Question 1

In a school, the total number of students (boys plus girls) is 150. If the number of boys is x, the number of girls becomes x% of the total number of students. How many boys are there in the school?

Accepted Answer

Introduction / Context:This question combines percentages and simple algebra to relate the numbers of boys and girls in a school. It tests your ability to translate a verbal relationship into an equation, where the number of girls is given as a percentage of the total number of students. Problems like this appear frequently in aptitude tests under percentage and ratio topics and help reinforce the interpretation of expressions such as "x% of a total".Given Data / Assumptions:The total number of students in the school is 150.The number of boys is x.The number of girls is therefore 150 - x.The number of girls is equal to x% of the total number of students.The total number of students is the sum of boys and girls.Concept / Approach:The main concept is that x% of the total number of students can be written as (x/100) * 150. Since the number of girls is given to be exactly this value, we can equate 150 - x to (x/100) * 150. That equation contains only one unknown, x, which represents the number of boys. Solving this linear equation gives the required value of x. Understanding how to convert "x% of 150" and correctly set up the equality is the key step here.Step-by-Step Solution:Step 1: Let the number of boys be x.Step 2: Since the total number of students is 150, the number of girls is 150 - x.Step 3: The question states that the number of girls equals x% of the total students.Step 4: x% of 150 is (x/100) * 150 = 1.5x.Step 5: Set up the equation: 150 - x = 1.5x.Step 6: Rearrange to get 150 = 1.5x + x = 2.5x.Step 7: Solve for x: x = 150 / 2.5 = 60.Step 8: Therefore, there are 60 boys in the school.Verification / Alternative check:With x = 60, the number of boys is 60 and the number of girls is 150 - 60 = 90. According to the condition, girls should be x% of the total, i.e., 60% of 150. Now calculate 60% of 150: (60/100) * 150 = 0.6 * 150 = 90. This matches the actual number of girls, confirming that the equation and solution are correct. Thus, 60 boys satisfy the relationship given in the problem.Why Other Options Are Wrong:If x were 70, the girls would be 80, but 70% of 150 is 105, not 80. If x were 80, the girls would be 70, but 80% of 150 is 120, which does not match. For x = 90, girls would be 60, whereas 90% of 150 is 135. Finally, x = 75 would mean girls are 75, but 75% of 150 is 112.5, again not equal. Therefore, only x = 60 satisfies the required condition that girls equal x% of the total students.Common Pitfalls:A common mistake is to misinterpret x% of the total as simply x, or to write 150 * x instead of (x/100) * 150. Some learners also mistakenly set x equal to 150 - x rather than relating 150 - x to a percentage of 150. Another error is to treat x% as x/10, which is incorrect. To avoid such mistakes, always remember that y% of a quantity T is (y/100) * T and set up the equation carefully before solving.Final Answer:The number of boys in the school is 60.

Question 2

In a class of 80 students and 5 teachers, each student receives sweets equal to 15% of the total number of students and each teacher receives sweets equal to 25% of the total number of students. How many sweets were distributed in total?

Accepted Answer

Introduction / Context:This problem deals with distribution of items (sweets) based on fixed percentages of a group size. It tests your understanding of how to apply percentages to a given base and then aggregate quantities for different subgroups. Such questions commonly appear in aptitude exams to assess your comfort with basic percentage calculations and multiplication.Given Data / Assumptions:The class has 80 students.There are 5 teachers.Each student gets sweets equal to 15% of the total number of students.Each teacher gets sweets equal to 25% of the total number of students.The total number of sweets distributed is required.We treat sweets as discrete items, but the calculations are done using percentage values of the student count.Concept / Approach:The key concept is that the number of sweets per person is based on a percentage of the student count, not the total people count. First, we calculate how many sweets each student receives by taking 15% of 80. Then we multiply that by the number of students. Next, we calculate how many sweets each teacher receives by taking 25% of 80 and then multiplying by the number of teachers. Finally, we add the two totals to get the overall number of sweets distributed. This simple, sequential approach ensures accuracy.Step-by-Step Solution:Step 1: Total number of students = 80.Step 2: Each student gets sweets equal to 15% of the total students, that is 15% of 80.Step 3: 15% of 80 = (15/100) * 80 = 12 sweets per student.Step 4: Total sweets for all students = 80 * 12 = 960 sweets.Step 5: Each teacher gets sweets equal to 25% of the total students, that is 25% of 80.Step 6: 25% of 80 = (25/100) * 80 = 20 sweets per teacher.Step 7: Total sweets for all teachers = 5 * 20 = 100 sweets.Step 8: Total sweets distributed = sweets for students + sweets for teachers = 960 + 100 = 1060 sweets.Verification / Alternative check:As a check, note that the total number of people is 85 (80 students plus 5 teachers), but the percentage bases are strictly the student count of 80. For students, 80 persons each getting 12 sweets clearly gives 960 sweets. For teachers, 5 persons each get 20 sweets, totalling 100 sweets. Adding these gives 1060. There is no other hidden condition or rounding involved, so the total 1060 is consistent and unique. A quick mental estimation also confirms the order of magnitude: around one thousand sweets, which matches the exact value we obtained.Why Other Options Are Wrong:Option 960 accounts only for the sweets given to students and ignores the sweets for teachers. Option 1020 would correspond to fewer sweets for teachers or incorrect percentage usage. Option 920 is even smaller and cannot be obtained by any logical calculation using the given percentages. Option 1000 is a rounded guess and does not match the exact arithmetic of 960 plus 100. Therefore, these options do not reflect the correct total distribution of sweets.Common Pitfalls:One common mistake is to take percentages of the total number of people (students plus teachers) instead of only students, which changes the base and results in wrong figures. Another error is to forget to multiply the per person sweets by the number of persons in each group. Some learners also confuse 15% and 25% as fractions like 1/15 or 1/25. To avoid these errors, always identify the correct base for the percentage and carefully multiply by the group size at the end.Final Answer:The total number of sweets distributed is 1060.

Question 3

One hour is what percentage of one full day (24 hours)?

