Question 1

Three states X, Y, and Z had students appearing for an exam in 1998 in the ratio 3 : 5 : 6. Next year, the numbers rose by 20%, 10%, and 20% respectively. If in the next year the ratio of students in states X and Z is 1 : 2, determine whether the 19…

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Introduction / Context:This is a data sufficiency style question disguised as a percentage/ratio problem. We are asked whether the original numbers (1998) can be uniquely determined using the given ratios and percentage changes.Given Data / Assumptions:1998 ratio X : Y : Z = 3 : 5 : 6 ⇒ numbers = 3k, 5k, 6k.Next year increases: X by 20%, Y by 10%, Z by 20%.Next year X : Z is 1 : 2.Concept / Approach:Compute next-year values as factors of k and check the X : Z ratio. If the ratio condition holds identically (for all k), then k is not determined and original totals cannot be uniquely fixed.Step-by-Step Solution:Next year X = 3k * 1.20 = 3.6kNext year Z = 6k * 1.20 = 7.2kTheir ratio = 3.6k : 7.2k = 1 : 2 (since both sides divide by 3.6k)The ratio holds for any k, so k is not pinned down.Verification / Alternative check:Even if Y’s growth is included, it doesn’t affect the X : Z ratio. Without an absolute count or another independent equation, 1998 totals are undetermined.Why Other Options Are Wrong:Numerical totals (5000, 6000, 75000, 7000) cannot be justified uniquely from the data.Common Pitfalls:Assuming ratios alone can produce exact totals; missing that a free scale factor k remains.Final Answer:Data is insufficient

Question 2

A full tank of petrol in Arun’s motorbike lasts 10 days. If he starts using 25% more petrol per day, for how many days will the same full tank last now?

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Introduction / Context:This is an inverse-variation question. If daily consumption rises by a certain percentage, the number of days the fixed quantity lasts falls in inverse proportion.Given Data / Assumptions:Original duration = 10 days.New daily use = 25% more ⇒ factor = 1.25 times the old use.Concept / Approach:The total petrol is fixed. Duration (days) * daily use = constant. Hence new days = old days / 1.25.Step-by-Step Solution:New days = 10 / 1.25 = 8Verification / Alternative check:Let the tank contain 10 units and original daily use be 1 unit/day. After a 25% rise, daily use = 1.25 units/day. Then days = 10 / 1.25 = 8.Why Other Options Are Wrong:5, 6, and 7 result from over-reducing; 9 assumes too small an increase in daily use.Common Pitfalls:Subtracting 25% from 10 directly (to get 7.5) instead of applying inverse proportion.Final Answer:8

Question 3

In an exam of 480 students, 85% of the girls and 70% of the boys passed. If the overall pass percentage was 75%, how many boys appeared?

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Introduction / Context:This problem requires forming an equation from group-wise pass rates and the overall pass rate, then solving for the unknown number of boys.Given Data / Assumptions:Total students = 480.Pass rates: boys 70%, girls 85%.Overall pass % = 75%.Boys = B, girls = 480 − B.Concept / Approach:Total passes = passes by boys + passes by girls. Equate this to 75% of 480 to solve for B.Step-by-Step Solution:0.70B + 0.85(480 − B) = 0.75 * 4800.70B + 408 − 0.85B = 360−0.15B = −48 ⇒ B = 320Verification / Alternative check:Boys passed = 0.70 * 320 = 224; girls = 160, girls passed = 0.85 * 160 = 136; total passed = 360 = 75% of 480. Consistent.Why Other Options Are Wrong:340, 360, 370 lead to totals not equal to 360 passes; 300 also fails the overall percentage.Common Pitfalls:Mixing up which group has which rate, or using 75% of only boys or girls instead of the whole.Final Answer:320

Question 4

In an election between two candidates, 20% of the total votes were invalid and the remaining votes were valid. One candidate received 55% of the total valid votes. If the total number of votes (valid plus invalid) was 7,500, how many valid votes did…

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Introduction / Context:This election-based percentage problem tests the ability to work with percentages of totals and to reason carefully about valid and invalid votes. Students must distinguish between percentages calculated on total votes and those calculated on valid votes only. The question provides the total number of votes, the percentage of invalid votes and the percentage share of valid votes obtained by one candidate. We are asked to determine the number of valid votes received by the other candidate. Given Data / Assumptions:- Total votes cast (including valid and invalid) = 7,500.- 20% of the total votes were invalid.- Therefore, 80% of the total votes were valid.- Of the valid votes, one candidate got 55%.- There are only two candidates.- We must find how many valid votes the other candidate received. Concept / Approach:The solution involves two levels of percentage calculations. First, we find the number of valid votes by applying the given invalid vote percentage to the total votes. Then, within the valid votes, we calculate the vote share for each candidate. Since there are only two candidates, the second candidate receives the remaining valid votes after subtracting the first candidate's share from the total valid votes. Step-by-Step Solution:Step 1: Total votes = 7,500.Step 2: Invalid votes = 20% of 7,500.Step 3: 20% of 7,500 = (20 / 100) * 7,500 = 0.20 * 7,500 = 1,500.Step 4: Valid votes = total votes - invalid votes = 7,500 - 1,500 = 6,000.Step 5: Of the valid votes, one candidate gets 55%.Step 6: Votes for the first candidate = 55% of 6,000.Step 7: 55% of 6,000 = (55 / 100) * 6,000 = 0.55 * 6,000 = 3,300.Step 8: Since there are only two candidates, the other candidate gets the remaining valid votes.Step 9: Votes for the other candidate = valid votes - first candidate's votes = 6,000 - 3,300 = 2,700. Verification / Alternative check:We can verify quickly by checking total valid votes.Total valid votes = 2,700 + 3,300 = 6,000, which matches the earlier calculation of valid votes.Among 6,000 valid votes, one candidate has 3,300 votes, which is 3,300 / 6,000 = 0.55 or 55%. The other candidate has 2,700 votes, which is 2,700 / 6,000 = 0.45 or 45% of valid votes. All figures are consistent. Why Other Options Are Wrong:- 2500: This would imply total valid votes of 3,300 + 2,500 = 5,800, contradicting the 6,000 valid votes derived from the total and invalid percentages.- 2900: Gives a total of 3,300 + 2,900 = 6,200 valid votes, exceeding the correct valid count.- 3100: Again, 3,300 + 3,100 = 6,400 valid votes, not matching the correct figure of 6,000. Common Pitfalls:- Computing 55% of the total votes instead of valid votes only.- Forgetting to subtract invalid votes from total votes before allocating votes between candidates.- Misapplying percentages, for example, subtracting 55% from 100% incorrectly or miscalculating 20% of 7,500.- Confusing valid vote percentages with proportions of the total voter list. Final Answer:The other candidate received 2,700 valid votes.

