Question 1

Reverse percentage to find the base number: If 35% of a number is equal to 112, what is the original number?

Accepted Answer

Introduction / Context:This reverse-percentage question asks you to determine the base quantity when a known percentage of it is given. Such problems are frequently used in finance, discounting, and statistics for back-calculations from partial information. Given Data / Assumptions: 35% of an unknown number N equals 112. We assume standard percentage definition: p% of N = (p/100) * N. Concept / Approach:Translate the statement into an equation: 0.35 * N = 112. Solve for N by dividing 112 by 0.35. Always ensure the division is done precisely, because common decimal errors can lead to wrong options being selected. Step-by-Step Solution: 0.35 * N = 112 N = 112 / 0.35 N = 320 Verification / Alternative check:Check by forward computation: 35% of 320 is 0.35 * 320 = 112, which matches the given condition exactly. Why Other Options Are Wrong:300 yields 0.35 * 300 = 105 (too low). 380 gives 133 (too high). 35 is just the percentage, not the number. 280 gives 98 (too low). Only 320 satisfies the equation exactly. Common Pitfalls:Accidentally computing 320 * 0.53 or mixing 35 and 0.35. Always convert percentages to decimal multipliers correctly: 35% → 0.35. Final Answer:320

Question 2

Number equals its own 75% plus 75: Seventy-five percent of a number, when added to 75, equals the number itself. What is that number?

Accepted Answer

Introduction / Context:This problem is a linear equation framed in percentage language. The number is equal to a fraction (75%) of itself plus a constant (75). Translating words into an algebraic equation is the main skill tested here, followed by simple solving. Given Data / Assumptions: If N is the number, then 75% of N plus 75 equals N. 75% = 0.75 in decimal form. Concept / Approach:Write the statement as an equation: 0.75N + 75 = N. Isolate N by moving like terms and then dividing by the coefficient. Double-check computation to avoid arithmetic slips when handling decimals and constants together. Step-by-Step Solution: 0.75N + 75 = N 75 = N − 0.75N = 0.25N N = 75 / 0.25 = 300 Verification / Alternative check:Compute 75% of 300 = 225; add 75 to get 300, which equals the original number, confirming the solution. Why Other Options Are Wrong:280, 305, 360, and 400 do not satisfy 0.75N + 75 = N. Substitution will show mismatches in each case. Common Pitfalls:Forgetting to convert 75% to 0.75 or mismanaging the subtraction step N − 0.75N. Keeping track of decimal places is crucial in percentage equations. Final Answer:300

Question 3

Comparative percentage: income difference framed correctly: Mukul’s income is 10% more than Sunil’s income. By what percent is Sunil’s income less than Mukul’s income?

Accepted Answer

Introduction / Context:A classic comparison trap: “A is 10% more than B” is not symmetric with “B is 10% less than A.” The percent decrease from the larger reference is different because the base changes. This question assesses understanding of base dependence in percentage comparisons. Given Data / Assumptions: Mukul’s income M = 1.10 * Sunil’s income S. We must find the percentage by which S is less than M, i.e., (M − S)/M * 100%. Concept / Approach:Set S = 100 units for simplicity. Then M = 110. The difference is 10. Express the difference as a percentage of M (the larger base) since the question asks “how much less than Mukul’s.” This yields a non-intuitive 9.09% instead of 10%. Step-by-Step Solution: Assume S = 100 ⇒ M = 110 Difference = M − S = 10 Percent less than M = 10 / 110 * 100% = 9.09% Verification / Alternative check:Algebraic: If M = 1.10S, then (M − S)/M = (0.10S)/(1.10S) = 1/11 = 9.09%. Why Other Options Are Wrong:10% mistakenly uses Sunil’s base; 8.09%, 7.90%, 7.09% are arbitrary and do not match the correct ratio 1/11. Common Pitfalls:Using the same percent in reverse. Always pay attention to the requested reference base for “more than” versus “less than.” Final Answer:9.09%

Question 4

Literacy rate among women from aggregated data: A country has a total population of 2,94,000, out of which 1,50,000 are males. Of every 100 males, 98 can read and write. Overall, 53% of the total population is literate. What percentage of women can …

