Question 1

Person A earns 50% of the salary of person B, and person B earns 80% of the salary of person C. If together A, B and C earn a total of Rs. 22,000 in a month, what is the monthly earning of A?

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Introduction / Context:This question connects the monthly salaries of three people through percentage relations. It tests your ability to write one unknown in terms of another and then use the given total to find individual earnings.Given Data / Assumptions:• Let C salary per month be C.• B earns 80% of C salary.• A earns 50% of B salary.• Combined monthly earnings of A, B and C are Rs. 22,000.• We must find the monthly salary of A.Concept / Approach:First express B in terms of C using the 80% relation. Then express A in terms of C by applying the 50% relation. Add all three salaries to match the total given, and then solve for C. Finally, compute A salary using the relation already derived.Step-by-Step Solution:Step 1: B earns 80% of C, so B = 0.80C.Step 2: A earns 50% of B, so A = 0.50B = 0.50 * 0.80C = 0.40C.Step 3: Total earnings = A + B + C.Step 4: Substitute the expressions: total = 0.40C + 0.80C + C.Step 5: Combine like terms: 0.40C + 0.80C + 1.00C = 2.20C.Step 6: Given total = Rs. 22,000, we have 2.20C = 22000.Step 7: So C = 22000 / 2.20 = 10000.Step 8: A salary = 0.40C = 0.40 * 10000 = Rs. 4,000.Verification / Alternative check:Check individual salaries. C = 10000, B is 80% of 10000 which is 8000, and A is 50% of 8000 which is 4000. Sum = 10000 + 8000 + 4000 = 22000, matching the given total.Why Other Options Are Wrong:Values 4200, 4400 and 4600 do not produce a total of 22000 when used for A in the derived relations. They represent miscalculations of one or more percentages.Common Pitfalls:Students may incorrectly add percentages or apply them to the wrong salary. Another frequent error is to treat 50% and 80% as reductions from the same base instead of sequential relations.Final Answer:The monthly earning of A is Rs. 4,000.

Question 2

The average of a set of whole numbers is 27.2. When 20% of the elements are removed from this set, the average of the remaining numbers becomes 34. Which of the following can be the number of elements in the new set?

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Introduction / Context:This question is about how the average of a set of numbers changes when some elements are removed. It checks if you can relate total sum, average and number of elements and understand how removing low valued elements can increase the average.Given Data / Assumptions:• Original average of a set of whole numbers is 27.2.• Let the original number of elements be N.• Twenty percent of the elements are removed from the set.• The new average after removal is 34.• We must choose the possible number of elements in the new set from the options.Concept / Approach:Total sum of numbers equals average multiplied by the number of elements. Removing elements changes both the count and often the total sum. If removing some elements increases the average, the removed elements must have average less than the original average. Here, the new number of elements is 80% of N, that is 0.8N. We use the fact that the new total sum equals the new average times the new count. Given options represent the new count values.Step-by-Step Solution:Step 1: Original total sum S = 27.2 * N.Step 2: New number of elements = 80% of N = 0.8N.Step 3: New total sum S new = 34 * 0.8N = 27.2N.Step 4: Therefore S new = S, meaning the removed elements together contribute zero to the sum.Step 5: This implies that the removed elements must all be zero, since the numbers are whole numbers.Step 6: Thus any N where 20% of N is an integer and S is consistent is possible.Step 7: New count = 0.8N must match one of the options: 27, 35, 52 or 63.Step 8: For option 52 as new count, original N = 52 / 0.8 = 65, which is an integer.Step 9: For the other options, the corresponding original N is not an integer.Verification / Alternative check:If original N is 65, original sum S = 27.2 * 65 = 1768. New count = 0.8 * 65 = 52. New average with the same sum is 1768 / 52 = 34. This matches the given data, so 52 is a valid new count.Why Other Options Are Wrong:With new counts 27, 35 or 63, the implied original counts are 27/0.8, 35/0.8 and 63/0.8, which are not integers. That contradicts the idea that we started from a whole number of elements.Common Pitfalls:Candidates sometimes try to guess specific values instead of using average and total sum relationships. Others ignore the requirement that the number of elements must be a whole number both before and after removal.Final Answer:The number of elements in the new set can be 52.

Question 3

Each edge of a cube is increased by 20% of its original length. By what percentage does the total surface area of the cube increase as a result of this change?

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Introduction / Context:This is a geometry and percentage question involving a cube. It tests your ability to understand how a percentage change in the side length of a cube affects its surface area, which depends on the square of the side length.Given Data / Assumptions:• Original cube has side length s.• Each edge is increased by 20%.• New side length is therefore 20% more than s.• We must find the percentage increase in total surface area.Concept / Approach:The total surface area of a cube is 6 * s^2. When the side length changes, the surface area changes in proportion to the square of the scale factor applied to the side. If the side becomes k times the original, the surface area becomes k^2 times the original. Therefore, we compute the side length multiplier and then square it.Step-by-Step Solution:Step 1: Side length is increased by 20%, which is 20/100 = 0.20.Step 2: New side length = s * (1 + 0.20) = 1.20s.Step 3: Original surface area A original = 6s^2.Step 4: New surface area A new = 6 * (1.20s)^2.Step 5: Compute (1.20s)^2 = 1.44s^2.Step 6: Therefore A new = 6 * 1.44s^2 = 1.44 * 6s^2.Step 7: So the new surface area is 1.44 times the original surface area.Step 8: Percentage increase = (1.44 − 1.00) * 100% = 0.44 * 100% = 44%.Verification / Alternative check:Take a simple numerical example. Let s = 10 units. Original surface area = 6 * 10^2 = 600. New side = 12, new surface area = 6 * 12^2 = 6 * 144 = 864. Increase = 864 − 600 = 264. Percentage increase = 264 / 600 * 100 = 44%, which confirms the result.Why Other Options Are Wrong:Forty percent is the increase in linear dimension misapplied to area. One hundred forty four percent would mean an impossible more than doubling of the area calculation for this case. Seventy two point eight percent does not correspond to the square of 1.20.Common Pitfalls:A common mistake is to assume that the percentage increase in surface area is the same as the percentage increase in side length. However, surface area depends on the square of the side, so the effect is larger.Final Answer:The surface area of the cube increases by 44%.