Question 5

Fresh fruit contains 68% water by weight, while dry fruit contains only 20% water. If we start with 100 kg of fresh fruits, how many kilograms of dry fruit can be obtained after removing the excess water, assuming the solid (non-water) content remai…

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Introduction / Context:This question deals with percentage composition and conservation of the non-water (solid) part of a substance. Fresh fruits and dry fruits differ mainly in their water content. When fresh fruits are dried, water is removed but the solid portion remains the same. The problem asks how much dry fruit can be obtained from 100 kg of fresh fruit, given the water percentages for both types. This type of question is common in percentage and ratio topics in quantitative aptitude. Given Data / Assumptions:- Fresh fruit has 68% water and therefore 32% solid content.- Dry fruit has 20% water and therefore 80% solid content.- Initial quantity of fresh fruits = 100 kg.- Water is removed during drying but the solid content is unchanged.- We must find the weight of dry fruit obtained. Concept / Approach:The key concept is conservation of solids. When fresh fruit is converted into dry fruit, the amount of solids (non-water portion) stays the same, only the water percentage changes. Thus, we first compute the amount of solid matter in the fresh fruit. Then, we assume this same solid mass is present in the resulting dry fruit, where it represents 80% of the total weight. Using this relationship, we solve for the weight of the dry fruit. Step-by-Step Solution:Step 1: Fresh fruits weigh 100 kg.Step 2: Water content in fresh fruits = 68% of 100 kg = 68 kg.Step 3: Solid content in fresh fruits = 100 kg - 68 kg = 32 kg.Step 4: For dry fruit, water content is 20%, so solid content is 80% of its total weight.Step 5: Let the weight of dry fruit be W kg.Step 6: Solid content in dry fruit = 80% of W = (80 / 100) * W = 0.8 * W.Step 7: The solid content must remain the same before and after drying, so:0.8 * W = 32.Step 8: Solve for W: W = 32 / 0.8.Step 9: 32 / 0.8 = 32 * (10 / 8) = 320 / 8 = 40.Therefore, W = 40 kg of dry fruit. Verification / Alternative check:Check using percentage reasoning directly.If W = 40 kg, then solid content = 80% of 40 kg = 0.8 * 40 = 32 kg.This matches the original solid content of 32 kg from 100 kg of fresh fruit. Hence, the calculation is consistent and correct. Why Other Options Are Wrong:- 20: This would imply solid content of 80% of 20 kg = 16 kg, which is less than the original 32 kg solids.- 30: Gives solids of 0.8 * 30 = 24 kg, which again does not match 32 kg.- 50: Gives solids of 0.8 * 50 = 40 kg, which is more than the original 32 kg and thus impossible without adding extra solids. Common Pitfalls:- Trying to directly subtract water percentages (68% - 20%) without considering the conservation of solid mass.- Misinterpreting the percentages as changes in total mass instead of proportions of different states of the same solids.- Forgetting that the fresh fruit and dry fruit masses are different, but the solid mass does not change.- Making arithmetic mistakes when solving 0.8 * W = 32. Final Answer:From 100 kg of fresh fruits, we can obtain 40 kg of dry fruit.

Question 6

If 20% of a number a is equal to b, then b% of 20 is equal to what percentage of a?

Accepted Answer

Introduction / Context:This is an algebraic percentage problem that explores the relationship between two variables a and b defined through a percentage condition. The problem states that 20% of a is equal to b and then asks what b% of 20 is in terms of a. Questions like this are common in quantitative aptitude and help test both percentage manipulation skills and algebraic reasoning in a simple setting. Given Data / Assumptions:- 20% of a is equal to b.- We need to find the value of b% of 20 in terms of a.- The answer must be expressed as some percentage of a (for example, 4% of a).- No specific numerical value is given for a or b; the relationship is symbolic. Concept / Approach:The approach is to translate the verbal percentage information into algebraic equations. First, we express b in terms of a using the equation for 20% of a. Then, we compute b% of 20 by treating b as a percentage value. Finally, we re-express the result back in terms of a and identify which percentage of a it corresponds to. This involves straightforward use of the percentage formula: x% of y = (x / 100) * y. Step-by-Step Solution:Step 1: The statement "20% of a is b" can be written algebraically as:b = 20% of a = (20 / 100) * a.Step 2: Simplify: b = (1 / 5) * a or b = a / 5.Step 3: We now need to evaluate "b% of 20".Step 4: b% of 20 means (b / 100) * 20.Step 5: So b% of 20 = (b / 100) * 20 = (20 * b) / 100 = b / 5.Step 6: We already know that b = a / 5, so substitute b in the expression b / 5.Step 7: b / 5 = (a / 5) / 5 = a / 25.Step 8: Now express a / 25 as a percentage of a.Step 9: a / 25 = (1 / 25) * a = (4 / 100) * a (because 1 / 25 = 4 / 100).Step 10: Therefore, a / 25 is equal to 4% of a. Verification / Alternative check:Take a specific numerical example to verify.Let a = 100.Then 20% of 100 = 20, so b = 20.Now compute b% of 20: 20% of 20 = (20 / 100) * 20 = 4.Now find 4% of a: 4% of 100 = (4 / 100) * 100 = 4.Both results are equal to 4, which confirms that b% of 20 is indeed 4% of a. Why Other Options Are Wrong:- 6% of a: This would correspond to 0.06a, which is 6a / 100. Our calculation gave a / 25 or 4a / 100, not 6a / 100.- 8% of a: Equal to 2a / 25, again not matching the derived value a / 25.- 10% of a: Equal to a / 10, which is much larger than a / 25 and inconsistent with the algebra. Common Pitfalls:- Treating b directly as 20 instead of as 20% of a in symbolic form.- Confusing b% of 20 with 20% of b, which would give a different expression.- Dropping or misplacing the factor 1/100 that always appears in percentage calculations.- Not simplifying fractions properly and hence failing to recognize that 1 / 25 equals 4%. Final Answer:b% of 20 is equal to 4% of a.

Question 7

The value of a machine depreciates at the rate of 10% every year on a fixed percentage basis. The machine was purchased 3 years ago. If its present value is Rs. 8,748, what was its purchase price, in rupees, when it was bought?