Accepted Answer

Introduction / Context:This data-sufficiency style percentage problem requires breaking totals into male and female groups, using given male literacy rates and the overall literacy percentage to deduce the counterpart female literacy. It mirrors census-style computations used in demographics and policy planning. Given Data / Assumptions: Total population = 2,94,000. Males = 1,50,000 ⇒ Females = 2,94,000 − 1,50,000 = 1,44,000. Male literacy: 98% of males are literate. Overall literacy: 53% of the total population. Concept / Approach:Compute male literates first. Compute total literates from the overall percentage. Subtract male literates from total literates to get female literates. Finally, divide female literates by total females and convert to percentage. Step-by-Step Solution: Male literates = 0.98 * 1,50,000 = 1,47,000 Total literates = 0.53 * 2,94,000 = 1,55,820 Female literates = 1,55,820 − 1,47,000 = 8,820 Female literacy% = 8,820 / 1,44,000 * 100% = 6.125% Verification / Alternative check:Sum literacy check: 1,47,000 (male) + 8,820 (female) = 1,55,820, matching overall literates, confirming internal consistency. Why Other Options Are Wrong:5.125%, 6.000%, 4.125%, 7.000% do not match the exact computation from the balanced totals. Common Pitfalls:Applying 53% separately to males and females or miscomputing female count as 1,40,000. Always keep track of group sizes and apply percentages carefully to the correct bases. Final Answer:6.125%

Question 5

Nested percentage of a percentage: If 16% of 40% of a number equals 8, what is the number?

Accepted Answer

Introduction / Context:Here, a percentage is taken of another percentage of a number. The key is to translate nested percentages into a single multiplier applied to the unknown. This technique is common in multi-stage discount or tax problems as well. Given Data / Assumptions:Let the number be N. We are told 16% of 40% of N equals 8. Concept / Approach:Convert the percentages to decimals and multiply: 16% of 40% of N is (0.16 * 0.40) * N = 0.064N. Then set 0.064N = 8 and solve for N by dividing both sides by 0.064. Step-by-Step Solution: 0.16 * 0.40 = 0.064 0.064 * N = 8 N = 8 / 0.064 = 125 Verification / Alternative check:Check forward: 40% of 125 = 50; 16% of 50 = 8. This matches the requirement exactly. Why Other Options Are Wrong:200 gives 0.064 * 200 = 12.8; 225 gives 14.4; 320 gives 20.48; 100 gives 6.4. Only 125 gives 8. Common Pitfalls:Adding percentages (16 + 40) instead of multiplying, or converting 16% to 16 rather than 0.16. Always convert percentages to decimal multipliers when applied to numbers. Final Answer:125

Question 6

Number exceeds its own 20% by 40: A number is greater than 20% of itself by 40. What is that number?

Accepted Answer

Introduction / Context:Translate a verbal statement about a number’s relationship to its own percentage into an algebraic equation. These appear often in profit-loss language and growth problems where a quantity is compared to a fraction of itself and an absolute difference is given. Given Data / Assumptions:Let N be the number. “Exceeds 20% of itself by 40” means N − 0.20N = 40. Concept / Approach:Compute the left side: N − 0.20N = 0.80N. Equate to 40 and solve for N by dividing. This yields a quick one-step calculation once properly translated. Step-by-Step Solution: N − 0.20N = 40 0.80N = 40 N = 40 / 0.80 = 50 Verification / Alternative check:20% of 50 is 10; 50 is 40 more than 10, so the statement holds perfectly. Why Other Options Are Wrong:60 gives 12 as 20% and the difference would be 48; 80 gives diff 64; 320 gives diff 256; 40 is not consistent with the equation. Common Pitfalls:Misreading “exceeds … by 40” as a percentage or using the wrong base. Keep distinction between absolute differences and percentage relations clear. Final Answer:50

Question 7

Convert mixed percentage to a fraction: Express 8 1/3% as a fraction in simplest form.