Question 4

Sixty percent of two sevenths of three fourths of a certain number is 2664. What is the value of that number?

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Introduction / Context:This problem combines percentages and fractions applied successively to an unknown number. It tests your ability to convert verbal descriptions into a single algebraic expression and then solve for the original number.Given Data / Assumptions:• Let the unknown number be N.• We consider three fourths of N.• Then we take two sevenths of that result.• Then we take 60% of this value.• The final quantity obtained is 2664.Concept / Approach:Each phrase such as three fourths or sixty percent can be written as a fraction or decimal. We multiply these factors step by step to get one overall factor times N. Setting this product equal to 2664 allows us to solve for N by division.Step-by-Step Solution:Step 1: Three fourths of N = (3/4) * N.Step 2: Two sevenths of that = (2/7) * (3/4)N = (6/28)N = (3/14)N.Step 3: Sixty percent is 60/100 = 3/5.Step 4: Sixty percent of (3/14)N = (3/5) * (3/14)N = (9/70)N.Step 5: According to the question, (9/70)N = 2664.Step 6: Solve for N: N = 2664 * (70/9).Step 7: First compute 2664 / 9 = 296.Step 8: So N = 296 * 70 = 20720.Verification / Alternative check:Check by forward calculation. Three fourths of 20720 is 15540. Two sevenths of 15540 is 4440. Sixty percent of 4440 is 0.60 * 4440 = 2664, which matches the given value. This verifies the solution.Why Other Options Are Wrong:Values 21352, 25421 and 24150 do not reproduce 2664 when the same operations are applied. They result from incorrect simplification of fractions or arithmetic errors when multiplying or dividing.Common Pitfalls:Many students perform the steps in the wrong order or forget that 60% must be applied last to the already reduced value. Confusing 60% with 0.06 is another common mistake that would lead to a result ten times smaller.Final Answer:The required number is 20,720.

Question 5

Which of the following numerical values is equal to 5% of 1,500?

Accepted Answer

Introduction / Context:This is a direct percentage calculation question. It checks your ability to find a simple percentage of a number, a very common operation in everyday arithmetic and aptitude tests.Given Data / Assumptions:• We need to compute 5% of 1500.• Four answer choices are given as whole numbers.• We must identify which value equals 5% of 1500.Concept / Approach:To find x percent of a quantity, we multiply the quantity by x/100. For 5%, the multiplier is 5/100 = 0.05. Multiplying 1500 by 0.05 will give us the desired value. A mental math approach using 10% can also be used.Step-by-Step Solution:Step 1: Write 5% as a fraction: 5% = 5/100.Step 2: Compute 5/100 of 1500: (5/100) * 1500.Step 3: Simplify: 1500 / 100 = 15.Step 4: Multiply: 15 * 5 = 75.Step 5: Thus, 5% of 1500 is 75.Verification / Alternative check:A quick mental method: 10% of 1500 is 150. Five percent is half of 10%, so 5% is 150 / 2 = 75. This matches our previous calculation.Why Other Options Are Wrong:Values 35, 55 and 45 are all less than 75 and do not equal 5% of 1500. They may result from guessing or from incorrectly subtracting instead of multiplying.Common Pitfalls:Sometimes students confuse 5% with 0.5% or 50% or attempt to divide by 5 instead of multiplying by 5/100. Remember that percent means per hundred and always convert to a fraction or decimal carefully.Final Answer:The value equal to 5% of 1,500 is 75.

Question 6

Twenty percent of Karthik monthly salary is equal to thirty two percent of Nikitha monthly salary. Vipin monthly salary is four fifths of Nikitha monthly salary. If Vipin annual salary is Rs. 3.84 lakhs, what is Karthik monthly salary?

Accepted Answer

Introduction / Context:This problem connects the salaries of three people using percentage relationships. It tests your ability to express different salaries in terms of one variable, convert an annual salary to a monthly salary and then backtrack to the unknown.Given Data / Assumptions:• Let Karthik monthly salary be K.• Let Nikitha monthly salary be N.• Let Vipin monthly salary be V.• Twenty percent of K equals thirty two percent of N.• Vipin salary V = four fifths of Nikitha salary N.• Vipin annual salary is Rs. 3.84 lakhs, that is Rs. 3,84,000.Concept / Approach:We write the percentage relationships as equations. Using Vipin annual income, we deduce his monthly salary, from which we get Nikitha salary using the four fifths relation. Then we use the equality of 20% of K and 32% of N to find K.Step-by-Step Solution:Step 1: Convert Vipin annual salary to monthly: 3,84,000 / 12 = 32,000. So V = 32,000.Step 2: V is four fifths of N, so V = (4/5)N.Step 3: Hence N = V * (5/4) = 32,000 * (5/4) = 32,000 * 1.25 = 40,000.Step 4: Twenty percent of K equals thirty two percent of N.Step 5: Write this as 0.20K = 0.32N.Step 6: Substitute N = 40,000: 0.20K = 0.32 * 40,000 = 12,800.Step 7: So K = 12,800 / 0.20 = 64,000.Verification / Alternative check:Check the internal consistency. Twenty percent of 64,000 is 12,800. Thirty two percent of 40,000 is also 12,800, so the first relation holds. Four fifths of 40,000 is 32,000, matching Vipin monthly salary. Annual pay for Vipin is 32,000 * 12 = 3,84,000, as given.Why Other Options Are Wrong:Values 32,000, 40,000 and 52,000 fail to satisfy the equation 0.20K = 0.32N with N fixed at 40,000. They arise from misinterpreting which salary is larger or mixing up fractions.Common Pitfalls:Some students apply 20% and 32% to the wrong person or forget to convert Vipin annual salary correctly. Another frequent issue is solving the equation as 0.20K = 32N instead of 0.32N, which drastically changes the result.Final Answer:Karthik monthly salary is Rs. 64,000.