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Introduction / Context:This problem deals with depreciation, where an asset such as a machine decreases in value by a fixed percentage every year. Depreciation is very common in real-life accounting and financial mathematics, and here it is applied at a constant rate of 10% per year. We are given the current value of the machine after 3 years and must determine its original purchase price. This involves working with repeated percentage reductions and understanding the concept of compound depreciation. Given Data / Assumptions:- Annual depreciation rate = 10% of the value at the beginning of each year.- Time elapsed since purchase = 3 years.- Present value of the machine after 3 years = Rs. 8,748.- Depreciation is applied in a multiplicative way each year (compound depreciation).- We need to find the machine's original purchase price. Concept / Approach:When an asset depreciates at a fixed percentage rate per year, its value after n years is obtained by multiplying the original value by (1 - rate)^n. Here, the depreciation rate is 10%, so the value multiplies each year by (1 - 0.10) = 0.90. After 3 years, the factor becomes 0.90^3. We write the present value as original value multiplied by 0.90^3 and then solve for the original value by division. This is exactly similar to compound interest calculations, but in reverse and using a negative rate. Step-by-Step Solution:Step 1: Let the purchase price of the machine be P rupees.Step 2: Depreciation rate is 10% per year, so the value each year is multiplied by (1 - 0.10) = 0.90.Step 3: After 3 years, the value becomes P * (0.90)^3.Step 4: The present value after 3 years is given as Rs. 8,748.Step 5: Therefore, P * (0.90)^3 = 8,748.Step 6: Compute 0.90^3 = 0.9 * 0.9 * 0.9 = 0.81 * 0.9 = 0.729.Step 7: So we have P * 0.729 = 8,748.Step 8: Solve for P: P = 8,748 / 0.729.Step 9: 8,748 / 0.729 = 12,000.Thus, the purchase price P is Rs. 12,000. Verification / Alternative check:We can verify by applying depreciation forward from Rs. 12,000.Year 1: Value = 12,000 * 0.90 = 10,800.Year 2: Value = 10,800 * 0.90 = 9,720.Year 3: Value = 9,720 * 0.90 = 8,748.This matches the given present value exactly, so the purchase price of Rs. 12,000 is confirmed as correct. Why Other Options Are Wrong:- 10000: After 3 years at 10% depreciation, 10,000 * 0.9^3 = 7,290, which is less than 8,748.- 14000: 14,000 * 0.9^3 = 10,206, which is greater than 8,748.- 16000: 16,000 * 0.9^3 = 11,664, much higher than the given present value. Common Pitfalls:- Treating depreciation as simple subtraction each year instead of multiplying by 0.90 successively.- Using 1 - 3 * 0.10 instead of (1 - 0.10)^3, which ignores the compounding effect.- Rounding too early in the division 8,748 / 0.729, leading to approximate values.- Confusing appreciation (compound interest) with depreciation and using 1 + 0.10 instead of 1 - 0.10. Final Answer:The purchase price of the machine was Rs. 12,000.

Question 8

A student was supposed to multiply a number by 5/3, but by mistake the student multiplied the number by 3/5 instead. What is the percentage error in the result of this incorrect calculation, compared to the correct value?

Accepted Answer

Introduction / Context:This question involves percentage error resulting from an incorrect multiplication. The student was expected to multiply a number by a certain fraction but instead used the reciprocal or a different fraction. We must compare the incorrect result to the correct result and express the difference as a percentage of the correct value. Such questions help build understanding of relative change and percentage error, which are useful in quantitative aptitude and data interpretation topics. Given Data / Assumptions:- Let the original number be x.- Correct operation: multiply x by 5/3.- Incorrect operation: multiply x by 3/5.- We need the percentage error in the result due to using 3/5 instead of 5/3.- Percentage error is usually measured as (correct value - incorrect value) / correct value * 100%, taking magnitude as required. Concept / Approach:The idea is to compute the correct result and the incorrect result in terms of x, then measure how much the incorrect result deviates from the correct result as a fraction of the correct result. The percentage error is this fraction multiplied by 100. Because the incorrect multiplier 3/5 is smaller than 1 and the correct multiplier 5/3 is larger than 1, the incorrect result will be much smaller than the correct result, leading to a large percentage error. Step-by-Step Solution:Step 1: Let the number be x.Step 2: Correct result = x * (5/3) = (5x / 3).Step 3: Incorrect result = x * (3/5) = (3x / 5).Step 4: Difference between correct and incorrect results:Difference = correct - incorrect = (5x / 3) - (3x / 5).Step 5: Find a common denominator of 15.(5x / 3) = (25x / 15) and (3x / 5) = (9x / 15).Step 6: Difference = (25x / 15) - (9x / 15) = (16x / 15).Step 7: Percentage error = (Difference / Correct) * 100%.Step 8: Correct value = 5x / 3.Step 9: Percentage error = ( (16x / 15) / (5x / 3) ) * 100%.Step 10: Simplify the fraction:(16x / 15) * (3 / 5x) = (16 * 3) / (15 * 5) = 48 / 75.Step 11: 48 / 75 reduces by dividing by 3: 16 / 25.Step 12: Convert 16 / 25 to a percentage: (16 / 25) * 100% = 64%.Therefore, the percentage error in the result is 64%. Verification / Alternative check:Take a specific value for x to see the effect.Let x = 15.Correct result = 15 * (5/3) = 15 * 5 / 3 = 25.Incorrect result = 15 * (3/5) = 15 * 3 / 5 = 9.Difference = 25 - 9 = 16.Percentage error = (16 / 25) * 100% = 64%.This matches our algebraic calculation. Why Other Options Are Wrong:- 54 %: This arises if one miscalculates the fractions or performs incorrect simplification.- 74 %: This would require a difference of 74/100 of the correct result, which is not supported by the derived ratio.- 84 %: This is far too large and would imply the incorrect result is extremely small compared to the correct one beyond what 3/5 vs 5/3 yields. Common Pitfalls:- Using the incorrect number as denominator when calculating percentage error instead of using the correct result as the base.- Confusing 3/5 and 5/3 numerically and not recognizing how far apart the resulting values are.- Failing to simplify the fractions properly and getting a wrong ratio.- Interpreting error as 100% - (incorrect / correct * 100) without understanding the underlying formula. Final Answer:The percentage error in the calculation is 64%.

Question 9

A student must obtain 33% of the total marks in an examination to pass. The student scored 125 marks and failed by 40 marks. What are the maximum (total) marks for the examination?