Accepted Answer

Introduction / Context:Converting a percentage into a fraction is a common operation in aptitude, especially for mental math. Mixed percentages like 8 1/3% require converting the mixed number to an improper fraction first and then dividing by 100 to reach a final fraction form. Given Data / Assumptions:We are given 8 1/3%, which equals 8.333...%. Concept / Approach:First, convert 8 1/3 to an improper fraction: 8 1/3 = 25/3. Then, interpret percent as “per 100”: (25/3)%. That equals (25/3) / 100 = 25 / (3 * 100) = 25/300. Finally, simplify 25/300 by dividing numerator and denominator by 25, giving 1/12. Step-by-Step Solution: 8 1/3% = (25/3)% (25/3)% = (25/3) / 100 = 25 / 300 25 / 300 simplifies to 1 / 12 Verification / Alternative check:As a decimal, 8 1/3% = 0.083333... which equals 1/12 (since 1/12 = 0.083333...). Why Other Options Are Wrong:25/3 is the percent value as a fraction, not the fraction of a whole. 3/25 = 12% (incorrect). 1/4 = 25%. 2/15 ≈ 13.33%. Common Pitfalls:Forgetting to divide by 100 when converting from percent to fraction. Always apply the “per hundred” step explicitly. Final Answer:1/12

Question 8

Convert decimal to percent correctly: What is 0.025 when expressed as a rate percent?

Accepted Answer

Introduction / Context:Decimal-to-percent conversion is fundamental in percentage arithmetic. Multiplying a decimal by 100 converts it to percent. This question reinforces accuracy with small decimals where misplaced decimal points are common mistakes. Given Data / Assumptions:The decimal is 0.025. Concept / Approach:Percent means “per hundred.” Therefore, to express a decimal d as a percent, compute d * 100% and append the percent symbol. Ensure the decimal point moves two places to the right during multiplication by 100. Step-by-Step Solution: 0.025 * 100% = 2.5% Hence, 0.025 equals 2.5% as a rate percent. Verification / Alternative check:Reverse: 2.5% back to decimal is 2.5/100 = 0.025, confirming the conversion is consistent both ways. Why Other Options Are Wrong:0.25% corresponds to 0.0025. 37.5% or 25% are unrelated. Formatting duplicates may confuse, but the numerically correct percent is 2.5% only. Common Pitfalls:Moving the decimal point one place instead of two, or forgetting the percent symbol. Always multiply by 100 and then attach %. Final Answer:2.5%

Question 9

Basic conversion: decimal to percent: Express 0.02 as a percentage.

Accepted Answer

Introduction / Context:This is a fundamental conversion: turning a decimal into a percentage. It appears in many entry-level quantitative aptitude tests to ensure comfort with shifting between decimal and percentage forms. Given Data / Assumptions:The decimal given is 0.02. Concept / Approach:To convert a decimal to a percentage, multiply by 100 and append the percent sign. So 0.02 * 100% equals 2%. The mental shortcut is moving the decimal point two places to the right and adding %. Step-by-Step Solution: 0.02 * 100% = 2% Verification / Alternative check:Reverse conversion: 2% = 2/100 = 0.02. This confirms consistency. Why Other Options Are Wrong:20% would be 0.2; 0.02% equals 0.0002; 0.2% is 0.002; 200% equals 2. All are incorrect conversions of 0.02. Common Pitfalls:Forgetting to multiply by 100 or accidentally multiplying by 10 only. Keep the “two decimal places right” rule in mind for decimals to percent. Final Answer:2%

Question 10

Fraction-to-percent comparison: What percentage of 2/7 is 1/35?

Accepted Answer

Introduction / Context:This requires comparing two fractions by forming a ratio and then converting the ratio to a percentage. It is a clean illustration of “what percent of A is B,” which translates to (B/A)*100%. Given Data / Assumptions:We need percent = (1/35) ÷ (2/7) * 100%. Concept / Approach:Division of fractions becomes multiplication by the reciprocal. Compute (1/35) * (7/2) and then multiply by 100 to express as percent. Simplify carefully to avoid mistakes in cancellation. Step-by-Step Solution: (1/35) ÷ (2/7) = (1/35) * (7/2) = 7 / 70 = 1/10 Percent = (1/10) * 100% = 10% Verification / Alternative check:Equivalently, note that 1/35 is exactly one-tenth of 2/7 (since 2/7 = 10/35). Hence 10% is immediate. Why Other Options Are Wrong:2.5%, 5%, 20%, and 25% do not equal the exact ratio 1/10. Only 10% matches. Common Pitfalls:Inverting the wrong fraction or accidentally adding fractions. Always write the percent question as (part/whole)*100%. Final Answer:10%