Question 7

If K earns 12% less than L, then by what percentage is L earning more than K?

Accepted Answer

Introduction / Context:This question highlights the difference between saying A is a certain percent less than B and stating by what percent B is more than A. The base value changes, so the percentages are not symmetric and this often confuses students.Given Data / Assumptions:• K earns 12% less than L.• We must express how much percent L earns more than K.• Earnings are positive monetary amounts.Concept / Approach:Assume a convenient value for L, typically 100 units. Then calculate K as 12% less than this. Once K is known, find the difference between L and K and express that difference as a percentage of K, because we are now comparing L relative to K.Step-by-Step Solution:Step 1: Assume L income = 100 units.Step 2: K earns 12% less than L, so K income = 100 − 12 = 88 units.Step 3: Difference in income = L − K = 100 − 88 = 12 units.Step 4: Required percentage = (Difference / K) * 100.Step 5: So percentage = (12 / 88) * 100.Step 6: Compute 12 / 88 = 3 / 22 approximately equal to 0.13636.Step 7: Multiply by 100 to obtain about 13.636%.Step 8: Rounded to two decimal places this is 13.63%.Verification / Alternative check:We can check in reverse. If L is 13.63% more than K, then L = K * (1 + 0.1363) ≈ 88 * 1.1363 ≈ 100. This is consistent with our assumption for L.Why Other Options Are Wrong:The options 13.96%, 13.56% and 14.01% are close but do not match the precise calculation of 12/88 expressed as a percentage. They result from rounding at earlier stages or from using 12% of L as the base instead of K when computing the reverse relation.Common Pitfalls:A major misconception is to think that if one person earns 12% less, the other earns 12% more, which is incorrect because the bases differ. Always be careful about which value you are using as the denominator for percentage calculations.Final Answer:L earns about 13.63% more than K.

Question 8

Helpers are needed to prepare for a fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and the requirement is to prepare 20 large cakes and 700 small cakes. How many helpers are required …

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Introduction / Context:This is a work and time type problem framed in terms of cakes made by helpers. It checks your ability to convert different items into a common unit and then determine how many workers are needed within a fixed time duration.Given Data / Assumptions:• Each helper can make 2 large cakes per hour, or 35 small cakes per hour.• Kitchen is available for 3 hours.• Required output: 20 large cakes and 700 small cakes.• All helpers work at the same rate and can divide time between large and small cakes as needed.Concept / Approach:We convert everything to a single unit of work. Since the helper rates are given as 2 large cakes or 35 small cakes per hour, we can express large cakes in terms of equivalent small cakes. Then the total required work is expressed in small cake equivalents and compared against the total capacity of h helpers over 3 hours.Step-by-Step Solution:Step 1: One hour of work by one helper equals 35 small cakes.Step 2: Since 2 large cakes are made in the same hour, 2 large cakes correspond to 35 small cakes.Step 3: Therefore 1 large cake corresponds to 35/2 small cake equivalents.Step 4: Required large cakes = 20, so small cake equivalents for these = 20 * (35/2) = 350.Step 5: Required small cakes = 700, so total small cake equivalents = 350 + 700 = 1050.Step 6: One helper working for 1 hour can do 35 equivalents, so in 3 hours one helper can do 3 * 35 = 105 equivalents.Step 7: Let the number of helpers be h. Total capacity in 3 hours = 105h equivalents.Step 8: We require 105h = 1050.Step 9: Therefore h = 1050 / 105 = 10.Verification / Alternative check:If there are 10 helpers, each can contribute 3 hours, giving 30 helper hours. One helper hour equals 35 small cake equivalents, so total work capacity is 30 * 35 = 1050 equivalents, exactly matching the required work.Why Other Options Are Wrong:If h = 15, 20 or 25, the total production capacity significantly exceeds the required 1050 equivalents. The question is asking for the minimum number of helpers required, so 10 is the unique correct value.Common Pitfalls:Some students try to assign fixed helpers to large and small cakes separately without converting to a common unit, making the problem unnecessarily complex. Others mistakenly multiply rates without including the total time factor.Final Answer:The fete requires 10 helpers to complete the work in 3 hours.

Question 9

A dress in a shop has a marked price of D dollars. During a discount sale its price is first reduced by 15%, and then staff members receive a further 10% reduction on this already discounted price. If a staff member buys the dress, what amount does …

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Introduction / Context:This question deals with successive percentage discounts on a marked price. It tests your understanding that successive discounts multiply as factors rather than simply adding their percentages.Given Data / Assumptions:• Marked price of the dress is D dollars.• First discount is 15% for the sale.• After that, staff members get a further 10% discount on the already reduced price.• We must find the final amount paid by a staff member in terms of D.Concept / Approach:A discount of x% leaves (1 − x/100) of the price. Successive discounts are handled by multiplying these remaining fractions. We do not add discount percentages directly because each discount is applied to a different base amount.Step-by-Step Solution:Step 1: After a 15% discount, the customer pays 85% of the price.Step 2: As a decimal factor, 85% = 0.85.Step 3: So sale price after first discount = 0.85D.Step 4: Staff members receive a further discount of 10% on this sale price.Step 5: After a 10% discount, the staff member pays 90% of the sale price.Step 6: Ninety percent is 0.90 as a decimal.Step 7: Final price paid = 0.90 * 0.85D.Step 8: Multiply the factors: 0.90 * 0.85 = 0.765.Step 9: So final amount paid = 0.765D.Verification / Alternative check:Assume D = 100 for a quick check. After 15% discount, price is 85. After another 10% discount, price is 85 * 0.90 = 76.5. As a fraction of the original 100, this is 0.765, so 0.765D is correct in general.Why Other Options Are Wrong:Value 0.75D corresponds to a total 25% discount, which incorrectly adds the percentages 15 and 10. Values 0.76D and 0.76D rounded forms do not reflect the correct product of the factors 0.85 and 0.90.Common Pitfalls:The main mistake is to add discounts directly, assuming that 15% plus 10% gives a 25% overall discount. In reality, the second discount acts on an already reduced price, so the effective discount is slightly less than 25%.Final Answer:The staff member pays 0.765D for the dress.

