CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus – Page 7
All 40 Percentages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 10.
A container has 40 liters of milk. 4 liters are removed and replaced with 4 liters of water. This process is repeated. The smallest number of times required for milk to be less than water is:
Answer: C. 7
Solution — first steps
Answer: C. 7 Detailed Solution: After each replacement, \( \frac{9}{10} \) of the milk remains.
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The population of a town in 2020 was 100,000. The population decreased by \( y\% \) from 2020 to 2021, and increased by \( x\% \) from 2021 to 2022.
If the population in 2022 was greater than in 2020 and \( x - y = 10 \), what was the lowest possible population in 2021?
If the population in 2022 was greater than in 2020 and \( x - y = 10 \), what was the lowest possible population in 2021?
Answer: B. 73,000
Solution — first steps
The lowest population in 2021 is 73,000. Using the formula for successive percentage change, the population reduces by 27%, giving \( 73,000 \) as the minimum.
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Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be
Answer: D. 17
Solution — first steps
Step 1. Mixture A has sugar fraction 2/5; mixture B has sugar fraction 3/10.
Step 2. They are combined in ratio 2:3, so sugar fraction in C is [2(2/5)+3(3/10)]/5.
Step 2. They are combined in ratio 2:3, so sugar fraction in C is [2(2/5)+3(3/10)]/5.
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A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
Answer: B. 15.5%
Solution — first steps
Step 1. For every Rs100 paid, the merchant receives 105 cm of cloth.
Step 2. After 5% discount, a billed metre sells for 110×0.95=Rs104.50, but only 95 cm is delivered.
Step 2. After 5% discount, a billed metre sells for 110×0.95=Rs104.50, but only 95 cm is delivered.
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Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
Answer: 36
Solution — first steps
Step 1. Let Gautam and Suhani's usual daily rates be g and s. Then g+s=1/20.
Step 2. The compensation statement gives 0.6g+1.5s=g+s.
Step 2. The compensation statement gives 0.6g+1.5s=g+s.
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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.