Question 11

Tiny proportion in mixed units: What percent of 7.2 kg is 18 grams? (Use 1 kg = 1000 g)

Accepted Answer

Introduction / Context:This tests unit conversion and percentage computation. When quantities are given in different units (kilograms and grams), convert them to a common unit before calculating the percentage, to avoid scale mismatches. Given Data / Assumptions: Total = 7.2 kg = 7200 g. Part = 18 g. Concept / Approach:Percent = (part / whole) * 100%. After converting 7.2 kg to 7200 g, compute 18/7200 and multiply by 100 to get the percentage. Keep an eye on decimal placement because the values are small. Step-by-Step Solution: Percent = (18 / 7200) * 100% = (18 * 100) / 7200 % = 1800 / 7200 % = 0.25% Verification / Alternative check:Reduce 18/7200 = 1/400; (1/400)*100% = 0.25%. This fractional route provides a neat mental math check. Why Other Options Are Wrong:0.025% and 0.0025% are off by factors of 10 or 100; 2.5% and 25% are large by orders of magnitude relative to 18 out of 7200. Common Pitfalls:Forgetting to convert kilograms to grams or mixing up numerator and denominator when forming the percentage fraction. Final Answer:0.25%

Question 12

Find the missing percent: ?% of 130 equals 10.4. What is the value of ?

Accepted Answer

Introduction / Context:This is a direct percent-back calculation: if some percentage of a quantity is known, recover the rate. Such problems are common in discounts, interest, and concentration questions. Given Data / Assumptions:Let p be the percentage value (not decimal). Then p% of 130 equals 10.4. Concept / Approach:Translate to equation: (p/100) * 130 = 10.4. Solve for p by isolating it: p = 10.4 * 100 / 130. Simplify the fraction carefully to avoid arithmetic errors. Step-by-Step Solution: (p/100) * 130 = 10.4 p = 10.4 * 100 / 130 p = 1040 / 130 = 8 Verification / Alternative check:8% of 130 = 0.08 * 130 = 10.4. This confirms correctness. Why Other Options Are Wrong:0.8 and 0.08 confuse percent with decimal fraction; 80 is ten times larger than required; 0.8% would yield only 1.04. Common Pitfalls:Forgetting to multiply by 100 when converting from decimal proportion to percent, or misplacing the decimal during division. Final Answer:8

Question 13

Convert a small percent to a fraction: What fraction is equivalent to 2/5%? (Express in simplest form.)

Accepted Answer

Introduction / Context:Percent to fraction conversion requires dividing by 100. When the percent itself is a fraction (like 2/5%), divide that fraction by 100 to find the fraction of a whole. Then simplify to the lowest terms. Given Data / Assumptions:We have 2/5%. Concept / Approach:Convert percent to a pure fraction: (2/5)% = (2/5)/100 = 2 / 500. Simplify by dividing numerator and denominator by 2 to obtain 1/250. Step-by-Step Solution: (2/5)% = (2/5) / 100 = 2 / 500 Simplify 2/500 ⇒ 1/250 Verification / Alternative check:As a decimal: 2/5% = 0.4% = 0.004. Fraction 1/250 = 0.004, confirming equivalence. Why Other Options Are Wrong:1/40 = 2.5%; 1/125 = 0.8%; 1/500 = 0.2%; 2/25 = 8%. None match 0.4%. Common Pitfalls:Forgetting the “per hundred” and treating 2/5% as 2/5 directly, or converting to 1/5 incorrectly. Final Answer:1/250

Question 14

Find equivalent percent: 30% of 140 equals ?% of 840. Find the missing percent.