Accepted Answer

Introduction / Context:This is a straightforward percentage problem that connects units of time. You are asked to express one hour as a percentage of an entire day. Questions like this are useful for building intuition about fractions and percentages of a whole, and they often appear in aptitude tests in simplified form to test basic numeric understanding and speed.Given Data / Assumptions:One full day consists of 24 hours.We are interested in comparing 1 hour to the full 24 hours.The answer must be expressed as a percentage.We assume the usual definition that a day has exactly 24 hours.Concept / Approach:To find what percent one quantity is of another, we take the ratio of the first quantity to the second and then multiply by 100. In this question, the relevant ratio is 1 hour divided by 24 hours. This ratio is then converted into a percentage by multiplying by 100%. There are no complications such as changing units because both values are already in hours. The concept is simply percentage of a whole.Step-by-Step Solution:Step 1: Total time in one day = 24 hours.Step 2: Required fraction = (time considered) / (total time) = 1 / 24.Step 3: To convert this fraction to a percentage, multiply by 100: (1 / 24) * 100%.Step 4: Compute 100 / 24 = 4.1666... approximately.Step 5: Round this to two decimal places to get approximately 4.17%.Step 6: Among the given options, the nearest standard representation is 4.16%.Verification / Alternative check:Another way to think about the ratio is to recall that 1/4 is 25%, 1/10 is 10%, and 1/20 is 5%. Since 1/24 is slightly smaller than 1/20, the percentage should be a bit less than 5%. Our computed value of about 4.17% matches this intuition. Also, multiplying 24 by 4.1666... / 100 should give roughly 1, which confirms the correctness of the calculation. Therefore, 4.16% is a valid approximation and matches the option closely.Why Other Options Are Wrong:Option 5.6% is greater than 1/20 of a day and would correspond to more than one hour. Option 3.35% is too small and would represent less than the true fraction. Option 6.7% is far too large, representing about 1.6 hours. Option 2.5% is also too small, equal to only 0.6 hours. Among the given options, only 4.16% properly approximates 1/24 of a day as a percentage.Common Pitfalls:Some learners mistakenly flip the ratio and compute 24/1 instead of 1/24, leading to nonsensical percentages greater than 100. Others may try to use approximate mental shortcuts without checking their logic and may pick an option that is clearly too high or too low. Another pitfall is forgetting to multiply by 100 when converting the fraction 1/24 into a percentage. Keeping the formula (part / whole) * 100% in mind helps avoid these mistakes.Final Answer:One hour is approximately 4.16% of a full day.

Question 4

The difference between a number and two-fifth of that number is 510. What is 10% of that number?

Accepted Answer

Introduction / Context:This question is a basic algebra and percentage problem based on a simple linear relationship. Instead of directly giving the number, the problem gives a relationship between the number and a fraction of it. Such questions are common in aptitude exams and help reinforce understanding of fractions, algebraic equations, and the calculation of a percentage of a quantity.Given Data / Assumptions:The unknown number is not given directly.The difference between the number and two-fifth of that number is 510.We are asked to find 10% of that number.The unknown number is assumed to be a positive real number as in typical aptitude questions.Concept / Approach:The core idea is to represent the unknown number by a variable, say N, and then translate the English statement into an algebraic equation. The difference between N and (2/5) * N is equal to 510. Once we solve for N, we compute 10% of N, which is (10/100) * N. This step-by-step algebraic approach avoids guesswork and works well for any similar fraction-based relationship.Step-by-Step Solution:Step 1: Let the unknown number be N.Step 2: Two-fifth of the number is (2/5) * N.Step 3: The difference between the number and two-fifth of it is N - (2/5) * N.Step 4: According to the question, N - (2/5) * N = 510.Step 5: Simplify the left side: N - (2/5) * N = (3/5) * N.Step 6: So we have (3/5) * N = 510.Step 7: Solve for N: N = 510 * (5/3) = 510 * (5 ÷ 3).Step 8: 510 ÷ 3 = 170, so N = 170 * 5 = 850.Step 9: Now compute 10% of N: 10% of 850 = (10/100) * 850 = 85.Verification / Alternative check:To verify, plug N = 850 back into the original condition. Two-fifth of 850 is (2/5) * 850 = 2 * 170 = 340. The difference between 850 and 340 is 850 - 340 = 510, which matches the value given in the problem. Next, 10% of 850 is indeed 85. Since both the algebraic equation and the verification step confirm our computations, the result is reliable.Why Other Options Are Wrong:If we tried 75 as 10% of the number, the original number would be 750. The difference between 750 and two-fifth of 750 (which is 300) would be 450, not 510. For 95, the number would be 950, and the difference between 950 and 380 would be 570, still not 510. For 105, the number would be 1050, giving a difference of 630, which is also incorrect. Option 65 leads to a number of 650, producing a difference of 390. Thus none of these options satisfy the condition except 85.Common Pitfalls:One common mistake is to misinterpret "two-fifth" as 2/50 or to subtract the fraction incorrectly. Another mistake is to take 510 as 2/5 of the number rather than the difference between the number and 2/5 of it. Some learners also forget to multiply by the reciprocal when solving (3/5) * N = 510. Carefully converting the language into a correct algebraic equation and performing fraction operations step by step helps avoid these errors.Final Answer:10% of the number is 85.

Question 5

A number is first increased by 20% and then decreased by 20%. What is the net percentage change in the value of the number?

Accepted Answer

Introduction / Context:This question illustrates how successive percentage changes work when the same percentage is used for an increase and then a decrease. Many people wrongly assume that a 20% increase followed by a 20% decrease returns the number to its original value, but this is not true because the base for the second change is different. Understanding this concept is crucial for topics like salary revisions, stock price changes, and compound percentage problems.Given Data / Assumptions:A number is increased by 20% in the first step.The resulting value is then decreased by 20% in the second step.We are asked to find the overall net percentage change.No actual number is given, so we can assume a convenient starting value, such as 100 units, for easy calculation.Concept / Approach:The core idea is to represent each percentage change as a multiplication factor. A 20% increase corresponds to multiplying by 1.20. A 20% decrease corresponds to multiplying by 0.80. When these are applied successively, the overall multiplier is the product of the two factors, that is 1.20 * 0.80. From this overall factor, we can determine the final value relative to the original and then express the change as a percentage increase or decrease.Step-by-Step Solution:Step 1: Assume the original number is 100 units for simplicity.Step 2: Increase it by 20%: new value = 100 + 20% of 100 = 100 + 20 = 120 units.Step 3: Now decrease this new value by 20%: 20% of 120 = (20/100) * 120 = 24.Step 4: Subtract this from 120: final value = 120 - 24 = 96 units.Step 5: Compare the final value with the original value of 100.Step 6: The change is 96 - 100 = -4 units, meaning a decrease of 4 units.Step 7: Express this as a percentage of the original: (4 / 100) * 100% = 4% decrease.Verification / Alternative check:Using multiplication factors, we can write the net effect more compactly. A 20% increase multiplies the number by 1.2, and a 20% decrease multiplies it by 0.8. The combined factor is 1.2 * 0.8 = 0.96. This means the final value is 96% of the original. A value of 96% corresponds to a 4% decrease from 100%. Both this factor method and the numerical example with 100 units give the same conclusion that there is a 4% overall decrease, confirming correctness.Why Other Options Are Wrong:Option "increase by 2%" would mean the final value is 102 units when starting from 100, which contradicts the computed 96 units. Option "decrease by 3%" would correspond to a final value of 97 units, again not matching 96. Option "increase by 5%" suggests a final value of 105 units, which is clearly inconsistent. Option "no change" assumes that the effects cancel each other, which is a common misconception. Only a 4% decrease matches the actual calculations.Common Pitfalls:Many learners mistakenly think that if you increase and then decrease by the same percentage, the net effect is zero. This happens because they treat percentages additively (20 - 20 = 0) rather than multiplicatively. Another pitfall is to incorrectly apply the second percentage to the original number instead of the increased value. To avoid these issues, always convert each change into a multiplier and apply them one after another to the current value, not the initial value each time.Final Answer:The number suffers a net decrease of 4%.

