CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus – Page 4
All 40 Percentages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 4 of 10.
A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was
Answer: B. 95000
Solution — first steps
Step 1. Convert each reported average bonus into a total bonus for that employee block.
Step 2. First 30 total =30×their average; last 30 total =30×their average.
Step 2. First 30 total =30×their average; last 30 total =30×their average.
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A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
Answer: 340
Solution — first steps
Step 1. Let total fruit count be T; mangoes=2T/5. Write apples A and bananas B, so A+B=3T/5.
Step 2. Total sold is T/5+96+2A/5=T/2. Therefore A=3T/4−240 and B=240−3T/20.
Step 2. Total sold is T/5+96+2A/5=T/2. Therefore A=3T/4−240 and B=240−3T/20.
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Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
Answer: B. 20808
Solution — first steps
Step 1. At 4% per annum compounded half-yearly, each half-year multiplier is1.02.
Step 2. Anil receives 22000(1.02)^12 after six years.
Step 2. Anil receives 22000(1.02)^12 after six years.
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After two successive increments, Gopal’s salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was ?
Answer: A. 25
Solution — first steps
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A 300 litre container. Water x litres, rest milk. Remove 2x litres solution, refill water. Final solution 72% milk. Find x.
Answer: 30
Solution — first steps
Set up quadratic: x² - 450x +12600=0 x=30
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Last day solving checklist
- Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
- Form the relationships. Translate each given condition into an equation or restriction.
- Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
- Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
- Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.
All 16 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Repeated fractional replacement | 6 | CAT 2021 S2 Q4 | 6 | 10.71% |
| 2 | Compound growth factors and equivalent simple interest | 6 | CAT 2021 S1 Q10 | 12 | 21.43% |
| 3 | Cost marked price discount and free item multipliers | 5 | CAT 2024 S1 Q21 | 17 | 30.36% |
| 4 | Successive percentage changes with unknown rates | 5 | CAT 2021 S2 Q18 | 22 | 39.29% |
| 5 | Weighted subgroup payroll or investment growth | 5 | CAT 2023 S2 Q8 | 27 | 48.21% |
| 6 | Percentages of groups and remaining shares | 5 | CAT 2021 S2 Q7 | 32 | 57.14% |
| 7 | Weighted sale revenue and overall profit | 4 | CAT 2021 S2 Q22 | 36 | 64.29% |
| 8 | Profit shares and successive trading transactions | 4 | CAT 2021 S2 Q8 | 40 | 71.43% |
| 9 | Percentage stocks constrained to integer counts | 3 | CAT 2023 S3 Q14 | 43 | 76.79% |
| 10 | Component percentages after adding mixtures | 3 | CAT 2021 S3 Q1 | 46 | 82.14% |
| 11 | Compound balances after repayments | 2 | CAT 2023 S2 Q12 | 48 | 85.71% |
| 12 | Workforce and efficiency percentages | 2 | CAT 2022 S3 Q16 | 50 | 89.29% |
| 13 | Simple interest rates and reinvestment | 2 | CAT 2022 S1 Q16 | 52 | 92.86% |
| 14 | Percentage changes in speed or angle | 2 | CAT 2025 S3 Q16 | 54 | 96.43% |
| 15 | Unit price percentage and quantity ratio | 1 | CAT 2021 S1 Q3 | 55 | 98.21% |
| 16 | Reciprocal day growth factors | 1 | CAT 2022 S2 Q7 | 56 | 100% |
Based on CAT Actual Quant Papers.