: Correct value = N * (5/2) = 2.5N.Step 2: Wrong value = N * (2/5) = 0.4N.Step 3: Difference between correct and wrong = 2.5N − 0.4N = 2.1N.Step 4: Percentage error = (2.1N / 2.5N) * 100.Step 5: Simplify the fraction 2.1 / 2.5 = 21 / 25 = 0.84.Step 6: Therefore percentage error = 0.84 * 100 = 84%. Verification / Alternative check: Take N = 10 for an easy check. Correct value = 10 * 5/2 = 25. Wrong value = 10 * 2/5 = 4. Difference = 21. Percentage error = (21/25) * 100 = 84%. This confirms our calculation. Why Other Options Are Wrong: 52% and 64% are obtained if the student confuses which value is taken as correct in the denominator. 77% results from rounding or using an incorrect difference. Only 84% matches the correct error fraction 21/25. Common Pitfalls: Students often reverse the roles of correct and wrong values or divide by the wrong quantity in the percentage error formula. Another mistake is directly subtracting the fractions 5/2 and 2/5 without multiplying them with the base number. Final Answer: The percentage error in the evaluation is 84%.

Question 14

In a competitive test, the minimum passing percentage for girls and boys is 35% and 40% respectively of the same maximum marks. A boy scores 483 marks and fails by 117 marks. What is the minimum passing marks required for a girl in this test?

Accepted Answer

Introduction / Context: This percentage question involves pass marks based on different minimum percentages for boys and girls. Such problems check whether you can move between actual marks, percentages and total maximum marks in exams. Given Data / Assumptions: • Minimum passing percentage for boys = 40%.• Minimum passing percentage for girls = 35%.• A boy scores 483 marks and fails by 117 marks.• Total maximum marks are the same for boys and girls.• We must find the minimum passing marks for girls. Concept / Approach: If a student fails by a certain number of marks, that amount is the difference between the required pass marks and the actual marks obtained. Once we know the pass marks for boys as a percentage of the total, we can find the total maximum marks. Then we use the girls passing percentage to find their pass marks. Step-by-Step Solution: Step 1: For the boy, required pass marks = 483 + 117 = 600.Step 2: These 600 marks represent 40% of the total maximum marks.Step 3: Let total maximum marks be M. Then 40% of M = 600.Step 4: So 0.40 * M = 600, hence M = 600 / 0.40 = 1500.Step 5: Girls need 35% of the same total marks to pass.Step 6: Required marks for girls = 0.35 * 1500 = 525. Verification / Alternative check: Check proportionality. If 40% of 1500 is 600, then 35% is slightly less than 600. Calculating 10% of 1500 is 150, so 30% is 450, and 5% is 75. Adding 450 and 75 gives 525, which confirms the value. Why Other Options Are Wrong: 625 is greater than the passing marks for boys and would correspond to more than 40%. 425 and 325 correspond to much lower percentages of 1500 and do not match 35%. Common Pitfalls: A common error is to apply the 35% directly on the boy marks instead of on the total maximum marks. Another mistake is forgetting to first add the failure margin to get the boy pass marks. Final Answer: The minimum passing marks for girls are 525.

Question 15

If 25% of a first number is subtracted from a second number, the second number becomes four sixths (that is, two thirds) of its original value. What is the ratio of the first number to the second number?