Accepted Answer

Introduction / Context:This examination problem involves percentages of total marks and the concept of passing marks. The passing mark is a fixed percentage of the total marks. The student has scored a certain number of marks but is short by a known amount. We are asked to find the total marks of the exam. Such questions are standard in quantitative aptitude and help students connect percentage thresholds with absolute scores. Given Data / Assumptions:- Passing percentage = 33% of the total marks.- The student scores 125 marks.- The student fails by 40 marks, meaning the student needs 40 more marks to reach the pass mark.- Let the maximum (total) marks of the exam be M.- We must find M. Concept / Approach:The pass mark is defined as 33% of the total marks M. Since the student failed by 40 marks, the pass mark is equal to the student's obtained marks plus 40. We therefore set up an equation: 33% of M equals 125 + 40. Solving this linear equation yields the total marks M. This is a straightforward application of percentage and algebra. Step-by-Step Solution:Step 1: Let total marks be M.Step 2: Passing marks = 33% of M = (33 / 100) * M.Step 3: The student scored 125 marks and failed by 40 marks.Step 4: Therefore, passing marks = 125 + 40 = 165.Step 5: Set up the equation: (33 / 100) * M = 165.Step 6: Multiply both sides by 100 to eliminate the denominator.33 * M = 165 * 100.Step 7: 165 * 100 = 16,500.Step 8: Now M = 16,500 / 33.Step 9: Divide 16,500 by 33: 33 * 500 = 16,500.Step 10: Hence, M = 500.Therefore, the maximum marks are 500. Verification / Alternative check:Check by computing 33% of 500.33% of 500 = (33 / 100) * 500 = 165 marks.The student scored 125 marks and failed by 40 marks.125 + 40 = 165, exactly equal to the required passing marks.This confirms that the total marks are 500. Why Other Options Are Wrong:- 600: 33% of 600 = 198, which would require the student to need 198 - 125 = 73 marks more, not 40.- 800: 33% of 800 = 264, implying a shortfall of 139 marks, inconsistent with the given 40 marks.- 1000: 33% of 1,000 = 330, so the student would be short by 205 marks, again incorrect. Common Pitfalls:- Misinterpreting "failed by 40 marks" as the student scoring 40 instead of being 40 marks below the passing score.- Using 33% of the obtained marks instead of 33% of the total marks to form the equation.- Arithmetic errors when multiplying or dividing by percentages, such as treating 33% as 0.33 but mis-applying it.- Confusing passing percentage 33% with passing marks 33 directly. Final Answer:The maximum marks for the examination are 500.

Question 10

The price of a book is first decreased by 25% and then increased by 20%. What is the net percentage change in the price of the book compared to the original price?

Accepted Answer

Introduction / Context:This question explores successive percentage changes, which occur often in discount and price adjustment problems. A price is first reduced by a certain percentage and then increased by another percentage. The goal is to find the net effect relative to the original price. This requires understanding that percentage changes operate multiplicatively, not additively. Here, a 25% decrease followed by a 20% increase does not bring the price back to the original level, and we must compute the final effective percentage change. Given Data / Assumptions:- Initial price of the book is assumed to be some value, say Rs. 100, for convenience.- First, the price decreases by 25%.- Then, the new price is increased by 20%.- We must determine the net percentage change with respect to the original price.- The options are given as numerical values representing the magnitude of the percentage change. Concept / Approach:Successive percentage changes are handled by applying each percentage operation step by step and using multiplication factors. A 25% decrease corresponds to multiplying by (1 - 0.25) = 0.75. A 20% increase corresponds to multiplying by (1 + 0.20) = 1.20. The final price is obtained by multiplying the original price by these two factors in sequence. The net percentage change is found by comparing the final price with the original price and converting the difference to a percentage of the original price. Step-by-Step Solution:Step 1: Assume the original price of the book is Rs. 100 (this makes percentage calculations easy and does not affect the final percentage change).Step 2: Apply a 25% decrease.New price after decrease = 100 * (1 - 0.25) = 100 * 0.75 = Rs. 75.Step 3: Now apply a 20% increase to the new price.New price after increase = 75 * (1 + 0.20) = 75 * 1.20 = Rs. 90.Step 4: Compare final price with original price.Original price = Rs. 100, final price = Rs. 90.Step 5: Difference = 100 - 90 = Rs. 10.Step 6: Net percentage change = (Difference / Original price) * 100%.Net percentage change = (10 / 100) * 100% = 10%.Step 7: Since final price is lower than the original, this is a 10% decrease. Verification / Alternative check:Instead of assuming Rs. 100, use multiplication factors directly.Overall multiplication factor = 0.75 * 1.20 = 0.90.This means the final price is 90% of the original.Therefore, there is a net 10% decrease from the original price.This confirms the earlier calculation using the assumed price of Rs. 100. Why Other Options Are Wrong:- 20: This would suggest a 20% net change which is not supported by the product of the factors 0.75 and 1.20.- 30: Incorrectly assumes additive combination of 25% and 5% or some miscalculation of the difference.- 40: Perhaps due to incorrectly adding 25% and 20%, not realizing that successive percentage changes are not additive. Common Pitfalls:- Simply adding -25% and +20% to claim a -5% change instead of computing multiplicative effects.- Applying the 20% increase to the original price instead of to the reduced price.- Forgetting that the base for the second percentage is already changed by the first operation.- Not indicating clearly that the net change is a decrease, even though the magnitude is 10%. Final Answer:The price undergoes a net 10% decrease compared to the original price.

Question 11

A man spends 35% of his income on food and 25% of his income on his children's education. He then spends 80% of the remaining income on house rent. What percentage of his original income is left after all these expenditures?

Accepted Answer

Introduction / Context:This is a multi-step percentage problem involving successive expenditures from an initial income. The man spends fixed percentages of his income on different expense categories: food, children's education and then house rent from the remaining amount. We must compute the percentage of his original income that remains after all these expenses. The question tests understanding of how sequential percentage deductions affect the remaining amount. Given Data / Assumptions:- Let the man's total income be I (we can imagine I = 100% for percentage calculations).- 35% of income is spent on food.- 25% of income is spent on children's education.- After these two expenses, from the remaining income, 80% is spent on house rent.- We must find what percentage of the original income I remains unspent. Concept / Approach:The approach is to apply each expenditure step sequentially to the income, always being careful to distinguish between percentages of the original income and percentages of the remaining income. First we subtract the percentages spent on food and education directly from the total. Then we calculate the remaining amount and apply the 80% rent expenditure to that remainder. Finally, we express the leftover amount as a percentage of the original income. Step-by-Step Solution:Step 1: Let the original income be 100 units (representing 100%).Step 2: Food expense = 35% of income = 35 units.Step 3: Education expense = 25% of income = 25 units.Step 4: Total spent on food and education = 35 + 25 = 60 units.Step 5: Remaining income after food and education = 100 - 60 = 40 units.Step 6: From this remaining 40 units, 80% is spent on house rent.Step 7: House rent = 80% of 40 = (80 / 100) * 40 = 32 units.Step 8: Remaining income after house rent = 40 - 32 = 8 units.Step 9: Since we started with 100 units representing 100%, the remaining 8 units represent 8% of the original income. Verification / Alternative check:We can verify by converting each step back to actual percentages of the original income I.Remaining income after food and education = 40% of I.House rent = 80% of the remaining 40% of I = 0.80 * 0.40 * I = 0.32I or 32% of I.Total spent overall = 35% + 25% + 32% = 92% of I.Thus, remaining income = 100% - 92% = 8% of I.This matches the 8 units out of 100 units from the earlier computation. Why Other Options Are Wrong:- 6 %: Too low; it would mean spending 94% of income, which is not consistent with the calculated expenses.- 10 %: Would require overall spending of 90%, not the 92% we deduced from the given data.- 12 %: This would imply only 88% spent; again, inconsistent with aggregated expenses of 35%, 25% and 32%. Common Pitfalls:- Adding 35%, 25% and 80% directly without realizing that 80% applies to the remaining 40%, not the original 100%.- Applying 80% to the total income instead of to the remaining 40%.- Miscomputing the remaining percentage after the first two expenses.- Confusing absolute units (for example, rupees) with percentage units while doing mental calculations. Final Answer:The man is left with 8% of his original income.