Question 6

In a city, 35% of the population consists of migrants, 20% of whom are from rural areas. Of the local population, 48% are female, while for rural and urban migrants the female percentages are 30% and 40% respectively. If the total population of the …

Accepted Answer

Introduction / Context:This question is a multi-step percentage and population distribution problem. It involves splitting the total population into local residents and migrants, then further dividing migrants into rural and urban groups, and finally applying different female population percentages to each group. Such layered percentage questions are frequently seen in data interpretation and quantitative aptitude sections, and they test your ability to manage multiple proportions cleanly.Given Data / Assumptions:Total population of the city = 7,28,400.35% of the total population are migrants.20% of the migrants are from rural areas; the remaining 80% of migrants are from urban areas.48% of the local (non-migrant) population are female.30% of rural migrants are female.40% of urban migrants are female.We must find the total number of females in the whole city.Concept / Approach:The strategy is to calculate the sizes of each subpopulation step by step and then apply the respective female percentages. First, we compute the number of migrants and locals using the 35% figure. Then we break migrants into rural and urban migrants using 20% and 80%. Next, we calculate the number of females in each of the three groups: locals, rural migrants, and urban migrants, using their given percentages. Finally, we sum the female counts across all groups to get the total female population. Careful ordering of these steps helps avoid confusion and arithmetic errors.Step-by-Step Solution:Step 1: Total population = 7,28,400.Step 2: Migrant population = 35% of 7,28,400 = 0.35 * 7,28,400 = 2,54,940.Step 3: Local population = total population - migrant population = 7,28,400 - 2,54,940 = 4,73,460.Step 4: Rural migrants = 20% of total migrants = 0.20 * 2,54,940 = 50,988.Step 5: Urban migrants = 80% of total migrants = 0.80 * 2,54,940 = 2,03,952.Step 6: Female locals = 48% of local population = 0.48 * 4,73,460 = 2,27,260.8.Step 7: Female rural migrants = 30% of rural migrants = 0.30 * 50,988 = 15,296.4.Step 8: Female urban migrants = 40% of urban migrants = 0.40 * 2,03,952 = 81,580.8.Step 9: Total female population = 2,27,260.8 + 15,296.4 + 81,580.8 = 3,24,138 (rounding to the nearest whole person).Verification / Alternative check:As a verification, we can approximate the calculations to check the scale. Migrants are about 2.55 lakh people, locals about 4.73 lakh. If roughly half of locals are female, that is about 2.36 lakh females, which is close to the exact 2.27 lakh. Among migrants, rural migrants are about 51 thousand with 30% females, giving about 15 thousand, and urban migrants are about 2.04 lakh with 40% females, giving about 81 thousand. Adding these approximate values (2.27 lakh, 0.015 lakh, 0.081 lakh) gives around 3.24 lakh, which matches the exact calculation of 3,24,138. This confirms that the arithmetic and logic are consistent.Why Other Options Are Wrong:Option 3,49,680 is larger than the total migrant population and would require an unrealistically high female percentage across all groups. Option 5,09,940 is well over half the total population and contradicts the given female percentages. The value 4,12,356 similarly does not arise from any valid combination of the given percentages. Option "None of these" is not correct because we have found a specific value that fits all conditions, namely 3,24,138. Therefore, only 3,24,138 accurately represents the total female population as per the given data.Common Pitfalls:Learners sometimes apply the female percentages directly to the total population instead of to each subgroup, which ignores the differences between locals, rural migrants, and urban migrants. Another common error is to treat 20% of the city population as rural migrants rather than 20% of the migrant population. Misplacing decimal points when dealing with large numbers is also frequent. To avoid these problems, always keep track of which percentage applies to which group and perform calculations step by step with clear labels.Final Answer:The total female population of the city is 3,24,138.

Question 7

A shopkeeper's earnings increase by 25% in the first year but decrease by 4% in the next year, and this pattern of +25% then -4% continues alternately. After 5 years, his earnings become Rs. 72,000. What is his present yearly earning (the earning at…

Accepted Answer

Introduction / Context:This question involves successive percentage changes over multiple years, alternating between an increase and a decrease. It is a typical compound percentage problem where the final value after several years is known, and we must find the starting value. Such questions appear in topics like growth and decay, salary progression, and investment returns, and they require careful handling of multiplication factors year by year.Given Data / Assumptions:The shopkeeper's earning increases by 25% in the first year.His earning decreases by 4% in the second year.This pattern of +25% and -4% continues alternately for 5 years.After 5 years, his earning becomes Rs. 72,000.We are asked to find his earning at the start of this 5-year period.Percent changes are applied year by year to the current earning, not to the original amount each time.Concept / Approach:Each percentage change can be represented as a multiplicative factor. A 25% increase corresponds to multiplying by 1.25, while a 4% decrease corresponds to multiplying by 0.96. With 5 years and an alternating pattern, the sequence of factors is: 1.25 (year 1), 0.96 (year 2), 1.25 (year 3), 0.96 (year 4), and 1.25 (year 5). The overall multiplier is the product of these five factors. If we denote the initial earning as E, then E multiplied by this overall factor equals 72,000. Solving E * overall factor = 72,000 yields the initial earning.Step-by-Step Solution:Step 1: Factor for a 25% increase = 1 + 25/100 = 1.25.Step 2: Factor for a 4% decrease = 1 - 4/100 = 0.96.Step 3: Over 5 years with alternating pattern, the sequence of factors is 1.25, 0.96, 1.25, 0.96, 1.25.Step 4: Group the factors: (1.25 * 1.25 * 1.25) * (0.96 * 0.96).Step 5: Compute 1.25^3 = 1.25 * 1.25 * 1.25 = 1.953125, but for this question we use the combined simplified factor 1.25^3 * 0.96^2 = 1.8.Step 6: Let the initial earning be E. Then E * 1.8 = 72,000.Step 7: Solve for E: E = 72,000 / 1.8.Step 8: 72,000 divided by 1.8 equals 40,000.Step 9: Therefore, the shopkeeper's present yearly earning is Rs. 40,000.Verification / Alternative check:We can verify by applying the annual changes to Rs. 40,000 step by step. After year 1, earning = 40,000 * 1.25 = 50,000. After year 2, earning = 50,000 * 0.96 = 48,000. After year 3, earning = 48,000 * 1.25 = 60,000. After year 4, earning = 60,000 * 0.96 = 57,600. After year 5, earning = 57,600 * 1.25 = 72,000. This matches the final earning given in the question, confirming that Rs. 40,000 is indeed the correct starting earning.Why Other Options Are Wrong:If the initial earning were Rs. 45,000, then applying the same factor of 1.8 would give a final earning of Rs. 81,000, not 72,000. For Rs. 42,000, the final amount would be 42,000 * 1.8 = 75,600, again not matching. For Rs. 46,000, the final value would be 82,800. Rs. 38,000 would yield a final value of 68,400. None of these match the required final earning of Rs. 72,000, so only Rs. 40,000 is correct.Common Pitfalls:Some learners wrongly add or subtract the percentages linearly (for example, considering 25% - 4% = 21% per two years) instead of multiplying factors. Others may mistakenly apply all percentages to the original figure rather than successively to the updated value each year. Another common mistake is approximating decimal factors too loosely, leading to significant rounding errors. The correct approach is to use multiplication factors accurately and to apply them consecutively over each year.Final Answer:The shopkeeper's present yearly earning is Rs. 40,000.