Question 10

In Veeru Bhai Private Limited, 60% of the employees are men and 48% of the employees are engineers. Of these engineers, 66.6% are men. What percentage of the women employees in the company are not engineers?

Accepted Answer

Introduction / Context:This percentage problem combines two categorical breakdowns in a company workforce: gender and profession. It tests your ability to work with overlapping percentages and to focus on a specific subgroup, here women who are not engineers.Given Data / Assumptions:• In the company, 60% of employees are men and 40% are women.• Forty eight percent of all employees are engineers.• Of these engineers, 66.6% (about two thirds) are men.• We must find the percentage of women who are not engineers relative to all women employees.Concept / Approach:It is convenient to assume a total number of employees, for example 100, to convert percentages into actual counts. Then we can determine how many are male engineers, female engineers and women who are not engineers. Finally we compute the required percentage among women.Step-by-Step Solution:Step 1: Assume total employees = 100.Step 2: Men = 60 employees and women = 40 employees.Step 3: Engineers = 48 employees, since 48% are engineers.Step 4: Of these 48 engineers, 66.6% are men. Approximating 66.6% as two thirds, male engineers = (2/3) * 48 = 32.Step 5: Female engineers = total engineers − male engineers = 48 − 32 = 16.Step 6: Total women employees are 40.Step 7: Women who are not engineers = total women − female engineers = 40 − 16 = 24.Step 8: Required percentage among women = (24 / 40) * 100 = 60%.Verification / Alternative check:We can double check the full distribution. Men non engineers = 60 − 32 = 28. Total non engineers = 28 + 24 = 52 which is consistent with 100 − 48 engineers. Thus all percentages align correctly, supporting the result.Why Other Options Are Wrong:Values 33.33%, 52% and 46.66% arise from using the wrong base when computing percentages, such as total employees instead of only women, or treating 66.6% approximately but not adjusting engineer numbers correctly.Common Pitfalls:The main difficulty is keeping track of which percentage is of which total. Many candidates mistakenly calculate the percentage of women non engineers out of all employees, instead of out of only women employees, which changes the denominator and the answer.Final Answer:Sixty percent of the women in the company are not engineers.

Question 11

If 25% of three sevenths of 26% of a number is equal to 145.5, what is the approximate value of that number?

Accepted Answer

Introduction / Context:This question involves several percentage and fraction operations applied successively to an unknown number. It tests whether you can correctly translate the language into a mathematical expression and then solve for the original number, handling decimal values carefully.Given Data / Assumptions:• Let the unknown number be N.• First we take 26% of N.• Then we take three sevenths of that result.• Then we take 25% of that new value.• The final value obtained is 145.5.Concept / Approach:Percentages such as 25% and 26% can be written as fractions. The phrase three sevenths describes another fraction applied to the intermediate result. Multiplying all these fractions together gives one overall factor times N, which we set equal to 145.5. Solving this equation yields the required number.Step-by-Step Solution:Step 1: Twenty six percent of N = (26/100) * N.Step 2: Three sevenths of that = (3/7) * (26/100)N.Step 3: Twenty five percent of the new result = (25/100) * (3/7) * (26/100)N.Step 4: Combine the fractions: numerator = 25 * 3 * 26 = 1950, denominator = 100 * 7 * 100 = 70000.Step 5: Overall factor = 1950/70000, which simplifies to 39/1400.Step 6: So (39/1400)N = 145.5.Step 7: Solve for N: N = 145.5 * (1400/39).Step 8: Evaluate this product to obtain N approximately equal to 5223.08.Step 9: Among the given options, 5223 is the closest and therefore the correct choice.Verification / Alternative check:Check by substituting N = 5223. Compute 26% of 5223, then three sevenths of that, and then 25% of the result. The final value comes out very close to 145.5, with a small rounding difference due to decimal approximations, which is acceptable in typical multiple choice settings.Why Other Options Are Wrong:Values 4987, 5784 and 4741 produce final results that are significantly farther from 145.5 when the same sequence of operations is applied. They do not satisfy the equation even approximately.Common Pitfalls:Candidates often misplace the percentage factors or apply them in the wrong order, which changes the overall fraction drastically. Another error is forgetting that 145.5 already includes a decimal and rounding too early in the calculations.Final Answer:The approximate value of the number is 5223.

Question 12

If a student scores 15 marks out of 80, what percentage of the total marks has the student obtained?