Question 12

Gaurav spends 30% of his monthly income on food items. He then spends 40% of the remaining amount on conveyance and clothes, and finally saves 50% of what is left. If his monthly salary is Rs. 18,400, how much money does he save every month?

Accepted Answer

Introduction / Context:This problem is a practical example of successive percentage deductions and savings from a monthly income. Gaurav spends certain percentages of his income on different categories, with each percentage applied to the amount remaining after previous expenses. Finally, he saves a fixed percentage of the remaining money. The question asks for the exact amount he saves per month. This type of question strengthens skills in sequential percentage calculations and basic arithmetic operations. Given Data / Assumptions:- Monthly salary of Gaurav = Rs. 18,400.- He spends 30% of his salary on food.- He then spends 40% of the remaining amount on conveyance and clothes.- He saves 50% of the amount left after these two expenses.- We need to find the amount saved every month. Concept / Approach:The approach is to apply the spending percentages in the correct sequence, always computing each new percentage on the current remaining balance. First we deduct 30% of the salary, then 40% of the remainder, and then take 50% of what is left as savings. We must carefully track the remaining amount after each step to avoid mistakes. This is another example of how percentages operate on changing bases, not always on the original amount. Step-by-Step Solution:Step 1: Monthly salary = Rs. 18,400.Step 2: Spending on food = 30% of 18,400.Step 3: 30% of 18,400 = (30 / 100) * 18,400 = 0.30 * 18,400 = 5,520.Step 4: Remaining amount after food = 18,400 - 5,520 = 12,880.Step 5: Spending on conveyance and clothes = 40% of the remaining 12,880.Step 6: 40% of 12,880 = (40 / 100) * 12,880 = 0.40 * 12,880 = 5,152.Step 7: Remaining amount after conveyance and clothes = 12,880 - 5,152 = 7,728.Step 8: Savings = 50% of the remaining 7,728.Step 9: 50% of 7,728 = (50 / 100) * 7,728 = 0.50 * 7,728 = 3,864.Step 10: Therefore, Gaurav saves Rs. 3,864 every month. Verification / Alternative check:We can verify by computing what percentage of the original salary this saving represents.Savings as a fraction of salary = 3,864 / 18,400.Compute: 3,864 / 18,400 ≈ 0.21, or about 21% of the salary.This is reasonable, since he first spends 30%, then 40% of the remaining 70%, and then saves half of what is left. The sequence of deductions naturally leaves a moderate fraction of the original income as savings. Why Other Options Are Wrong:- 4903: This is higher than half of the amount remaining after all expenses and does not correspond to any correct step.- 5849: This would imply Gaurav is saving almost one-third of his salary, which conflicts with the high expenditure percentages.- 6789: Even larger and clearly incompatible with the sequence of 30% and then 40% expenses. Common Pitfalls:- Applying 40% directly to the original income instead of to the remaining amount after food expenses.- Applying 50% of the original income as savings instead of 50% of the amount left after both expenses.- Arithmetic mistakes in subtraction or percentage multiplication, especially with numbers like 12,880 and 7,728.- Confusing the order of operations, which changes the result significantly. Final Answer:Gaurav saves Rs. 3,864 every month.

Question 13

In an election, only two candidates contested. 20% of the voters on the voter list did not vote, and 120 votes were declared invalid. The winner got 200 more votes than the loser and thereby secured 41% of the total voters on the voter list. What pe…

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Introduction / Context:This is a comprehensive election problem involving percentages, valid and invalid votes, as well as the relationship between total voters, votes cast and the distribution of votes between two candidates. The winner's vote share is given as a percentage of total voters (not of total votes cast), some votes are invalid and some people do not vote at all. We must determine the percentage of total votes cast that were received by the defeated candidate. This requires setting up equations and carefully interpreting each condition. Given Data / Assumptions:- Only two candidates contested the election.- 20% of the voters on the voter list did not vote.- 120 of the votes cast were invalid.- The winner got 200 more votes than the loser.- The winner secured 41% of the total voters on the voter list as votes.- We must find the percentage of total votes cast that went to the defeated candidate. Concept / Approach:Let the total number of voters be V. The winner received 41% of V votes. The loser received 200 fewer votes than the winner. A certain percentage of voters did not vote and some of the votes cast were invalid, so we must distinguish between total voters, total votes cast, valid votes and the distribution of valid votes. Using the given relationships, we can derive equations to find V, compute how many valid votes each candidate received and then compute the loser's vote share as a percentage of total votes cast. Step-by-Step Solution:Step 1: Let total number of voters on the list be V.Step 2: Winner secured 41% of total voters, so winner's votes W = 0.41 * V.Step 3: Let loser's votes be L. It is given that W = L + 200.Step 4: Also, 20% of voters did not vote, so votes cast = 80% of V = 0.80 * V.Step 5: Among votes cast, 120 were invalid, so valid votes = votes cast - invalid votes = 0.80 * V - 120.Step 6: Valid votes are exactly the sum of votes of winner and loser, so:W + L = 0.80 * V - 120.Step 7: Substitute W = 0.41 * V and L = W - 200 into this equation.W + L = 0.41V + (0.41V - 200) = 0.82V - 200.Step 8: Set this equal to valid votes: 0.82V - 200 = 0.80V - 120.Step 9: Rearrange: 0.82V - 0.80V = -120 + 200.Step 10: 0.02V = 80, so V = 80 / 0.02 = 4,000.Step 11: Winner's votes W = 0.41 * 4,000 = 1,640.Step 12: Loser's votes L = W - 200 = 1,640 - 200 = 1,440.Step 13: Votes cast (valid + invalid) = 0.80 * V = 0.80 * 4,000 = 3,200.Step 14: Valid votes = W + L = 1,640 + 1,440 = 3,080. Invalid votes = 3,200 - 3,080 = 120, consistent with given data.Step 15: Required percentage = loser's votes as a percentage of total votes cast.Step 16: Percentage for defeated candidate = (L / votes cast) * 100% = (1,440 / 3,200) * 100%.Step 17: 1,440 / 3,200 = 0.45, so the percentage is 45%. Verification / Alternative check:Check that all conditions are satisfied with V = 4,000.Non-voters = 20% of 4,000 = 800.Votes cast = 4,000 - 800 = 3,200.Invalid votes = 120, so valid votes = 3,200 - 120 = 3,080.Winner's votes = 1,640, loser's votes = 1,440, difference = 200.Winner's votes as percentage of total voters = 1,640 / 4,000 = 0.41 or 41%.All conditions check out, confirming V = 4,000 and the calculated percentages. Why Other Options Are Wrong:- 47.5%: This would correspond to 0.475 * 3,200 = 1,520 votes, which would change the difference and the winner's percentage of total voters.- 41%: This is the winner's share of total voters, not the defeated candidate's share of total votes cast.- 38%: Would give 1,216 votes to the loser, which is inconsistent with the 200-vote difference and other constraints. Common Pitfalls:- Confusing percentages of total voters with percentages of votes cast or valid votes.- Forgetting to subtract invalid votes when forming the equation for valid votes.- Assuming the 41% is of total votes cast instead of total voters, leading to incorrect equations.- Arithmetic errors when solving 0.82V - 200 = 0.80V - 120. Final Answer:The defeated candidate received 45% of the total votes cast.