Question 8

When the price of rice decreases by 10%, a girl can buy 1 kg more rice for Rs. 270. What was the original price of rice per kilogram?

Accepted Answer

Introduction / Context:This question is a typical application of percentage decrease in price leading to an increase in quantity purchasable with the same amount of money. It combines unitary method, percentages, and simple algebra. Such problems are frequently asked in exams under the topics of percentage, profit and loss, and consumption changes because they illustrate the inverse relationship between price and quantity for a fixed budget.Given Data / Assumptions:A girl spends Rs. 270 on rice.When the price of rice decreases by 10%, she can buy 1 kg more rice for the same Rs. 270.We are asked to find the original price of rice per kilogram.The price change is a 10% decrease from the original price.No other changes in spending or consumption are mentioned.Concept / Approach:Let the original price of rice be P rupees per kilogram. After a 10% decrease, the new price becomes 0.9P. With Rs. 270, the quantity of rice that can be bought at the original price is 270 / P kilograms, and the quantity at the reduced price is 270 / (0.9P) kilograms. The problem states that this new quantity is exactly 1 kg more than the old quantity. We translate that condition into an equation and solve for P. This algebraic approach neatly links the price decrease percentage with the change in quantity.Step-by-Step Solution:Step 1: Let the original price be P rupees per kg.Step 2: After a 10% decrease, the new price is 90% of P, that is 0.9P rupees per kg.Step 3: Quantity bought at original price = 270 / P kg.Step 4: Quantity bought at reduced price = 270 / (0.9P) kg.Step 5: According to the question, the new quantity is 1 kg more than the old quantity: 270 / (0.9P) = 270 / P + 1.Step 6: Simplify 270 / (0.9P). Note that 270 / (0.9P) = 270 / P * (1 / 0.9) = (270 / P) * (10/9) = 300 / P.Step 7: So the equation becomes 300 / P = 270 / P + 1.Step 8: Subtract 270 / P from both sides: (300 / P) - (270 / P) = 1, which simplifies to 30 / P = 1.Step 9: Therefore P = 30.Step 10: The original price of rice is Rs. 30 per kg.Verification / Alternative check:At the original price of Rs. 30 per kg, Rs. 270 buys 270 / 30 = 9 kg of rice. After a 10% decrease, the new price is 90% of 30 = Rs. 27 per kg. At this price, Rs. 270 buys 270 / 27 = 10 kg of rice. The difference in quantity is 10 - 9 = 1 kg, which matches the condition given in the problem. Thus, the solution P = 30 is fully verified and consistent.Why Other Options Are Wrong:If the original price were Rs. 36, after a 10% decrease it would be Rs. 32.40. Then Rs. 270 would buy approximately 7.5 kg and 8.33 kg, not differing by exactly 1 kg. If the price were Rs. 28, the new price would be Rs. 25.20, and the resulting quantities would not differ by precisely 1 kg. If the price were Rs. 40, the new price would be Rs. 36, and the quantities would again not satisfy the 1 kg difference. Rs. 32 similarly fails to produce the required change. Only Rs. 30 leads to exactly 1 kg additional rice for Rs. 270 after a 10% price decrease.Common Pitfalls:Some learners confuse the base for the 10% decrease, incorrectly subtracting 10 rupees instead of 10% of the price. Others mis-handle the algebraic equation and fail to simplify 270 / (0.9P) correctly, or they do not realise that the increase in quantity must be exactly 1 kg. Using trial and error with options can be time consuming and error-prone. Writing a clear equation from the relationship and simplifying step by step is the most reliable strategy.Final Answer:The original price of rice was Rs. 30 per kilogram.

Question 9

An agent receives a commission of 2.5% on the sale of cloth. On a certain day, he earns Rs. 12.50 as commission. What was the total value of cloth sold through him on that day?

Accepted Answer

Introduction / Context:This question is a simple application of percentage and commission. The commission percentage and the actual commission amount are given, and we must find the total sales value that produced this commission. Such problems are standard in topics involving brokerage, agency commissions, or sales incentives and help strengthen the link between percentage rates and their corresponding base values.Given Data / Assumptions:The commission rate is 2.5% of the sale value of cloth.The agent receives Rs. 12.50 as commission on a particular day.We are asked to find the total value of cloth sold through the agent on that day.Commission is calculated directly as a percentage of the sales amount with no additional conditions.Concept / Approach:The concept is straightforward: commission equals commission rate multiplied by the sales amount. If we let the sales amount be S, then the commission is (2.5/100) * S. Setting this equal to Rs. 12.50 and solving for S gives the sales amount. This is a direct percentage equation where the unknown is the base value corresponding to a known percent of it.Step-by-Step Solution:Step 1: Let the total value of cloth sold be S rupees.Step 2: The commission rate is 2.5%, so commission = (2.5/100) * S.Step 3: We are told that the commission amount is Rs. 12.50.Step 4: Set up the equation: (2.5/100) * S = 12.50.Step 5: Rewrite (2.5/100) as 0.025. So 0.025 * S = 12.50.Step 6: Solve for S by dividing both sides by 0.025: S = 12.50 / 0.025.Step 7: 12.50 divided by 0.025 equals 500.Step 8: Therefore, the total value of cloth sold is Rs. 500.Verification / Alternative check:We can verify by computing 2.5% of Rs. 500 directly. Calculate 1% of 500, which is 5. Then 2.5% of 500 is 2.5 * 5 = 12.5 rupees. This matches the commission given in the question. The calculation is consistent, and the answer S = 500 is verified.Why Other Options Are Wrong:For a sales value of 300, 2.5% would be 7.50 rupees, which is less than the given commission. For 700, 2.5% would be 17.50 rupees, which is more than 12.50. For 900, 2.5% is 22.50 rupees, also incorrect. For 250, 2.5% is 6.25 rupees. None of these match the commission of Rs. 12.50. Only when the sales value is Rs. 500 do we obtain the correct commission amount.Common Pitfalls:A common error is to confuse 2.5% with 1/2 or to misplace the decimal when writing 2.5% as a fraction or decimal. Some learners attempt to divide 12.50 by 2.5 directly without converting the percentage properly, which gives 5 instead of the correct 500. Always remember that a percentage must be divided by 100 when converted into a decimal factor, so 2.5% equals 0.025, not 2.5. Using the correct factor ensures accurate results.Final Answer:The total value of cloth sold through the agent was Rs. 500.

Question 10

Find the value of 45% of 750 minus 25% of 480.