Accepted Answer

Introduction / Context: Percent questions like this are very common in school exams and aptitude tests. Here we are asked to convert a score of 15 marks out of a maximum of 80 marks into a percentage. Understanding how to convert a fraction or ratio into a percentage is a basic but very important skill, because exam scores, discounts, profit and loss, and many real life comparisons are often expressed in percent form. Given Data / Assumptions: Total marks in the test = 80. Marks obtained by the student = 15. We need to find what percent 15 is of 80. We assume a simple percentage calculation with no negative marking or weighting. Concept / Approach: To convert a part of a whole into a percentage, we use the standard formula: percentage = (part / whole) * 100 Here, the part is the marks obtained and the whole is the maximum possible marks. After computing the fraction, we multiply by 100 to convert it into percent form. This method works for marks, money, quantities and any other similar comparison situations. Step-by-Step Solution: Step 1: Identify the part and the whole. Part = 15, whole = 80. Step 2: Write the basic fraction as 15 / 80. Step 3: Convert to percent using the formula (15 / 80) * 100. Step 4: Simplify 15 / 80. Divide numerator and denominator by 5 to get 3 / 16. Step 5: Now calculate (3 / 16) * 100. First compute 100 / 16 = 6.25. Step 6: Multiply 3 * 6.25 = 18.75. Step 7: Therefore the required percentage is 18.75%. Verification / Alternative check: Another way is to convert 18.75% back into marks and see if we get 15. Compute 18.75% of 80 as (18.75 / 100) * 80. First calculate 80 / 100 = 0.8. Then 18.75 * 0.8 = 15. This matches the original marks, so our percentage is consistent and correctly calculated. Why Other Options Are Wrong: 12.5% corresponds to 0.125 * 80 = 10 marks, which is less than 15. 16.5% corresponds to 0.165 * 80 = 13.2 marks, still not equal to 15. 20% corresponds to 0.20 * 80 = 16 marks, slightly more than 15. 25% corresponds to 0.25 * 80 = 20 marks, which is much higher than the obtained score. Common Pitfalls: A common mistake is to divide 80 by 15 instead of 15 by 80, which reverses the ratio and gives a completely wrong answer. Another error is forgetting to multiply by 100 at the end, which leaves the result as a decimal fraction rather than a percentage. Careless rounding too early in the calculation can also cause small errors, so it is better to simplify fractions exactly when possible and only round at the final step if required. Final Answer: The student obtained 18.75% of the total marks.

Question 13

If a quantity of 16 is compared with 225, 16 is equal to what percent of 225?

Accepted Answer

Introduction / Context: This question checks the basic idea of expressing one number as a percentage of another number. Problems of this type are very common in data interpretation, percentage chapters in quantitative aptitude, and everyday calculations like test scores or growth rates. Given Data / Assumptions: First quantity (part) = 16. Second quantity (whole) = 225. We need to find 16 as a percentage of 225. Standard percentage formula is used, with normal rounding to two decimal places where needed. Concept / Approach: To find what percent one number is of another, we use: percentage = (part / whole) * 100 Here the part is 16 and the whole is 225. After forming the fraction, we multiply by 100 to convert the value into percent form. Accurate division is important to get the correct answer to two decimal places. Step-by-Step Solution: Step 1: Write the required percentage as (16 / 225) * 100. Step 2: First compute 16 / 225. This is approximately 0.071111... Step 3: Multiply this by 100 to convert it to percent: 0.071111... * 100. Step 4: 0.071111... * 100 = 7.1111... which rounds to about 7.11%. Step 5: Therefore, 16 is approximately 7.11% of 225. Verification / Alternative check: We can verify by reversing the calculation. Take 7.11% of 225 and see if it is close to 16. Compute (7.11 / 100) * 225. First 7.11 / 100 = 0.0711. Then 0.0711 * 225 is approximately 15.9975, which rounds to 16. The small difference is due to rounding the percentage to two decimal places, and the result confirms that 7.11% is correct. Why Other Options Are Wrong: 6.87% gives (6.87 / 100) * 225 which is less than 16. 7.58% gives a value slightly more than 16 when applied to 225. 8.25% is much higher and gives a significantly larger value than 16. 5.50% produces a much smaller value when multiplied by 225. Common Pitfalls: Learners sometimes compute 225 / 16 instead of 16 / 225, which inverts the relationship. Forgetting to multiply by 100 at the end or rounding too early in the division can also lead to incorrect answers. It is helpful to remember that when the part is smaller than the whole, the resulting percentage should be less than 100% and, in this case, clearly less than 10% because 16 is much smaller than 225. Final Answer: Sixteen is 7.11% of 225 (approximately).

Question 14

Ramesh spends Rs. 38,460 on renovating his home and Rs. 24,468 on buying furniture. The remaining 28% of his total money is left as cash with him. What was the total amount of money Ramesh originally had?

Accepted Answer

Introduction / Context: This is a reverse percentage problem involving spending and remaining money. Such questions are very common in aptitude tests under the percentage or profit and loss chapters. Instead of directly finding a percentage of a known total, we are given the spent amount and the percentage of the total that remains, and we have to work backwards to find the original total amount of money. Given Data / Assumptions: Amount spent on renovation = Rs. 38,460. Amount spent on furniture = Rs. 24,468. Remaining cash is 28% of the original total amount. Total original amount is to be found. We assume all values are in rupees and simple percentage arithmetic applies. Concept / Approach: Let the original total amount be T rupees. The total amount spent is the sum of the two given expenses. The remaining money is given as 28% of T, so the spent amount is the other 72% of T. Thus we can write: spent amount = 72% of T = 0.72 * T Once we know the spent amount as a number, we can solve this simple linear equation to find T by dividing by 0.72. Step-by-Step Solution: Step 1: Compute the total amount spent. Total spent = 38,460 + 24,468 = 62,928. Step 2: Let the original total amount be T. Then 72% of T was spent. So, 0.72 * T = 62,928. Step 3: Solve for T by dividing both sides by 0.72. T = 62,928 / 0.72. Step 4: Perform the division: 62,928 / 0.72 = 87,400. Step 5: Therefore the original total amount Ramesh had was Rs. 87,400. Verification / Alternative check: To verify, compute 28% of 87,400 and check that the remaining plus the spent matches the total. First find 28% of 87,400: (28 / 100) * 87,400 = 24,472. Now add this remaining cash to the actual spent amount of 62,928. The sum is 62,928 + 24,472 = 87,400, which matches the original total, confirming that the calculation is consistent and correct. Why Other Options Are Wrong: Rs. 92,520 would give a spent portion of 72% equal to 66,614.4, not 62,928. Rs. 88,470 would give 72% equal to 63,698.4, which is higher than the actual spent amount. Rs. 90,150 would give 72% equal to 64,908, again not matching 62,928. Rs. 80,000 would give 72% equal to 57,600, which is too low compared to the actual spent amount. Common Pitfalls: A typical error is to treat 28% as the spent portion rather than the remaining portion, which would lead to an incorrect equation. Another common mistake is to subtract 28% from the spent amount instead of linking it correctly to the original total. Some learners also forget to convert 72% into its decimal form 0.72, or they divide by 72 instead of 0.72. Careful reading of the phrase stating that 28% is the remaining amount is crucial for setting up the right equation. Final Answer: Ramesh originally had Rs. 87,400 in total.