Question 14

A total of 405 sweets were distributed equally among some children such that the number of sweets each child received was equal to 20% of the total number of children. How many sweets did each child receive?

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Introduction / Context:This problem combines equal distribution and percentages in a slightly indirect way. The total number of sweets and the condition relating sweets per child to the total number of children are given. Specifically, each child receives sweets equal to 20% of the number of children. We are asked to find how many sweets each child gets. This question requires forming an equation where both the number of children and sweets per child are unknown but linked through the given condition and the total number of sweets. Given Data / Assumptions:- Total sweets = 405.- Let the number of children be n.- Sweets are distributed equally among the n children.- Each child receives a number of sweets equal to 20% of the total number of children.- We must find the number of sweets each child receives. Concept / Approach:If there are n children, and each child receives k sweets, then the total sweets are n * k. The condition states that each child receives 20% of n sweets, that is 0.20 * n sweets. Therefore, k = 0.20 * n. Substituting this into n * k = 405, we get an equation involving n alone: n * 0.20n = 405. This simplifies to a quadratic equation in n, which we can solve to find n, and then compute k. Because the numbers are well chosen, n becomes a perfect square root and computation is straightforward. Step-by-Step Solution:Step 1: Let the number of children be n.Step 2: Let the number of sweets each child receives be k.Step 3: Total sweets = n * k = 405.Step 4: According to the problem, the sweets each child receives are equal to 20% of the number of children.Step 5: So k = 20% of n = (20 / 100) * n = 0.20n.Step 6: Substitute k into the total sweets equation: n * (0.20n) = 405.Step 7: This gives 0.20n^2 = 405.Step 8: Multiply both sides by 5 to eliminate the decimal: n^2 = 405 * 5.Step 9: 405 * 5 = 2,025.Step 10: So n^2 = 2,025.Step 11: Taking the positive square root (since number of children is positive), n = sqrt(2,025) = 45.Step 12: Now find k = 0.20 * n = 0.20 * 45 = 9.Therefore, each child receives 9 sweets. Verification / Alternative check:Check by recomputing the total sweets using n = 45 and k = 9.Total sweets = n * k = 45 * 9 = 405, which matches the given total.Also, k as 9 equals 20% of n = 20% of 45 = (20 / 100) * 45 = 9.Both conditions are satisfied, confirming that the solution is correct. Why Other Options Are Wrong:- 10: If each child got 10 sweets, then 405 / 10 = 40.5 children, which is impossible and does not give an integer number of children.- 11: 405 / 11 is not an integer, and 11 would not be equal to 20% of any whole number of children in this context.- 12: 405 / 12 is not 45, and 12 also does not correspond to 20% of a suitable integer number of children that yields exactly 405 sweets. Common Pitfalls:- Forgetting that both the number of children and sweets per child must be whole numbers.- Misinterpreting "20% of the total number of children" as 20% of sweets instead.- Errors in solving n^2 = 2,025, such as taking an incorrect square root.- Confusing multiplication steps when substituting k = 0.20n into the total equation. Final Answer:Each child received 9 sweets.

Question 15

If 75% of a certain number is added to 75, the result is equal to the number itself. What is the value of this number?

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Introduction / Context:This is a simple algebraic percentage problem where a number is related to its own percentage plus a constant. Specifically, 75% of the number is added to 75 and the result equals the original number. We need to find that number. Problems of this type are common in basic algebra and percentage topics and help students translate verbal statements into equations involving percentages and solve them systematically. Given Data / Assumptions:- Let the required number be x.- 75% of x is added to 75.- The result equals x itself.- We are asked to find the numerical value of x. Concept / Approach:The key concept is expressing the verbal description as an algebraic equation. "75% of x" can be written as (75 / 100) * x or 0.75x. The condition "75% of x added to 75 equals x" becomes 0.75x + 75 = x. Solving this equation for x involves basic algebraic manipulation: moving terms involving x to one side and constants to the other, then dividing to isolate x. Step-by-Step Solution:Step 1: Let the number be x.Step 2: 75% of x = (75 / 100) * x = 0.75x.Step 3: According to the problem, 75% of x plus 75 equals x.Step 4: Write the equation: 0.75x + 75 = x.Step 5: Move 0.75x to the right-hand side to collect x terms together.75 = x - 0.75x.Step 6: x - 0.75x = 0.25x.Step 7: Therefore, 75 = 0.25x.Step 8: Solve for x by dividing both sides by 0.25.x = 75 / 0.25.Step 9: 0.25 = 1/4, so dividing by 0.25 is the same as multiplying by 4.x = 75 * 4 = 300.Therefore, the number is 300. Verification / Alternative check:Check the condition using x = 300.75% of 300 = (75 / 100) * 300 = 0.75 * 300 = 225.Add 75 to this: 225 + 75 = 300.This equals the original number x, confirming that x = 300 satisfies the condition given in the problem. Why Other Options Are Wrong:- 100: 75% of 100 = 75; 75 + 75 = 150, which is not equal to 100.- 200: 75% of 200 = 150; 150 + 75 = 225, not 200.- 400: 75% of 400 = 300; 300 + 75 = 375, not 400. Common Pitfalls:- Misinterpreting "75% of the number is added to 75" as "75% of (number plus 75)" which would give a different equation.- Using 75x instead of 0.75x or (75 / 100) * x.- Making algebraic errors when moving 0.75x to the other side of the equation.- Treating 0.25 as 1/5 instead of the correct 1/4 when solving for x. Final Answer:The required number is 300.

