Practice Questions
Concept Explanation
Percentage means "per hundred." It expresses a part of a whole as a fraction with denominator 100. Placement papers frequently test fraction-to-percent, decimal-to-percent, and finding a percentage of a quantity.
Core Conversions
- Fraction to %: multiply by 100. Example: 3/4 = 0.75 = 75%.
- Decimal to %: multiply by 100. Example: 0.075 = 7.5%.
- % to fraction: divide by 100. Example: 25% = 25/100 = 1/4.
Finding a Percentage of a Number
x% of N = (x/100) × N. Example: 20% of 450 = (20/100) × 450 = 90.
Reverse: Number from Its Percentage
If x% of a number is V, then number = V × (100/x). Example: 25% of N = 75 → N = 75 × 4 = 300.
What Percent One Number Is of Another
Required % = (part/whole) × 100. Example: 45 is what % of 180? → (45/180) × 100 = 25%.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33⅓% |
| 3/8 | 0.375 | 37.5% |
| 2/5 | 0.4 | 40% |
| 5/8 | 0.625 | 62.5% |
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Q1 EasyA fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:ExplanationAfter selling 40%, 60% remain. If 60% of the original stock is 420, then original = 420 × (100/60) = 700 apples.
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Q2 EasyIf 25% of a number is 75, what is the number?ExplanationLet the number be N. (25/100) × N = 75, so N = 75 × 4 = 300.
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Q3 EasyA student scored 108 marks out of 360 in an examination. What is the percentage score obtained?ExplanationPercentage score = (108/360) × 100 = 30%.
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Q4 EasyWhat is 20% of 450?Explanation20% of 450 = (20/100) × 450 = 90.
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Q5 EasyExpress 0.075 as a percentage.Explanation0.075 × 100 = 7.5%.
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Q6 MediumIf A = x% of y and B = y% of x, then which of the following is true?Explanationx% of y = (x/100) × y and y% of x = (y/100) × x. Both equal xy/100, so A = B always.
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Q7 MediumTwo students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:ExplanationLet the marks be x and (x + 9). Then x + 9 = (56/100)(2x + 9). Solving gives x = 33, so the marks are 42 and 33.
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Q8 MediumWhat percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?ExplanationNumbers with 1 or 9 in the unit place from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 — 14 numbers. Required percentage = (14/70) × 100 = 20%.
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Q9 MediumIf 20% of a = b, then b% of 20 is the same as:Explanation20% of a = b means b = a/5. Then b% of 20 = (a/500) × 20 = a/25 = 4% of a.
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Q10 MediumIn a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?ExplanationStudents above 8 years = 48 + (2/3) × 48 = 80. This is 80% of total enrolment. Total students = 80 × (100/80) = 100.
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Q11 MediumIf x% of 250 is 40, find the value of x.Explanation(x/100) × 250 = 40 → x = (40 × 100)/250 = 16.
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Q12 MediumWhich fraction is equivalent to 37.5%?Explanation37.5% = 37.5/100 = 375/1000 = 3/8.
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Q13 HardA batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?ExplanationRuns from boundaries and sixes = (3 × 4) + (8 × 6) = 60. Runs by running = 110 − 60 = 50. Required percentage = (50/110) × 100 = 500/11 = 45 5/11%.
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Q14 HardTwo numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.Explanation0.05A + 0.04B = (2/3)(0.06A + 0.08B). Simplifying gives A/B = 4/3, so the required ratio is 4 : 3.
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DS1 Easy
What is the value of N?
Statement IN is 30% of 400.
Statement IIN is 20 more than 100.
ExplanationStatement I: N = 0.30 × 400 = 120. Statement II: N = 100 + 20 = 120. Each statement alone gives N = 120. -
DS2 Medium
An HR analytics worksheet asks what percent one quantity is of another. What percent is x of y?
Statement IThe value of x is 45.
Statement IIThe value of y is 180.
ExplanationRequired value = (x/y) × 100. Statement I gives x but not y; Statement II gives y but not x. Both together give (45/180) × 100 = 25%.
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DS3 Medium
In a reverse-percentage practice set, candidates must find an unknown number. What is the number?
Statement I20% of the number is 84.
Statement IIThe number exceeds 400 by 20.
ExplanationStatement I: N = 84 × 5 = 420. Statement II: N = 420. Each statement alone is sufficient. -
DS4 Hard
A placement trainer asks whether a candidate's percentage score crosses the halfway mark. Is the percentage greater than 50%?
Statement IThe decimal equivalent of the percentage is 0.55.
Statement IIThe fraction equivalent of the percentage is 11/20.
ExplanationStatement I gives 55%. Statement II: 11/20 = 0.55 = 55%. Each statement alone answers yes.