Accepted Answer

Introduction / Context: This problem involves two unknown numbers related by a percentage subtraction condition. It tests your ability to translate percentage statements into algebraic equations and then derive a ratio of two quantities. Given Data / Assumptions: • Let the first number be A.• Let the second number be B.• Twenty five percent of A is subtracted from B.• After subtraction, B becomes four sixths of its original value, that is two thirds of B.• We must find the ratio A : B. Concept / Approach: Percentages can be turned into fractions. Twenty five percent is 25/100 = 1/4. Four sixths simplifies to 2/3. We set up an equation for the new value of B after subtracting one quarter of A, express it as 2/3 of B and then solve for the relationship between A and B. Finally we write the ratio in simplest form. Step-by-Step Solution: Step 1: Amount subtracted from B is 25% of A = (1/4) * A.Step 2: New value of B after subtraction = B − (A/4).Step 3: According to the statement, this equals four sixths (two thirds) of B.Step 4: So B − A/4 = (2/3) * B.Step 5: Rearrange: B − (2/3)B = A/4.Step 6: Left side gives (1/3)B = A/4.Step 7: Cross multiply: 4B = 3A.Step 8: So A : B = 4 : 3. Verification / Alternative check: Pick simple numbers satisfying the ratio 4 : 3. Let A = 4 and B = 3. Then 25% of A = 1. New value of B after subtraction = 3 − 1 = 2. Two thirds of original B is 2. This matches the condition, so the ratio is validated. Why Other Options Are Wrong: Ratios 2:3, 3:2 and 5:3 do not satisfy the equation B − 25% of A = (2/3)B when you test them with sample integer values, so they do not fit the given condition. Common Pitfalls: Candidates sometimes treat four sixths as 4/6 without simplifying to 2/3, which does not change the answer but may confuse arithmetic. Another error is subtracting 25% of B instead of 25% of A. Final Answer: The required ratio of the first number to the second number is 4 : 3.

Question 16

Madhu obtains 32% of the maximum marks in a bank examination and fails by 8 marks. Kumar, who appears for the same examination, secures 42% of the total marks and scores 16 marks more than the cut off. What are the cut off marks in the examination?

Accepted Answer

Introduction / Context: This question combines percentage marks and pass or cut off marks. It checks how well you convert percentages into actual scores using the same total marks and then use the information to determine the cut off. Given Data / Assumptions: • Let the maximum marks in the exam be M.• Madhu scores 32% of M and fails by 8 marks.• Kumar scores 42% of M and gets 16 marks more than the cut off.• The cut off is the minimum marks needed to pass.• We must find the value of the cut off in marks. Concept / Approach: Let C be the cut off. Madhu has C − 8 marks, and this equals 32% of M. Kumar has C + 16 marks, and this equals 42% of M. We can form two equations in M and C, subtract one from the other to eliminate C and solve for M, then substitute back to find C. Step-by-Step Solution: Step 1: Madhu score equation: 0.32M = C − 8.Step 2: Kumar score equation: 0.42M = C + 16.Step 3: Subtract the first equation from the second.Step 4: Left side: 0.42M − 0.32M = 0.10M.Step 5: Right side: (C + 16) − (C − 8) = 24.Step 6: So 0.10M = 24, hence M = 24 / 0.10 = 240.Step 7: Substitute M into Madhu equation: 0.32 * 240 = C − 8.Step 8: Compute 0.32 * 240 = 76.8, so C − 8 = 76.8.Step 9: Therefore C = 76.8 + 8 = 84.8. Verification / Alternative check: Check with Kumar. Forty two percent of 240 is 100.8. The difference between Kumar marks and cut off is 100.8 − 84.8 = 16, which matches the question data, so the cut off value is correct. Why Other Options Are Wrong: Values 76.8 and 78.8 do not satisfy both student conditions at the same time when substituted back. The option 86.8 also fails the required difference relationships. Common Pitfalls: A common mistake is to treat the percentages as if they were directly the cut off instead of solving the simultaneous equations. Mixing up who failed by 8 and who got 16 more than the cut off also leads to wrong equations. Final Answer: The cut off marks in the examination are 84.8.

Question 17

A jar contains 20 litres of pure milk. First, 4 litres of milk are taken out and replaced with an equal quantity of water. Then again 4 litres of this new mixture are removed from the jar. What is the final quantity of milk left in the jar?