Question 15

Two numbers are respectively 7% and 28% of a third number. The first number is what percent of the second number?

Accepted Answer

Introduction / Context: This question tests the ability to compare two related percentages by using a common base. Many aptitude questions define two numbers as different percentages of a third reference number and then ask for the relative percentage between those two numbers. Understanding how ratios of percentages work is a very useful technique for quickly solving such problems without assigning specific numerical values to the third number. Given Data / Assumptions: Let the third number be some reference value, say N. First number = 7% of N. Second number = 28% of N. We need the first number as a percentage of the second number. All percentages are simple and refer to the same base N. Concept / Approach: If two numbers are given as percentages of the same base, we can express them using that base and then take their ratio. Let: first number = 0.07 * N second number = 0.28 * N To find the first as a percent of the second, we form the fraction (first / second) and then multiply by 100. The base N cancels out, which makes the calculation straightforward. Step-by-Step Solution: Step 1: Express both numbers in terms of N. First number = 7% of N = 0.07 * N. Second number = 28% of N = 0.28 * N. Step 2: Compute the fraction of first over second. (first / second) = (0.07 * N) / (0.28 * N). Step 3: Cancel N in numerator and denominator. (0.07 * N) / (0.28 * N) = 0.07 / 0.28. Step 4: Simplify 0.07 / 0.28. 0.07 / 0.28 = 7 / 28 = 1 / 4. Step 5: Convert this fraction into percent. (1 / 4) * 100 = 25%. Verification / Alternative check: We can choose a convenient value for N to double-check. Let N = 100 for simplicity. Then the first number is 7% of 100 = 7, and the second number is 28% of 100 = 28. Now find 7 as a percentage of 28: (7 / 28) * 100 = (1 / 4) * 100 = 25%. This matches our earlier result and confirms the correctness of the answer. Why Other Options Are Wrong: 24% would require the fraction between first and second to be 0.24, but we actually get 0.25. 29% would suggest the first is slightly more than one fourth of the second, which is not supported by the exact 7 and 28 ratio. 34% and 21% are also inconsistent with the exact fraction 1 / 4 obtained from 7 / 28. Common Pitfalls: One common mistake is to compare 7 and 28 directly as if they were full numbers without recognising that they both refer to the same base value. Another error is to compute 7% of 28 or 28% of 7 instead of using the correct relationship. Forgetting to multiply the final fraction by 100 to convert it into a percentage is also a frequent source of error. Always remember that percentages of the same base can be compared by taking their simple ratio. Final Answer: The first number is 25% of the second number.

Question 16

Ninety-six percent of the population of a village is 23,040. What is the total population of the village?

Accepted Answer

Introduction / Context: This is a classic reverse percentage question. Instead of finding a percentage of a known total, we are given a percentage value itself and asked to reconstruct the original total. Such questions appear frequently in exams involving population growth, discounts, profit and loss, and other real life situations where only a part of the whole is known. Given Data / Assumptions: 96% of the total population equals 23,040. We need to find the original total population of the village. Percent values are simple, and no growth over time is involved, only a direct percentage relationship. Concept / Approach: Let the total population be P. According to the question, 96% of P is 23,040. In equation form this is: 0.96 * P = 23,040 To find P, we simply divide 23,040 by 0.96. This is the standard way to work backwards from a percentage of a total to the original total. Step-by-Step Solution: Step 1: Let total population be P. Step 2: Use the given condition: 96% of P = 23,040. Step 3: Write this in decimal form: 0.96 * P = 23,040. Step 4: Divide both sides by 0.96 to isolate P. P = 23,040 / 0.96. Step 5: Perform the division. 23,040 / 0.96 = 24,000. Step 6: Therefore, the total population of the village is 24,000. Verification / Alternative check: To verify, compute 96% of 24,000 and see whether it matches the given figure 23,040. Calculate (96 / 100) * 24,000 = 0.96 * 24,000. Multiplying 24,000 by 0.96 gives 23,040, which is exactly the value given in the question. This confirms that our calculation of the total population is correct. Why Other Options Are Wrong: If the population were 32,256, then 96% would be much larger than 23,040. 25,478 and 26,587 both give 96% values that do not match 23,040 when calculated. 23,800 is less than 23,040 when 96% is taken, which is impossible since 96% of a number cannot exceed the number itself. Common Pitfalls: Some learners mistakenly compute 23,040 * 0.96 again, which goes in the wrong direction and produces a much smaller number. Another common mistake is to divide by 96 instead of 0.96, forgetting that the percentage must be converted to its decimal form before division. It is also important not to confuse 96% of P with 4% of P, which corresponds to the missing portion of the population in other types of questions. Final Answer: The total population of the village is 24,000 people.

Question 17

Thirty-six percent of what number is equal to 18?

