Practice Questions
Concept Explanation
Mixed percentage problems combine two or more ideas: successive change, comparison, population, marks, income, or error — typical of final-round placement aptitude sections.
Strategy
- Translate words into multipliers (e.g. "20% more" → ×1.2).
- Identify the correct base for each percentage.
- Draw a quick table for multi-step problems.
Alligation Link
When mixing two solutions with different concentrations, weighted averages connect to percentage concepts.
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Q1 EasyA fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:Explanation60% of original = 420 → original = 420 × 100/60 = 700 apples.
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Q2 EasyIf A = x% of y and B = y% of x, then which of the following is true?Explanationx% of y = xy/100 and y% of x = xy/100. Therefore A = B always.
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Q3 MediumA 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 by running = 110 − (3×4 + 8×6) = 50. Required % = (50/110) × 100 = 45(5/11)%.
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Q4 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 marks be (x + 9) and x. Then x + 9 = (56/100)(2x + 9) → x = 33. Marks are 42 and 33.
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Q5 MediumWhat percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?ExplanationNumbers with unit digit 1 or 9: 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69 — total 14. Percentage = (14/70) × 100 = 20%.
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Q6 MediumIf 30% of A is 40% of B, then A:B is:Explanation0.3A = 0.4B → A/B = 4/3.
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Q7 MediumA number is increased by 20%, then the result is decreased by 25%. Net change is:Explanation1.2 × 0.75 = 0.9 → 10% decrease.
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Q8 MediumA shop marks goods 40% above CP and gives 20% discount. Profit percent is:ExplanationSP = 1.4 × 0.8 = 1.12 × CP → 12% profit.
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Q9 MediumSuccessive discounts of 10% and 20% equal a single discount of:ExplanationRemaining = 0.9 × 0.8 = 0.72 → 28% discount.
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Q10 MediumTown population 80,000: +15% then −10%. Final population is:Explanation80,000 × 1.15 × 0.9 = 82,800.
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Q11 HardPopulation 50,000 increases 10% annually for 2 years. Final population is:Explanation50,000 × 1.1² = 60,500.
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Q12 HardIn an exam, A scores 20% more than B and B scores 25% less than C. If C scored 400, A scored:ExplanationB = 0.75 × 400 = 300. A = 1.2 × 300 = 360.
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Q13 HardA student needs 40% to pass. He gets 35% and fails by 40 marks. Maximum marks are:Explanation5% of max = 40 → max = 800.
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Q14 HardIf 20% of (A + B) = 50% of (A − B), then A:B is:Explanation0.2(A+B) = 0.5(A−B) → 2A+2B = 5A−5B → 7B = 3A → A:B = 7:3.
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DS1 Medium
In a campus cricket match, the scorer needs to find what fraction of a batsman's total came from running. What percent of his total score did he make by running between the wickets?
Statement IThe batsman scored 110 runs in total, including 3 boundaries and 8 sixes.
Statement IIEach boundary counts as 4 runs and each six counts as 6 runs; all remaining runs were scored by running.
ExplanationRuns by running = 110 − (3×4 + 8×6) = 50. Percentage = (50/110) × 100 = 45(5/11)%. Statement I alone gives all data needed. -
DS2 Medium
Two candidates appeared for a placement test. What are their individual marks?
Statement IOne candidate scored 9 marks more than the other.
Statement IIThe higher scorer's marks equal 56% of the sum of both candidates' marks.
ExplanationLet marks be (x + 9) and x. Then x + 9 = 0.56(2x + 9) → x = 33, marks are 42 and 33. Both statements are needed.
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DS3 Medium
A retailer applies successive price changes on an article. What is the net percentage change in the selling price?
Statement IThe marked price is 40% above the cost price of Rs. 500.
Statement IIA discount of 20% on the marked price is offered to the customer.
ExplanationMP = 500 × 1.4 = Rs. 700. SP = 700 × 0.8 = Rs. 560. Profit = 12% on CP. Both statements are needed. -
DS4 Hard
A town planner projects population growth over two years. What is the final population after the growth period?
Statement IThe initial population of the town is 50,000.
Statement IIThe population grows at a rate of 10% per year for exactly 2 years.
ExplanationFinal population = 50,000 × 1.1² = 60,500. Both the initial count and growth rate/duration are required.