Accepted Answer

Introduction / Context:This is a direct numerical computation involving two separate percentage calculations and a subtraction. It tests calculation accuracy and comfort with basic percentages. Questions like this help build speed and confidence with mental arithmetic or quick written calculation, which is important in many competitive exams where time is limited.Given Data / Assumptions:We must calculate 45% of 750.We must calculate 25% of 480.The required value is the difference: (45% of 750) minus (25% of 480).No rounding is involved because all values are exact.Concept / Approach:The approach is to evaluate each percentage separately and then subtract. Percentages can be converted to fractions for simpler computation. For example, 45% is 45/100, and 25% is 25/100. We multiply these fractions by the respective numbers to find the percentage values. Breaking down the numbers into factors also makes calculations simpler. After both results are obtained, we subtract the second from the first to get the final answer.Step-by-Step Solution:Step 1: Compute 45% of 750.Step 2: 45% of 750 = (45/100) * 750.Step 3: Simplify 750 * 45/100 = 7.5 * 45 = 337.5.Step 4: Next, compute 25% of 480.Step 5: 25% of 480 = (25/100) * 480.Step 6: Simplify 480 * 25/100 = 4.8 * 25 = 120.Step 7: Now find the difference: 337.5 - 120.Step 8: 337.5 - 120 = 217.5.Step 9: Therefore, the required value is 217.50.Verification / Alternative check:We can check our calculations in another way by using fraction breakdown. Note that 45% of 750 can be written as (9/20) * 750. Since 750 / 20 = 37.5, 37.5 * 9 = 337.5, which matches our earlier value. Similarly, 25% of 480 is (1/4) * 480 = 120. Subtracting 120 from 337.5 again gives 217.5. As both methods agree, the result is confirmed.Why Other Options Are Wrong:Option 337.50 is just the value of 45% of 750 and ignores the subtraction of 25% of 480. Option 376.21 is not supported by any reasonable calculation and appears to be a random value. Option 120 is only the value of 25% of 480 and not the difference of the two quantities. Option 185.50 does not match the correct subtraction result. Only 217.50 is consistent with the step-by-step percentage calculations.Common Pitfalls:Some learners mistakenly add the two percentage values instead of subtracting, or they mix up which number to take each percentage from. Others misplace the decimal point when multiplying by percentage fractions, for example, treating 45% as 4.5 instead of 0.45. To avoid these errors, clearly write each operation, convert percentages to fractions or decimals carefully, and double-check the final subtraction.Final Answer:The value of 45% of 750 minus 25% of 480 is 217.50.

Question 11

How many litres of pure acid are present in 8 litres of a 20% acid solution?

Accepted Answer

Introduction / Context:This question deals with percentage concentration in a solution. A 20% acid solution means that 20% of the total volume is pure acid and the rest is typically some other substance such as water. This type of problem is very common in mixture and solution questions in quantitative aptitude, chemistry basics, and everyday reasoning about concentrations.Given Data / Assumptions:Total volume of the solution = 8 litres.The solution is 20% acid by volume.We are asked to find the volume of pure acid in the solution.We assume the solution is homogeneous and that 20% concentration is measured by volume.Concept / Approach:To find the volume of pure acid, we simply take 20% of the total volume of the solution. In percentage terms, this is (20/100) times the total volume. Because the total volume is given as 8 litres, multiplying 8 by 0.2 or 20/100 gives the volume of acid. This is a direct and straightforward calculation involving percentages and unit consistency.Step-by-Step Solution:Step 1: Total volume of solution = 8 litres.Step 2: Concentration of acid in the solution = 20%.Step 3: Volume of pure acid = 20% of 8 litres.Step 4: Compute 20% of 8 = (20/100) * 8.Step 5: (20/100) * 8 = 0.2 * 8 = 1.6.Step 6: Therefore, the volume of pure acid is 1.6 litres.Verification / Alternative check:Another quick way to see this is to recognise that 10% of 8 litres is 0.8 litres. Therefore, 20% is twice that value, which is 1.6 litres. This mental math check matches our detailed calculation, confirming that 1.6 litres is correct. Since all operations are simple and there are no additional conditions or changes in concentration, the answer is unambiguous.Why Other Options Are Wrong:Option 1.4 litres corresponds to 17.5% of 8 litres, which is less than the given 20% concentration. Option 1.5 litres corresponds to 18.75% of 8 litres, again not matching 20%. Option 1.7 litres is slightly higher than 20% of 8 litres and would represent about 21.25%. Option 1.2 litres corresponds to 15% of 8 litres. Only 1.6 litres exactly corresponds to 20% of 8 litres, so the other options do not fit the problem statement.Common Pitfalls:Some learners confuse percentage of volume with percentage points and may mistakenly compute 20% of 10 litres or misread the total volume. Others might misplace the decimal when multiplying by 0.2. To avoid mistakes, clearly identify the base quantity (8 litres), convert the percentage to a fraction (20/100), and perform the multiplication carefully. Quick mental checks like using 10% and doubling it can also help verify the result.Final Answer:There are 1.6 litres of pure acid in the 8-litre solution.

Question 12

Evaluate 56% of 225 plus 20% of 150, given that 56% of 225 + 20% of 150 = ? - 109. Find the value of '?'.

Accepted Answer

Introduction / Context:This question combines percentage calculations with a simple linear equation involving an unknown represented by a question mark. You are asked to evaluate two percentage expressions, add them, and then relate the total to an expression of the form ? - 109. Problems like this appear frequently in arithmetic aptitude to test accurate percentage computation and equation solving skills.Given Data / Assumptions:We must compute 56% of 225.We must compute 20% of 150.The equation is 56% of 225 + 20% of 150 = ? - 109.We must find the value of the unknown quantity ?.No rounding is needed because the numbers chosen give exact decimal results.Concept / Approach:The first step is to evaluate each percentage term. We can convert 56% and 20% to fractions or decimals and multiply by the respective numbers. Once we have these two values, we add them together to find the left side of the equation. Then we use basic algebra to solve for ?, since ? - 109 must equal that computed sum. This direct approach keeps the problem simple and mechanical.Step-by-Step Solution:Step 1: Compute 56% of 225.Step 2: 56% of 225 = (56/100) * 225.Step 3: 225 * 56/100 = 2.25 * 56 = 126.Step 4: Next, compute 20% of 150.Step 5: 20% of 150 = (20/100) * 150 = 0.2 * 150 = 30.Step 6: Add the two results: 126 + 30 = 156.Step 7: According to the equation, 56% of 225 + 20% of 150 = ? - 109.Step 8: So we have 156 = ? - 109.Step 9: Solve for ?: ? = 156 + 109 = 265.Verification / Alternative check:We can verify by substituting ? = 265 back into the equation. The right side becomes 265 - 109 = 156. The left side we have already computed as 126 + 30 = 156. Since both sides match, the equation holds true and the value ? = 265 is confirmed. There are no approximations involved, so the result is exact.Why Other Options Are Wrong:Option 264 would give 264 - 109 = 155, which does not match the left side, 156. Option 220 would give 220 - 109 = 111, which is far from 156. Option 241 would give 241 - 109 = 132, again not matching the left side. The option 265 correctly satisfies the equation, but in the original list the correct numerical value is not among the main numeric options, so the best match in the provided choices is "None". Hence, "None" is the correct option since the actual value 265 is not one of the three given numeric alternatives.Common Pitfalls:Some learners miscalculate 56% of 225 by incorrectly splitting the percentage or misplacing the decimal. Others may forget to include 109 when solving for ? and mistakenly set ? equal to 156 instead of 265. A few may also misread the equation and subtract in the wrong direction. To avoid these mistakes, carefully compute each percentage, write down the intermediate sum, and then solve the equation step by step, ensuring that the operations on both sides of the equation are correct.Final Answer:The value of the unknown '?' is 265, so the correct choice from the options is "None".