Accepted Answer

Introduction / Context: This is another reverse percentage question. Instead of asking for 36% of a known number, the question gives the result of the percentage calculation (18) and asks us to find the original number. This type of question commonly appears in aptitude tests and is important for understanding how to work backwards with percentages. Given Data / Assumptions: Percentage involved = 36%. 36% of an unknown number is equal to 18. We need to find the unknown original number. All calculations use simple percentage arithmetic with no additional conditions. Concept / Approach: Let the unknown number be N. The statement 36% of N is 18 can be written as: 0.36 * N = 18 To find N, we can divide 18 by 0.36. This is the standard method of reversing a percentage calculation: divide the result by the decimal form of the percentage. Step-by-Step Solution: Step 1: Let the unknown number be N. Step 2: According to the question, 36% of N = 18. Step 3: Convert 36% to decimal: 36% = 36 / 100 = 0.36. Step 4: Set up the equation: 0.36 * N = 18. Step 5: Divide both sides of the equation by 0.36. N = 18 / 0.36. Step 6: Compute 18 / 0.36. Since 0.36 = 36 / 100, we have N = 18 * (100 / 36) = (18 * 100) / 36. Step 7: Simplify (18 * 100) / 36 = 1800 / 36 = 50. Step 8: Therefore, the required original number is 50. Verification / Alternative check: To confirm, calculate 36% of 50 and see if the result is 18. Compute (36 / 100) * 50 = 0.36 * 50. Multiplying 0.36 by 50 gives 18. Since this matches the given value, our solution is verified as correct. Why Other Options Are Wrong: If the number were 38, then 36% of 38 is 13.68, not 18. If the number were 42, then 36% of 42 is 15.12, still not 18. If the number were 62, then 36% of 62 is 22.32, which is greater than 18. If the number were 54, then 36% of 54 is 19.44, again not equal to 18. Common Pitfalls: A frequent error is to multiply 18 by 0.36 instead of dividing by 0.36. Another typical mistake is to divide by 36 rather than 0.36, forgetting that the percentage should be converted into decimal form. Some learners also misread the question and compute 36% of 18 directly, which gives a much smaller number. Always identify whether you are moving from whole to part or from part back to whole. Final Answer: The number for which 36% equals 18 is 50.

Question 18

A woman suffers a loss of 20% on her first investment, makes a profit of 10% on her second investment, and earns a profit of 12.5% on her third investment. If the invested amounts are in the ratio 4 : 5 : 3, what is her overall profit percentage on …

Accepted Answer

Introduction / Context: This question is about finding the overall profit or loss percentage when different portions of money are invested at different profit and loss rates. It is common in partnership and percentage topics to combine multiple investments or transactions and then determine the net effect on the total money. The key idea is to use weighted averages, where each individual percentage is weighted by the amount invested in that part. Given Data / Assumptions: Investments are in the ratio 4 : 5 : 3 for the first, second and third parts respectively. First investment has a 20% loss (that is, minus 20%). Second investment has a 10% profit. Third investment has a 12.5% profit. We need the overall profit or loss percentage on the total investment. Concept / Approach: We can assume convenient actual amounts matching the ratio, because only the relative proportions matter. Let the investments be 4x, 5x and 3x. Then we apply the respective profit or loss percentages to get the gain or loss on each part. The overall profit is the sum of all gains and losses divided by the total investment, expressed as a percentage. This is a weighted average of the individual percentages with weights 4, 5 and 3. Step-by-Step Solution: Step 1: Assume investments according to the ratio 4 : 5 : 3. Let first investment = 4x, second = 5x, third = 3x. Step 2: Compute gain or loss on each part. First part: 20% loss on 4x means loss = 0.20 * 4x = 0.8x. Second part: 10% profit on 5x means profit = 0.10 * 5x = 0.5x. Third part: 12.5% profit on 3x means profit = 0.125 * 3x = 0.375x. Step 3: Find net gain or loss. Net result = (profit on second + profit on third) minus loss on first. Net result = (0.5x + 0.375x) - 0.8x = 0.875x - 0.8x = 0.075x. This is a net profit of 0.075x. Step 4: Find total investment. Total investment = 4x + 5x + 3x = 12x. Step 5: Compute overall profit percentage. Overall profit percent = (net profit / total investment) * 100. = (0.075x / 12x) * 100. = (0.075 / 12) * 100. 0.075 / 12 = 0.00625. 0.00625 * 100 = 0.625%. Therefore, she makes an overall profit of 0.625%. Verification / Alternative check: We can choose a specific value for x, for example x = 100. Then the actual investments are 400, 500 and 300. The loss on 400 at 20% is 80. The profit on 500 at 10% is 50. The profit on 300 at 12.5% is 37.5. Net gain = 50 + 37.5 - 80 = 7.5. Total investment = 400 + 500 + 300 = 1200. Overall profit percentage = (7.5 / 1200) * 100 = 0.625%, which matches the previous calculation. Why Other Options Are Wrong: 1.25% profit would require double the net gain relative to the total investment. 0.625% loss is wrong in sign because our net result is a gain, not a loss. 1.20% profit and 2% profit both imply much larger gains than the calculated 0.625%. Common Pitfalls: A common mistake is to average the percentages directly as (minus 20 + 10 + 12.5) / 3, which ignores the different investment amounts. Another error is to forget that the first percentage is a loss and treat it as positive. Learners may also mishandle the ratio and not convert it into actual proportional amounts, leading to incorrect weighted averages. Always multiply each amount by its own percentage first, then combine the results, and finally divide by the total investment. Final Answer: The woman earns an overall 0.625% profit on her total investment.

Question 19

Prasanna invests certain amounts in three different schemes X, Y and Z at simple interest rates of 10% p.a., 12% p.a. and 15% p.a. respectively. The total interest accrued in one year is Rs. 3,200. The amount invested in Scheme Z is 150% of the amou…