Accepted Answer

Introduction / Context:This question equates two amounts computed as percentages of different bases. The technique is to compute the left side numerically, then express that value as a percentage of the new base on the right side. Given Data / Assumptions:Compute 30% of 140 and set it equal to x% of 840. Solve for x. Concept / Approach:Let x be the required percent. Then (x/100)*840 = 0.30*140. Solve for x: x = (0.30*140*100)/840. Simplify to avoid mistakes. Step-by-Step Solution: Left value = 0.30 * 140 = 42 42 = (x/100) * 840 x = 42 * 100 / 840 = 5% Verification / Alternative check:Check: 5% of 840 = 0.05 * 840 = 42, matching the left side exactly. Why Other Options Are Wrong:15%, 24%, and 60% would give 126, 201.6, and 504 respectively—none equal 42. 3.5% gives 29.4, also incorrect. Common Pitfalls:Setting up the equation with reversed bases or forgetting to multiply by 100 when solving for the percent variable. Final Answer:5%

Question 15

Solve for an unknown percent in a mixed expression: Find ? such that ?% of 250 + 25% of 68 = 67.

Accepted Answer

Introduction / Context:We have a linear equation in an unknown percentage. Break the expression into two parts: the unknown portion applied to one number, and a fixed percentage applied to another number. Then solve algebraically for the unknown percentage. Given Data / Assumptions: ?% of 250 + 25% of 68 = 67. Let p be the unknown percent value (not decimal). Concept / Approach:Compute the known part first: 25% of 68. Then subtract it from 67 to isolate p% of 250. Finally, convert the resulting percent-of relation into a direct percent p by scaling. Step-by-Step Solution: 25% of 68 = 0.25 * 68 = 17 So, p% of 250 = 67 − 17 = 50 (p/100) * 250 = 50 ⇒ p = 50 * 100 / 250 = 20 Verification / Alternative check:Check: 20% of 250 = 50; 25% of 68 = 17; total = 67. Verified. Why Other Options Are Wrong:10, 12, 15, 25 yield totals other than 67 when substituted, so they do not satisfy the equation. Common Pitfalls:Confusing percent with decimal or failing to compute 25% of 68 accurately. Always isolate the unknown term methodically. Final Answer:20

Question 16

Percent of a percent (self-multiplication): What is 25% of 25% equal to (expressed as a decimal)?

Accepted Answer

Introduction / Context:When a percentage is applied to another percentage, the result is their product as decimals. This illustrates that “percent of percent” rapidly leads to smaller numbers due to multiplication of two fractions less than 1. Given Data / Assumptions:Compute 25% of 25%. Concept / Approach:Convert percentages to decimals before multiplying: 25% = 0.25. Then 25% of 25% = 0.25 * 0.25 = 0.0625. The question explicitly asks for decimal form, not percent or fraction. Step-by-Step Solution: 25% = 0.25 25% of 25% = 0.25 * 0.25 = 0.0625 Verification / Alternative check:As a percent, 0.0625 = 6.25%. So 25% of 25% equals 6.25% of a whole, matching another common representation. Why Other Options Are Wrong:6.25 is 625%; 0.625 is 62.5%; 0.000625 is 0.0625%; 0.25 is just 25% itself. Common Pitfalls:Adding 25 and 25 to get 50 or forgetting to convert to decimals. Always multiply the decimal equivalents for “of.” Final Answer:0.0625

Question 17

Tiny percent of a large number: The number 0.05 is what percent of 20?

Accepted Answer

Introduction / Context:This is a ratio-to-percent conversion. We compare a small quantity (0.05) to a larger base (20) and then scale by 100 to express the relationship in percent terms. This is common in error rates and very low concentration problems. Given Data / Assumptions:Compute percent = (0.05 / 20) * 100%. Concept / Approach:Form the fraction of the part over the whole and multiply by 100. Ensure correct decimal manipulation because the numbers differ by orders of magnitude. Step-by-Step Solution: (0.05 / 20) * 100% = (0.05 * 100) / 20 % = 5 / 20 % = 0.25% Verification / Alternative check:As a decimal, 0.25% = 0.0025. 0.0025 * 20 = 0.05, which confirms the calculation. Why Other Options Are Wrong:2.5% corresponds to 0.5/20; 25% corresponds to 5/20; 0.025% and 0.5% are off by factors of 10 or 2 relative to 0.25%. Common Pitfalls:Forgetting to multiply by 100 to convert to percent or misplacing the decimal point during division. Final Answer:0.25%

Question 18

Solve for a multiplier from a percent-of relation: Find the value of ? that satisfies: ? × 15 = 37.5% of 220.