Question 13

If P is 140 and this value is 40% more than Q, then what is the value of (3/25) of Q?

Accepted Answer

Introduction / Context:This question joins percentage comparison between two variables with a fractional calculation on one of them. It is a typical aptitude style problem where you need to interpret "40% more than" correctly, find the unknown quantity, and then compute a fraction of it. Such problems help reinforce both percentage and fraction skills, which are essential for a wide range of quantitative topics.Given Data / Assumptions:P is given as 140.P is 40% more than Q.We must find the value of (3/25) * Q.No other conditions or constraints are given.Concept / Approach:When a quantity P is 40% more than Q, it means P = Q + 40% of Q = 1.4 * Q. From this equation, we can solve for Q by dividing P by 1.4. Once Q is known, computing (3/25) * Q is straightforward. The key concept is to correctly interpret the phrase "40% more than" as a multiplicative relationship, not a simple difference without reference to Q.Step-by-Step Solution:Step 1: Given P = 140.Step 2: P is 40% more than Q, so P = 1.4 * Q.Step 3: Substitute P = 140 into the equation: 140 = 1.4 * Q.Step 4: Solve for Q by dividing both sides by 1.4: Q = 140 / 1.4.Step 5: 140 / 1.4 = 100, so Q = 100.Step 6: Now compute (3/25) of Q: (3/25) * Q = (3/25) * 100.Step 7: (3/25) * 100 = 3 * (100 / 25) = 3 * 4 = 12.Step 8: Therefore, (3/25) of Q is 12.Verification / Alternative check:To verify, we can start from Q = 100 and check the relationship with P. If Q is 100, then 40% of Q is 40, and 40% more than Q is Q + 40 = 140. This matches the given value of P. Next, computing (3/25) of Q as 3/25 * 100 directly gives 12, confirming that the calculations and the interpretation of "40% more than" are correct.Why Other Options Are Wrong:If we tried 9, then Q would incorrectly be treated such that 3/25 of Q equals 9, implying Q = 75, which does not satisfy the relation P = 140 = 1.4 * 75. Option 18 would imply Q = 150, giving P = 1.4 * 150 = 210, not 140. Option 24 implies Q = 200, giving P = 280, again inconsistent. Option 15 implies Q = 125, with P = 175, not 140. Thus none of these values satisfy all given conditions except 12.Common Pitfalls:Some learners misinterpret "P is 40% more than Q" as P = Q + 40, rather than P = Q + 0.4 * Q, which leads to incorrect equations. Others might invert the relationship and treat Q as 40% more than P. A further error is to compute 3/25 of P rather than of Q. To avoid these mistakes, carefully translate verbal percentage phrases into algebraic expressions and track which variable is being compared to which.Final Answer:The value of (3/25) of Q is 12.

Question 14

A batsman scores 120 runs in an innings, including 3 boundaries and 8 sixes. What percentage of his total score does he make by running between the wickets?

Accepted Answer

Introduction / Context:This question applies basic arithmetic and percentage concepts to a cricket scoring scenario. The batsman scores some runs through boundaries and sixes, and the remainder are scored by running between the wickets. You are asked to find the fraction of his total score contributed by running and express it as a percentage. Sports-based percentage questions like this are common in aptitude tests and help connect maths to real life contexts.Given Data / Assumptions:Total runs scored by the batsman = 120.He hits 3 boundaries, each worth 4 runs.He hits 8 sixes, each worth 6 runs.The remaining runs are scored by running between the wickets.We must find the percentage of total runs that come from running.Concept / Approach:The steps are straightforward. First, calculate the runs scored from boundaries and from sixes separately. Then, add these to get total runs from hits to the fence or over it. Subtract this from the overall score to determine how many runs came from running between the wickets. Finally, express that running score as a percentage of the total score by using the formula (runs from running / total runs) * 100%.Step-by-Step Solution:Step 1: Total runs scored = 120.Step 2: Runs from boundaries (4 runs each) = 3 * 4 = 12 runs.Step 3: Runs from sixes (6 runs each) = 8 * 6 = 48 runs.Step 4: Total runs from boundaries and sixes combined = 12 + 48 = 60 runs.Step 5: Runs scored by running between the wickets = total runs - runs from boundaries and sixes = 120 - 60 = 60 runs.Step 6: Now compute the percentage of total runs scored by running = (runs by running / total runs) * 100%.Step 7: This is (60 / 120) * 100% = 0.5 * 100% = 50%.Step 8: Therefore, 50% of his total score is made by running between the wickets.Verification / Alternative check:We can see that in this particular innings, the batsman scores 60 runs by big hits and 60 runs by running. Since the total is 120, it is clear that half of his runs come from running and half from boundaries and sixes. Half of any total is 50%, so this confirms the percentage found by the detailed calculation. The symmetry in the numbers (60 runs from each source) makes the verification intuitive and convincing.Why Other Options Are Wrong:Option 40% would correspond to 48 runs from running, which would imply 72 runs from boundaries and sixes, but that contradicts the given hit counts. Option 45% would correspond to 54 running runs, again inconsistent with the remaining scoring pattern. Option 55% would require 66 runs by running and 54 from boundaries and sixes, which cannot occur with 3 boundaries and 8 sixes. Option 35% would mean only 42 runs by running, which is also impossible given the total and the scoring strokes. Only 50% matches the computed distribution of runs.Common Pitfalls:Some learners forget to multiply the number of boundaries and sixes by 4 and 6 respectively and instead mistakenly add the counts directly. Others may subtract incorrectly or compute the percentage using the wrong base (for example, dividing by the runs from hits instead of the total score). To avoid these issues, carefully calculate runs from each scoring mode, find the running runs by subtraction, and then use the standard percentage formula (part / whole) * 100% with the total score as the whole.Final Answer:The batsman scored 50% of his runs by running between the wickets.

Question 15

In a certain examination, 34% of the students failed in Mathematics and 42% of the students failed in English. If 20% of the students failed in both subjects, what percentage of students passed in both Mathematics and English?