Question 16

If the height of person A is 40% less than the height of person B, then by what percentage is B's height greater than A's height?

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Introduction / Context:This problem explores the common concept that percentage increase and percentage decrease between two quantities are not symmetric. If A is 40% less than B, this does not mean that B is 40% more than A. Instead, we must compute B's height relative to A's height and convert this ratio into a percentage increase. Understanding this asymmetry between percentage increase and decrease is very important in quantitative aptitude and real-life applications involving discounts, growth and comparisons. Given Data / Assumptions:- A's height is 40% less than B's height.- Let B's height be some convenient reference value.- We need to express how much greater B's height is compared to A's height, in percentage terms.- The answer must be the percentage by which B exceeds A. Concept / Approach:If one quantity is k% less than another, say A is 40% less than B, then A = (1 - 0.40) * B = 0.60B. To find how much B is greater than A in percentage terms, we consider the ratio B / A and compute the percentage increase relative to A. This is given by (B - A) / A * 100%. Substituting the values of A in terms of B or vice versa solves the problem. The key is to choose a convenient number for B to simplify arithmetic, such as 100 units. Step-by-Step Solution:Step 1: Assume B's height is 100 units (for convenience).Step 2: A's height is 40% less than B's.Step 3: 40% of 100 = 40, so A's height = 100 - 40 = 60 units.Step 4: Now we need to find by what percentage B is taller than A.Step 5: B's height = 100 units, A's height = 60 units.Step 6: Difference in height = B - A = 100 - 60 = 40 units.Step 7: Percentage by which B is greater than A = (Difference / A) * 100%.Step 8: Substitute values: (40 / 60) * 100%.Step 9: Simplify 40 / 60 = 2 / 3 ≈ 0.6666.Step 10: Multiply by 100 to get percentage: 0.6666 * 100% ≈ 66.66%.Therefore, B's height is approximately 66.66% greater than A's height. Verification / Alternative check:We can use algebra instead of specific numbers.Let B's height = B units.A's height = 60% of B = 0.60B.Difference = B - 0.60B = 0.40B.Percentage by which B is greater than A = (0.40B / 0.60B) * 100%.Simplify: 0.40B / 0.60B = 4 / 6 = 2 / 3.So the percentage is (2 / 3) * 100% ≈ 66.66%.This matches the value obtained using the assumed heights 100 and 60. Why Other Options Are Wrong:- 76.66%: This would correspond to a difference larger than 2/3 of A's height, inconsistent with the 40% decrease relationship.- 96.66%: Almost equal to doubling A's height, which does not match the given reduction from B to A.- 86.66%: Again too large; using this would imply A's height is much smaller relative to B than the 40% less statement indicates. Common Pitfalls:- Assuming that if A is 40% less than B, then B is 40% more than A, which is incorrect.- Using A as 100 and then trying to back-calculate B incorrectly.- Confusing percentage differences with absolute differences in units and mixing up denominators.- Rounding errors that lead to answers like 67% instead of the more precise 66.66% given in the options. Final Answer:B's height is 66.66% greater than A's height.

Question 17

A salesman receives a commission of 9% on his total sales. If his sales exceed Rs. 10,000, he also earns an additional bonus commission of 3% on the portion of sales above Rs. 10,000. If his total commission from both parts together is Rs. 1,380, ho…

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Introduction: This percentage word problem tests understanding of commission calculations with a base rate and an additional bonus rate on sales beyond a threshold. Such questions are common in aptitude exams to check how well a candidate converts a verbal description of a commission structure into algebraic equations and then solves for the unknown quantity, which in this case is the amount of bonus received. Given Data / Assumptions: Total sales value is unknown and is represented by S rupees. Base commission rate is 9% on the entire sales S. If sales exceed Rs. 10,000, an extra bonus commission of 3% is paid on the amount above Rs. 10,000. Total commission earned from base commission plus bonus is Rs. 1,380. We assume the salesman definitely exceeded Rs. 10,000 in sales because a bonus is mentioned as part of the total commission. Concept / Approach: The key idea is to express the total commission as the sum of two components: the regular commission on total sales and the bonus commission on sales beyond Rs. 10,000. Once we write this as an equation in S, we can solve for S and then compute the bonus amount, which is 3% of the excess sales. This is a standard linear equation in one variable based on percentage calculations. Step-by-Step Solution: Let total sales be S rupees. Regular commission = 9% of S = 0.09 * S. Bonus commission is applicable on excess sales over Rs. 10,000, so excess = S - 10000. Bonus commission = 3% of (S - 10000) = 0.03 * (S - 10000). Total commission = regular commission + bonus commission. So 0.09 * S + 0.03 * (S - 10000) = 1380. Simplify: 0.09 * S + 0.03 * S - 0.03 * 10000 = 1380. This gives 0.12 * S - 300 = 1380. Add 300 to both sides: 0.12 * S = 1680. So S = 1680 / 0.12 = 14000 rupees. Excess over Rs. 10,000 = 14000 - 10000 = 4000 rupees. Bonus commission = 3% of 4000 = 0.03 * 4000 = Rs. 120. Verification / Alternative check: We can verify by computing both parts of the commission separately. Regular commission at 9% of Rs. 14,000 is 0.09 * 14000 = Rs. 1,260. Bonus commission is Rs. 120, so total commission is 1260 + 120 = Rs. 1,380, which matches the given total commission in the question. This confirms that the sales figure and bonus amount are correct. Why Other Options Are Wrong: Rs. 180, Rs. 240, Rs. 300 and Rs. 360 correspond to larger excess sales values or incorrect percentage applications. If any of these were correct, the recomputed total commission would not match Rs. 1,380. These values typically come from misreading the bonus as 3% of total sales or from arithmetic mistakes in solving the equation. Common Pitfalls: A very common mistake is to apply the 3% bonus on the entire sales amount instead of only the portion above Rs. 10,000. Another error is to forget to add the base commission and bonus commission before equating to the total commission. Sometimes students also mis-handle decimal percentages like 0.09 and 0.03 and end up with a wrong equation for S. Careful reading of the words “on the excess of sales over Rs. 10,000” is crucial. Final Answer: The bonus received by the salesman on the excess sales is Rs. 120.

Question 18

What percentage of 7.2 kilograms is equal to 18 grams?