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Introduction / Context: This is a standard repeated replacement mixture question. It tests your understanding of how the concentration of a liquid changes when some quantity is removed and replaced with another liquid, here water, more than once. Given Data / Assumptions: • Initial volume in the jar = 20 litres of pure milk.• First operation: remove 4 litres of milk and add 4 litres of water.• Second operation: remove 4 litres of the resulting milk water mixture.• Total volume is always kept at 20 litres.• We must find the final amount of milk left. Concept / Approach: For each operation, we track the fraction of milk in the jar. When a mixture is taken out, the quantity of milk removed equals the milk fraction multiplied by the volume removed. After removing mixture, water or milk is added back to restore total volume. Repeating this process allows us to compute the new amount of milk. Step-by-Step Solution: Step 1: Initially milk = 20 litres, water = 0 litres.Step 2: Remove 4 litres of pure milk, so milk left = 20 − 4 = 16 litres.Step 3: Add 4 litres of water. Now total = 20 litres with 16 litres milk and 4 litres water.Step 4: Milk fraction after first operation = 16/20 = 4/5 = 0.8.Step 5: Second operation, remove 4 litres of mixture.Step 6: Milk removed this time = 0.8 * 4 = 3.2 litres.Step 7: Milk left after removal = 16 − 3.2 = 12.8 litres.Step 8: Adding back 4 litres of water only changes the water amount, not milk quantity, so milk remains 12.8 litres. Verification / Alternative check: We can also use the standard replacement formula: remaining quantity of milk = initial volume * (1 − withdrawn volume / total volume) raised to the number of operations. Here milk amount after two operations = 20 * (1 − 4/20)^2 = 20 * (1 − 0.2)^2 = 20 * 0.8^2 = 20 * 0.64 = 12.8 litres, matching the previous method. Why Other Options Are Wrong: Values 14.5, 11.6 and 10.46 litres do not correspond to the correct fraction power for two replacement steps. They may result from applying the formula only once or from arithmetic mistakes in the fractional calculations. Common Pitfalls: Candidates often think that exactly 8 litres of milk are removed in two steps, ignoring the fact that the second removal takes out a mixture, not pure milk. Forgetting to square the factor in the replacement formula is another frequent error. Final Answer: The final quantity of milk left in the jar is 12.8 litres.

Question 18

One third of the boys and one half of the girls in a college participate in a sports event. The total number of participating students is 300, out of which 100 are boys. What is the total number of students enrolled in the college?

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Introduction / Context: This is a percentage and ratio based counting problem involving boys and girls in a college. It tests your ability to convert fractions into actual numbers and to use the given participant information to determine total enrolment. Given Data / Assumptions: • One third of the boys participate in the sport.• One half of the girls participate in the sport.• Total participants in the event = 300 students.• Among these participants, 100 are boys.• We must find the total number of students in the college. Concept / Approach: Let the total number of boys be B and the total number of girls be G. The number of boys who participate is B/3, which is given as 100. The total participants are B/3 + G/2 = 300. From these two equations we can find B and G and then compute the total number of students B + G. Step-by-Step Solution: Step 1: From the given data, B/3 = 100.Step 2: So B = 100 * 3 = 300 boys in the college.Step 3: Total participants are B/3 + G/2 = 300.Step 4: Substitute B/3 = 100, we get 100 + G/2 = 300.Step 5: Therefore G/2 = 200 and G = 400.Step 6: Total students in the college = B + G = 300 + 400 = 700. Verification / Alternative check: Check participation counts. One third of 300 boys is 100, which matches the given number of participating boys. One half of 400 girls is 200. Total participants = 100 + 200 = 300, which exactly matches the question, confirming the calculation. Why Other Options Are Wrong: Values 550, 575 and 625 do not satisfy both the conditions simultaneously when you calculate the participating boys and girls according to the given fractions. Common Pitfalls: Many students wrongly assume that 100 boys represent one third of total students instead of one third of the boys only. Another mistake is to forget that the total 300 participants include both boys and girls. Final Answer: The total number of students in the college is 700.

Question 19

In an examination with a maximum of 500 marks, candidate P gets 10% less marks than Q. Candidate Q gets 25% more marks than R and R gets 20% less marks than S. If P scores 360 marks, then what percentage of the maximum marks does S obtain?