Accepted Answer

Introduction / Context:This percentage question tests basic set theory and the inclusion exclusion principle for two overlapping groups. Many aptitude exams use this model of failure or pass percentages in two subjects such as Mathematics and English. You are asked to find the percentage of students who passed in both subjects when you know how many failed in each subject and how many failed in both subjects together. Given Data / Assumptions:We assume the total number of students is 100%, that is, the whole population of candidates.34% of the students failed in Mathematics.42% of the students failed in English.20% of the students failed in both Mathematics and English.Every student either passes or fails in a subject; there is no other category. Concept / Approach:The key concept is the inclusion exclusion rule for two sets. For any two events A and B, we have:percentage in A or B = percentage in A + percentage in B – percentage in both A and B.Here A is the set of students who failed in Mathematics and B is the set of students who failed in English. Once we know the percentage of students who failed in at least one of the two subjects, we can subtract that from 100% to obtain the percentage who passed in both subjects. Step-by-Step Solution:Step 1: Let total students be 100% for easy calculation.Step 2: Percentage of students who failed Mathematics = 34%.Step 3: Percentage of students who failed English = 42%.Step 4: Percentage of students who failed in both Mathematics and English = 20%.Step 5: Use inclusion exclusion to find the percentage who failed in at least one subject.Failed in at least one subject = 34% + 42% – 20% = 56%.Step 6: Percentage of students who passed in both subjects = 100% – 56% = 44%. Verification / Alternative check:If you imagine 100 students, then 56 students fail in at least one subject and 44 students do not fail in any subject, which means they pass in both Mathematics and English. This matches the computed 44%, so the answer is consistent and reasonable. Why Other Options Are Wrong:34% is only the Mathematics failure percentage and has nothing to do with students passing in both subjects.54% is close but it would imply that only 46% failed in at least one subject, which does not fit the given data.64% would mean only 36% failed in at least one subject, which contradicts the sum of individual failures.56% is actually the percentage who failed in at least one subject, not those who passed in both. Common Pitfalls:Many students simply add 34% and 42% and subtract this from 100% without adjusting for the double counted 20%, which is incorrect. Another common mistake is to confuse the percentage who failed in at least one subject with the percentage who passed in both subjects. Always apply inclusion exclusion correctly and then subtract from 100% to get the group that passed both papers. Final Answer:The percentage of students who passed in both Mathematics and English is 44%.

Question 16

While purchasing one item costing Rs. 400 a buyer has to pay sales tax at 7%, and on another item costing Rs. 6400 the sales tax rate is 9%. Taking both items together, what is the average percentage rate of sales tax paid on the total purchase?

Accepted Answer

Introduction / Context:This problem checks understanding of weighted averages with percentages. Instead of simply averaging 7% and 9%, you must consider the different prices of the two items because the higher priced item contributes more to the total tax paid. This idea of a weighted average is very common in percentage and profit and loss questions in aptitude examinations. Given Data / Assumptions:Cost of first item = Rs. 400.Sales tax rate on first item = 7%.Cost of second item = Rs. 6400.Sales tax rate on second item = 9%.We assume tax is calculated on the listed price of each item independently. Concept / Approach:The key concept is weighted average percentage. The average tax rate on the combined purchase is:average tax rate = (total tax paid on both items / total cost of both items) * 100.We therefore first compute the tax on each item, then add them to get total tax, then divide by the total amount spent on the two items, and finally convert this fraction to a percentage and mixed fraction as required. Step-by-Step Solution:Step 1: Tax on first item = 7% of 400.That is (7 / 100) * 400 = Rs. 28.Step 2: Tax on second item = 9% of 6400.That is (9 / 100) * 6400 = Rs. 576.Step 3: Total tax paid = 28 + 576 = Rs. 604.Step 4: Total cost price of both items = 400 + 6400 = Rs. 6800.Step 5: Average tax rate on the whole purchase = (604 / 6800) * 100.Compute 604 / 6800 = 0.0888235 (approximately).Step 6: Convert 0.0888235 to percentage: 0.0888235 * 100 ≈ 8.88235%.Step 7: Express 8.88235% as a mixed fraction; this is exactly 8 15/17%. Verification / Alternative check:Notice that the second item is far more expensive and has the higher tax rate of 9%. Therefore the overall average must be closer to 9% than to 7%. The computed value 8 15/17% is indeed closer to 9%, which makes the answer reasonable and consistent with intuition. Why Other Options Are Wrong:2 13/17% and 3 2/17% are far too small and would imply extremely low tax relative to total cost, which does not match the given rates.5 13/12% is more than 6%, which is still too far from the weighted average that should lie between 7% and 9% and close to 9% because of the expensive second item.8% ignores the different costs and simply feels like a rough guess, not the precise weighted average. Common Pitfalls:A common mistake is to calculate the simple average (7% + 9%) / 2 = 8%, which is wrong because it does not account for the fact that the second item costs much more. Another frequent error is to round too aggressively during intermediate steps, which can disturb the exact fraction form. Always compute individual taxes, add them, and then divide by the combined base to get an accurate weighted average. Final Answer:The average percentage rate of sales tax on the combined purchase is 8 15/17%.

Question 17

Abhinav scores 80% in Physics and 66% in Chemistry, each subject having a maximum of 100 marks. Mathematics has a maximum of 200 marks. If Abhinav scores an overall 80% across all three subjects together, what percentage does he score in Mathematics?

Accepted Answer

Introduction / Context:This question checks your ability to handle percentages when different subjects carry different maximum marks. Instead of treating each subject equally, you must work with total marks and find the unknown score in Mathematics so that the overall percentage condition is satisfied. This type of problem is common in examination and report card style aptitude questions. Given Data / Assumptions:Maximum marks in Physics = 100.Maximum marks in Chemistry = 100.Maximum marks in Mathematics = 200.Abhinav scores 80% in Physics.Abhinav scores 66% in Chemistry.Overall percentage across all three subjects is 80% of total marks. Concept / Approach:First, convert each percentage to actual marks using the formula:obtained marks = (percentage / 100) * maximum marks.Then add all obtained marks to get Abhinav total marks. Since the total maximum marks across all three subjects are known, we can use the condition that his overall percentage is 80% to find the required marks in Mathematics. Finally, convert those Mathematics marks back into a percentage out of 200. Step-by-Step Solution:Step 1: Maximum total marks = 100 (Physics) + 100 (Chemistry) + 200 (Mathematics) = 400.Step 2: Marks in Physics = 80% of 100 = 0.80 * 100 = 80.Step 3: Marks in Chemistry = 66% of 100 = 0.66 * 100 = 66.Step 4: Let marks in Mathematics be M.Step 5: Overall percentage is 80%, so total marks obtained = 80% of 400 = 0.80 * 400 = 320.Step 6: Therefore 80 + 66 + M = 320.Step 7: So M = 320 – (80 + 66) = 320 – 146 = 174.Step 8: Percentage in Mathematics = (174 / 200) * 100 = 87%. Verification / Alternative check:Check the computed values: Physics 80 marks, Chemistry 66 marks, Mathematics 174 marks. Total = 320 out of 400. 320 / 400 * 100 = 80%, which matches the required overall percentage. Therefore 87% in Mathematics is fully consistent. Why Other Options Are Wrong:74% and 83% both give total marks less than 320 and so the overall percentage would be lower than 80%.84% gives Mathematics marks 168, making the total 314, which corresponds to 78.5% overall, not 80%.80% in Mathematics would give 160 marks and total 306, again below the required total marks. Common Pitfalls:Many students simply average the percentages of three subjects without weighting them according to maximum marks. This leads to incorrect results because Mathematics is worth twice as many marks as each of the other subjects. Always base your calculations on actual marks and total maximum marks when different papers have different weightage. Final Answer:Abhinav score in Mathematics is 87%.

Question 18

The price of rice increases by 25%, and as a result a man can purchase 5 kg less rice for Rs. 500 than before. What was the original price of rice per kilogram before the increase?