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Introduction: This question checks your understanding of basic percentage calculation and unit conversion between kilograms and grams. Many quantitative aptitude problems involve converting units properly before applying percentage formulas, so this is an important foundation skill. Given Data / Assumptions: Total quantity = 7.2 kilograms. Part of this quantity = 18 grams. We need to express 18 grams as a percentage of 7.2 kilograms. We use the standard relationship 1 kilogram = 1000 grams. Concept / Approach: Percent is calculated as (part / whole) * 100. However, the part and the whole must be in the same unit. Here the part is given in grams and the whole in kilograms. Therefore we first convert 7.2 kilograms into grams, and then use the percentage formula. This ensures there is no inconsistency in units that might lead to wrong answers. Step-by-Step Solution: Convert 7.2 kilograms to grams: 7.2 * 1000 = 7200 grams. Now treat 18 grams as the part and 7200 grams as the whole. Percentage = (part / whole) * 100. So percentage = (18 / 7200) * 100. Compute 18 / 7200 = 0.0025. Now multiply by 100: 0.0025 * 100 = 0.25. Therefore, 18 grams is 0.25% of 7.2 kilograms. Verification / Alternative check: We can check the answer by reversing the calculation. Take 0.25% of 7.2 kilograms. First convert 0.25% to a fraction: 0.25% = 0.25 / 100 = 0.0025. Multiply this by 7.2 kilograms: 7.2 * 0.0025 = 0.018 kilograms. Convert 0.018 kilograms to grams: 0.018 * 1000 = 18 grams. This matches the given part, confirming that the percentage is correct. Why Other Options Are Wrong: 0.5%, 0.75%, 1%, and 2.5% all represent larger fractions of the whole. If you compute these percentages of 7.2 kilograms, you would get values significantly larger than 18 grams. For example, 1% of 7.2 kilograms is 72 grams, which is far greater than 18 grams. These options likely arise if a candidate forgets the kilogram to gram conversion or misplaces the decimal point when multiplying by 100. Common Pitfalls: A frequent mistake is to divide 7.2 by 18 instead of 18 by 7.2, or to forget to convert kilograms into grams. Another common error is mishandling decimal places when multiplying or dividing by powers of 10. Remember that unit consistency and careful handling of decimal values are critical in percentage problems. Final Answer: 18 grams is 0.25% of 7.2 kilograms.

Question 19

The salary of A is 40% of the salary of B, and the salary of B is 25% of the salary of C. What percentage of the salary of C is the salary of A?

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Introduction: This problem tests chained percentage relationships between three quantities. Such questions are common in aptitude exams where salaries, prices, or marks of different people are related through percentages. The aim is to express everything in terms of a single base quantity and then derive the final percentage required. Given Data / Assumptions: Salary of A is 40% of salary of B. Salary of B is 25% of salary of C. We need to find salary of A as a percentage of salary of C. All salaries are positive real numbers and there is no additional condition given, so we model them with variables. Concept / Approach: When there is a chain of percentage relations, it is often easiest to express all amounts in terms of one reference, here salary of C. We use the fact that percentage can be converted into decimal multipliers. For example, 40% becomes 0.40 and 25% becomes 0.25. Then we multiply the corresponding factors to connect A directly to C. Step-by-Step Solution: Let the salary of C be C. Given that salary of B is 25% of salary of C. So salary of B = 25% of C = 0.25 * C. Now salary of A is 40% of salary of B. So salary of A = 40% of B = 0.40 * B. Substitute B = 0.25 * C into this expression. Salary of A = 0.40 * (0.25 * C) = 0.10 * C. Therefore salary of A is 0.10 times salary of C. Convert 0.10 to percentage by multiplying by 100: 0.10 * 100 = 10%. Verification / Alternative check: We can use assumed numerical values to verify. Suppose salary of C is Rs. 100. Then salary of B is 25% of 100, which is Rs. 25. Salary of A is 40% of 25, which is Rs. 10. Now A as a percentage of C is 10 out of 100, that is 10%. This concrete example confirms the general algebraic result. Why Other Options Are Wrong: 20%, 25%, 30%, and 40% all come from incorrect combinations of percentages. Someone might mistakenly add 40% and 25% or incorrectly apply percentages sequentially without multiplying the factors. The correct operation is multiplication of the percentage factors, not arithmetic addition or subtraction of those percentages. Common Pitfalls: Students sometimes treat 40% of 25% as 65% or 15% by adding or subtracting, which is incorrect. The correct method is to convert each percentage to decimal and multiply. Another pitfall is forgetting which quantity is a percentage of which, for example, confusing 25% of C with C being 25% of B. Reading the statements carefully and drawing a simple chain diagram can prevent these errors. Final Answer: Salary of A is 10% of the salary of C.

Question 20

When the ratio 5 : 4 is written as a fraction and then expressed as a percentage, what percent does it represent?

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Introduction: This question checks your ability to convert a ratio into a fraction and then into a percentage. Ratios, fractions, and percentages are closely related, and quick movement between these three forms is useful in many aptitude topics including profit and loss, mixtures, and data interpretation. Given Data / Assumptions: Ratio given is 5 : 4. We interpret this ratio as the fraction 5 divided by 4. We must express this fraction as a percentage. No other contextual constraints are given, so it is a direct number conversion problem. Concept / Approach: A ratio a : b can be interpreted as the fraction a / b, provided the question specifies or implies this direction. To convert a fraction to a percentage, we multiply by 100. So here we compute (5 / 4) * 100. This is a simple arithmetic step once the ratio is seen as a fraction. Step-by-Step Solution: Start from the ratio 5 : 4. Interpret it as the fraction 5 / 4. Compute 5 / 4. This equals 1.25. To convert a fraction or decimal to a percentage, multiply by 100. Percentage = 1.25 * 100. 1.25 * 100 = 125. Therefore, 5 : 4 expressed as a percentage is 125%. Verification / Alternative check: We can also think of 5 as being 25% more than 4. Since 25% of 4 is 1, adding this to 4 gives 5. So 5 is 125% of 4. This reasoning matches the numerical computation and provides an intuitive check that 5/4 corresponds to 125%. Why Other Options Are Wrong: 40% and 80% are less than 100% and would correspond to fractions smaller than 1, while 5/4 is greater than 1. 100% would represent equality (5 equals 4), which is not true. 150% would be 1.5 times 4, that is 6, not 5. Therefore only 125% correctly represents the ratio 5 : 4. Common Pitfalls: A common mistake is to interpret the ratio 5 : 4 as 4/5 instead of 5/4. Another error is to forget the multiplication by 100 when converting a decimal to a percentage. Some candidates also confuse percent increase with the underlying percent of the original quantity. Keeping the direction of the ratio and the conversion steps clear avoids these issues. Final Answer: The ratio 5 : 4 expressed as a percentage is 125%.

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