Accepted Answer

Introduction / Context:This problem links a product to a percentage of a known number. The approach is to first compute the percentage value on the right-hand side, then divide by the given factor to isolate the unknown. It is a basic algebra step often used in scaling and proportion exercises. Given Data / Assumptions:We must solve ? * 15 = 37.5% of 220. Concept / Approach:Compute 37.5% of 220 using decimal form: 37.5% = 0.375. Then 0.375 * 220 gives the RHS. Finally, divide by 15 to obtain the unknown ?. Keep calculations precise to avoid rounding errors. Step-by-Step Solution: 37.5% of 220 = 0.375 * 220 = 82.5 So ? * 15 = 82.5 ⇒ ? = 82.5 / 15 = 5.5 Verification / Alternative check:Back-substitute: 5.5 * 15 = 82.5, which matches the computed percentage value. Consistency confirmed. Why Other Options Are Wrong:82.5 is the RHS value, not ?. 8250 is a misplaced scaling. 11 would give 165 on the left. 7.5 would give 112.5, both inconsistent with 82.5. Common Pitfalls:Using 0.35 instead of 0.375 for 37.5% or forgetting to divide by 15 at the final step. Final Answer:5.5

Question 19

Percentage conversion and scaling: Evaluate (0.756 × 3/4) and express the result as a rate percent.

Accepted Answer

Introduction / Context:This problem checks comfort with decimal–fraction multiplication and converting the final value into a percentage. The phrase “rate percent” simply means “express the numerical value as a percent.”Given Data / Assumptions:Expression to compute: (0.756) * (3/4).Convert the final decimal to a percent by multiplying by 100.No rounding instruction is given; the multiplication yields an exact terminating decimal.Concept / Approach:First multiply the decimal and the fraction. Then convert the resulting decimal into percent. Remember: x as a percent = x * 100%.Step-by-Step Solution:Compute the product: 0.756 * 3/4 = 0.756 * 0.75.0.756 * 0.75 = 0.567 (since 756 * 75 = 56700 and we place three decimal digits).Convert to percent: 0.567 * 100% = 56.7%.Verification / Alternative check:Another path: 3/4 of 0.756 means take 75% of 0.756. Ten percent of 0.756 is 0.0756, so 70% is 0.5292, and 5% is 0.0378. Add: 0.5292 + 0.0378 = 0.567. Then to percent: 56.7%.Why Other Options Are Wrong:18.9% and 37.8% correspond to taking 1/4 or 1/2 instead of 3/4.75% confuses the fraction 3/4 with the final numeric result.42.5% is an arbitrary distractor not supported by the computation.Common Pitfalls:Mixing the order of operations or forgetting to convert the final decimal to percent. Keep the multiplication separate from the percent conversion step.Final Answer:56.7%

Question 20

Percentage equation with an unknown in the denominator: Solve 30% of (80 / ?) = 24 and find the value of the missing number.

Accepted Answer

Introduction / Context:This item tests translating a short verbal/compact expression into an equation and solving for an unknown that appears in the denominator. It is a direct percentage application with basic algebraic isolation.Given Data / Assumptions:Equation: 30% of (80 / ?) = 24.30% means 0.30.The unknown is positive and nonzero.Concept / Approach:Replace “30% of” by multiplication with 0.30. Then isolate the unknown by standard algebra. Because 80 and 30% are compatible numbers, the arithmetic is clean.Step-by-Step Solution:0.30 * (80 / ?) = 24.Compute 0.30 * 80 = 24, so the left side becomes 24 / ?.Thus 24 / ? = 24 ⇒ ? = 1.Verification / Alternative check:Plugging back: 30% of (80 / 1) = 30% of 80 = 24, which matches the right-hand side exactly.Why Other Options Are Wrong:3/10, 3/17, 2, 5/8: Substituting these values does not produce 24 on the right once evaluated.Common Pitfalls:Forgetting that “of” means multiply; or attempting to divide 30% by the unknown rather than multiplying 30% with (80 / ?).Final Answer:1

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