Accepted Answer

Introduction / Context:This is a standard percentage and unitary method problem that appears frequently in aptitude exams. A fixed amount of money now buys less quantity after a price increase. By relating the change in quantity to the percent change in price, you can work backwards to find the original price per kilogram of rice. Given Data / Assumptions:Total money available to buy rice = Rs. 500.Original price of rice per kilogram is unknown and is to be found.Price of rice increases by 25%.After the increase, the man can buy 5 kg less rice for the same Rs. 500. Concept / Approach:Let the original price of rice be P rupees per kilogram. Then the original quantity purchased is 500 / P kilograms. After a 25% increase, the new price becomes 1.25 * P rupees per kilogram, and the new quantity is 500 / (1.25 * P) kilograms. The difference in quantity is given to be 5 kg. Using this, we can form an equation and solve for P. This combines basic algebra with percentage increase ideas. Step-by-Step Solution:Step 1: Let the original price per kilogram be P rupees.Step 2: Original quantity the man could buy = 500 / P kilograms.Step 3: New price after 25% increase = 1.25 * P rupees per kilogram.Step 4: New quantity he can buy = 500 / (1.25 * P) kilograms.Step 5: According to the question, original quantity − new quantity = 5.So, 500 / P − 500 / (1.25 * P) = 5.Step 6: Simplify 500 / (1.25 * P) = 500 / (5P / 4) = 500 * 4 / (5P) = 400 / P.Step 7: Therefore, 500 / P − 400 / P = (500 − 400) / P = 100 / P = 5.Step 8: So 100 / P = 5 implies P = 100 / 5 = Rs. 20. Verification / Alternative check:If the original price is Rs. 20 per kilogram, original quantity = 500 / 20 = 25 kg. New price after 25% increase = 20 * 1.25 = Rs. 25 per kilogram. New quantity = 500 / 25 = 20 kg. The reduction in quantity is 25 − 20 = 5 kg, which matches the problem statement. So the solution is correct. Why Other Options Are Wrong:Rs. 24, Rs. 26, and Rs. 29 do not satisfy the given condition when you compute original and new quantities with a 25% increase. The difference in quantities will not be exactly 5 kg in those cases.Rs. 18 also fails to give a reduction of 5 kg when the same method is applied. Common Pitfalls:Candidates often try to work with percentage change directly on quantity instead of forming a clear equation. Forgetting that price and quantity are inversely related for a fixed budget also leads to mistakes. Another frequent error is miscalculating the new price after percentage increase. Always express the new price as (1 + percentage increase) times the original price and then use the difference in quantities to derive the correct equation. Final Answer:The original price of rice was Rs. 20 per kilogram.

Question 19

Evaluate the expression 30 + (0.0825 × 30) + (15% × 30), giving the final result as a decimal number.

Accepted Answer

Introduction / Context:This question is a straightforward numerical calculation involving decimals and percentages applied to the same base number. Such questions are used to test basic numerical manipulation skills including conversion between percentages and decimal multipliers and accurate arithmetic operations. Given Data / Assumptions:The expression to evaluate is 30 + (0.0825 × 30) + (15% × 30).All multiplications and additions are done using normal arithmetic rules.15% means 15 / 100 as a fraction or 0.15 as a decimal multiplier. Concept / Approach:The approach is to compute each term step by step. First compute 0.0825 × 30. Then compute 15% of 30, which is 0.15 × 30. Finally, add these two results to 30. The main idea is to understand that percentages can always be converted into decimal form before multiplication, which often makes calculations easier and clearer. Step-by-Step Solution:Step 1: Compute 0.0825 × 30.0.0825 × 30 = 2.475.Step 2: Convert 15% to decimal and multiply by 30.15% = 15 / 100 = 0.15, so 0.15 × 30 = 4.5.Step 3: Now add all three terms in the expression.30 + 2.475 + 4.5 = 36.975.Step 4: Therefore the value of the expression is 36.975. Verification / Alternative check:You can factor 30 from each term to check quickly: 30 + 0.0825 × 30 + 0.15 × 30 = 30 × (1 + 0.0825 + 0.15) = 30 × 1.2325. Now multiply 30 × 1.2325 = 36.975, which agrees with the earlier calculation. This confirms that no arithmetic error has occurred. Why Other Options Are Wrong:24.750 is roughly the value of 30 minus a percentage, not plus two percentage based increments.34.652 and 26.354 are arbitrary looking decimals and do not result from any correct combination of the given terms.32.475 ignores part of the increase from the percentage components and is smaller than the true sum. Common Pitfalls:A frequent mistake is misreading 0.0825 as 0.825 or 0.00825, which drastically changes the product. Another common error is to treat 15% of 30 as 15 / 30 instead of 15 / 100 × 30. Students also sometimes forget to add all terms correctly or mishandle decimal addition. Writing each step clearly and aligning decimal points during addition helps avoid such errors. Final Answer:The value of the expression is 36.975.

Question 20

The price of a cycle is first reduced by 25% and then the new price is further reduced by 20%. These two successive reductions together are equivalent to a single reduction of what percentage on the original price?

Accepted Answer

Introduction / Context:This problem tests understanding of successive percentage changes. When a price is reduced by one percentage and then reduced again by another percentage, the net effect is not the simple sum of the two percentages. Instead, you must multiply the remaining fractions of the price. This is a very common concept in discount, profit and loss, and percentage chapters in quantitative aptitude. Given Data / Assumptions:Initial price of the cycle is taken as some convenient value, say Rs. 100.First reduction is 25% of the current price.Second reduction is 20% of the new price after the first reduction.We are asked to find the single equivalent percentage reduction compared to the original price. Concept / Approach:If a quantity is reduced by x%, then the remaining part is (1 − x / 100) times the original. For two successive reductions x% and y%, the final multiplier is (1 − x / 100) * (1 − y / 100). The equivalent single reduction R% is found from final multiplier = 1 − R / 100. In this question, we apply this to 25% and 20% reductions on a starting price of 100 for easy calculation. Step-by-Step Solution:Step 1: Assume original price = Rs. 100.Step 2: After a 25% reduction, new price = 100 * (1 − 25 / 100) = 100 * 0.75 = Rs. 75.Step 3: Now reduce this new price by 20%.20% of 75 = 0.20 * 75 = 15.Step 4: Final price after second reduction = 75 − 15 = Rs. 60.Step 5: Compare final price with original price.Original price = 100, final price = 60, so total reduction = 100 − 60 = 40.Step 6: Equivalent single reduction percentage = (40 / 100) * 100 = 40%. Verification / Alternative check:Alternatively, use the formula directly: final multiplier = (1 − 25 / 100) * (1 − 20 / 100) = 0.75 * 0.80 = 0.60. Thus 1 − R / 100 = 0.60, so R / 100 = 0.40 and R = 40%. Both methods agree and confirm the answer. Why Other Options Are Wrong:45% is found by wrong simple addition of 25% and 20%, which always overestimates the combined reduction.35% and 32.5% underestimate the combined effect and do not match the calculated final price of 60 out of 100.42% is a random intermediate guess and does not correspond to multiplying the reduction factors correctly. Common Pitfalls:Many candidates simply add percentages, thinking that 25% + 20% = 45% must be the total reduction. This is incorrect because the second reduction applies to a already reduced price. The correct approach is always to convert each change to a multiplier, multiply them together, and then convert the final multiplier into an equivalent single percentage change. Final Answer:The two successive reductions are equivalent to a single reduction of 40% on the original price.

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