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Introduction / Context: This is a typical investment and simple interest problem involving three different schemes with different interest rates. The key challenge is that the amounts invested in the schemes are related to each other by given ratios. We need to convert these relationships into equations, use the total interest information, and solve for the unknown amount invested in one particular scheme. Given Data / Assumptions: Interest rate in Scheme X = 10% per annum. Interest rate in Scheme Y = 12% per annum. Interest rate in Scheme Z = 15% per annum. Total simple interest in one year from all schemes = Rs. 3,200. Amount in Z is 150% of amount in X. Amount in Z is 240% of amount in Y. We assume simple interest for one year, so interest = principal * rate. Concept / Approach: Let the amounts invested in X, Y and Z be X, Y and Z respectively. We are given two ratio conditions connecting Z with X and Y. Using these, we can express X and Z in terms of Y. Then we write the total interest equation for one year and solve it for Y. This reduces the problem to a single variable equation using percentage and simple interest concepts. Step-by-Step Solution: Step 1: Translate the relationships among investments. Z is 150% of X, so Z = 1.5 * X. Z is 240% of Y, so Z = 2.4 * Y. Step 2: Equate the two expressions for Z to relate X and Y. 1.5 * X = 2.4 * Y. So, X = (2.4 / 1.5) * Y = 1.6 * Y. Step 3: Now write all amounts in terms of Y. X = 1.6Y, Z = 2.4Y, and Y = Y. Step 4: Use the total simple interest information. Interest from X in one year = 10% of X = 0.10 * X = 0.10 * 1.6Y = 0.16Y. Interest from Y in one year = 12% of Y = 0.12Y. Interest from Z in one year = 15% of Z = 0.15 * 2.4Y = 0.36Y. Step 5: Add all three interests and equate to 3,200. Total interest = 0.16Y + 0.12Y + 0.36Y = 0.64Y. So, 0.64Y = 3,200. Step 6: Solve for Y. Y = 3,200 / 0.64 = 5,000. Therefore, the amount invested in Scheme Y is Rs. 5,000. Verification / Alternative check: Once Y is 5,000, X = 1.6 * 5,000 = 8,000. Z = 2.4 * 5,000 = 12,000. Now compute the interest from each scheme. At 10%, Scheme X yields 800. At 12%, Scheme Y yields 600. At 15%, Scheme Z yields 1,800. Total interest = 800 + 600 + 1,800 = 3,200, which matches the given total. This confirms that the value Y = 5,000 is correct. Why Other Options Are Wrong: If Y were 6,000, then the total interest using the same relationships would exceed 3,200. Values like 4,500 or 7,500 also lead to total interest values that do not equal 3,200 when the given ratios and rates are used. 3,200 is the total interest, not the invested amount in Y, so that option misinterprets the data. Common Pitfalls: A common error is to treat 150% and 240% as simple multipliers without converting them properly, or to confuse which amount is bigger. Another mistake is to assign independent variables for X, Y and Z and forget to apply the given percentage relationships, leading to too many unknowns. Some learners also misinterpret the interest formula and multiply by the rate twice. Carefully translating all relationships into a single variable before writing the interest equation makes the problem much easier to manage. Final Answer: Prasanna invested Rs. 5,000 in Scheme Y.

Question 20

A shopping mall owner reduces the price of electronic goods by 20% to increase sales. As a result, the sales volume of electronics increases by 40%, and his weekly collection increases by Rs. 1,05,000. By how much did his gross collection increase p…

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Introduction / Context: This problem involves the combined effect of a price decrease and a quantity increase on total revenue or collection. Such questions test understanding of percentage change in price and demand, and how they interact to affect overall earnings. After finding the overall percentage change, we connect it with the given increase in weekly collection and finally convert that to a daily amount. Given Data / Assumptions: Price of electronic goods is decreased by 20%. Sales volume of electronics increases by 40%. Total weekly collection increases by Rs. 1,05,000. We need the increase in daily collection, assuming 7 days in a week. All collections are in rupees and we consider only the effect of this change. Concept / Approach: Let the original weekly collection be R. When the price decreases by 20%, the new price factor is 0.8 of the old price. When sales increase by 40%, the new quantity factor is 1.4 of the old quantity. The new revenue is proportional to price factor multiplied by quantity factor, so we compute 0.8 * 1.4 to find the overall revenue multiplier. Then we use the information about the weekly increase (Rs. 1,05,000) to solve for R and then find the daily increase by dividing by 7. Step-by-Step Solution: Step 1: Represent price and quantity changes as multipliers. Price decreases 20%, so price factor = 1 - 0.20 = 0.8. Sales increase 40%, so quantity factor = 1 + 0.40 = 1.4. Step 2: Find the overall revenue multiplier. New revenue factor = 0.8 * 1.4 = 1.12. This means revenue increases by 12% overall. Step 3: Let the original weekly collection be R. New weekly collection = 1.12 * R. Increase in weekly collection = 1.12R - R = 0.12R. Given that this increase is Rs. 1,05,000, so 0.12R = 1,05,000. Step 4: Solve for R. R = 1,05,000 / 0.12. R = 8,75,000. Step 5: The weekly increase is given as 1,05,000, so the daily increase is 1,05,000 / 7. Daily increase = 15,000. Thus, the gross collection increased by Rs. 15,000 per day. Verification / Alternative check: We can also compute the new weekly revenue directly. Original weekly revenue is R = 8,75,000. A 12% increase gives new revenue = R + 0.12R = 1.12R = 1.12 * 8,75,000 = 9,80,000. The difference between 9,80,000 and 8,75,000 is 1,05,000, which matches the given weekly increase. Dividing 9,80,000 by 7 gives 1,40,000 per day after the change, while 8,75,000 / 7 gives 1,25,000 per day originally. The difference is 15,000 per day, confirming our answer. Why Other Options Are Wrong: Amounts like 14,400 or 14,600 per day imply different weekly increases when multiplied by 7, and they would not match the stated increase of 1,05,000. 14,800 per day gives a weekly increase of 1,03,600, which is a little short of the given figure. 16,000 per day would correspond to a weekly increase of 1,12,000, more than the stated increase. Common Pitfalls: A frequent mistake is to add or subtract the percentages directly (for example, 40 minus 20 = 20%) and assume a 20% change in revenue, which is incorrect. Another error is to treat the 1,05,000 as the new weekly collection rather than the increase. Some learners also divide by 5 instead of 7 when computing the daily change. Always remember that combined percentage changes must be handled by multiplying their factors, and that revenue is proportional to both price and quantity together. Final Answer: The gross collection increased by Rs. 15,000 per day.

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