Accepted Answer

Introduction / Context: This question connects the marks of four candidates through successive percentage increases and decreases. It tests your ability to express each person’s marks in terms of a reference candidate and then convert the final result into a percentage of maximum marks. Given Data / Assumptions: • Maximum marks in the exam = 500.• P gets 10% less than Q.• Q gets 25% more than R.• R gets 20% less than S.• P scores 360 marks.• We must find S percentage of 500 marks. Concept / Approach: We express every candidate’s marks as a multiple of S marks. Decreases and increases are converted to multiplicative factors. Finally we equate P expression to the given 360 marks and solve for S. Then we convert S marks into a percentage of the maximum 500 marks. Step-by-Step Solution: Step 1: Let S marks be x.Step 2: R gets 20% less than S, so R = 0.80x.Step 3: Q gets 25% more than R, so Q = 1.25 * 0.80x = 1.00x.Step 4: P gets 10% less than Q, so P = 0.90 * Q = 0.90x.Step 5: Given P = 360 marks, so 0.90x = 360.Step 6: Solve for x: x = 360 / 0.90 = 400.Step 7: Thus S scored 400 marks out of a maximum of 500.Step 8: Percentage obtained by S = (400 / 500) * 100 = 80%. Verification / Alternative check: Check backward: S = 400, R is 20% less so R = 320, Q is 25% more than R so Q = 400, and P is 10% less than Q so P = 360. All conditions match the values, confirming the result. Why Other Options Are Wrong: Values 77, 74 and 83% do not give P = 360 when you propagate increases and decreases as per the given relationships. They arise from misinterpreting percentages or using addition instead of multiplication. Common Pitfalls: Students sometimes treat a 20% decrease as subtracting 20 marks rather than 20% of the current marks. Another mistake is to apply the percentages in the wrong order or to the wrong candidate. Final Answer: S secures 80% of the maximum marks.

Question 20

A man reads three sevenths of a book on the first day and two fifths of the remaining part on the second day. If 36 pages of the book still remain unread, how many pages does the book contain in total?

Accepted Answer

Introduction / Context: This problem is about reading fractions of a whole on different days. It checks your understanding of operations with fractions and how to work backwards from the remaining part to the total quantity. Given Data / Assumptions: • Let the total number of pages in the book be N.• On day one, the man reads three sevenths of the book.• On day two, he reads two fifths of the remaining pages.• After two days, 36 pages remain unread.• We must find the value of N. Concept / Approach: First, compute the remaining fraction of the book after the first day. Then apply the second day reading fraction to that remainder. The final remainder is given as a specific number of pages. We convert this relation into an equation in N and solve. Step-by-Step Solution: Step 1: Pages read on day one = (3/7) * N.Step 2: Remaining pages after day one = N − (3/7)N = (4/7)N.Step 3: On day two he reads two fifths of the remaining pages, that is (2/5) * (4/7)N = (8/35)N.Step 4: Pages remaining after day two = (4/7)N − (8/35)N.Step 5: Convert to common denominator 35: (4/7)N = (20/35)N, so remaining = (20/35 − 8/35)N = (12/35)N.Step 6: This remaining amount equals 36 pages.Step 7: So (12/35)N = 36, hence N = 36 * (35/12).Step 8: Simplify: 36/12 = 3, so N = 3 * 35 = 105. Verification / Alternative check: Check directly. Three sevenths of 105 is 45 pages, so 60 remain. Two fifths of 60 is 24, leaving 36 pages unread. This matches the given condition, confirming that 105 pages is correct. Why Other Options Are Wrong: Values 101, 98 and 109 do not produce a remaining count of 36 when the same fractional reading steps are applied. They arise from arithmetic errors with fractions or from subtracting fractions incorrectly. Common Pitfalls: A typical mistake is to apply two fifths to the original number of pages instead of the remaining pages. Another issue is failing to convert fractions to a common denominator when subtracting them. Final Answer: The book contains 105 pages in total.

Percentage Questions