CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus – Page 5
All 40 Percentages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 5 of 10.
Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value after 5 years is 25:36, then the minimum number of years required for the value to exceed Rs 20000 is _____
Answer: 9
Solution — first steps
16 → n=9
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
Answer: 72 and 80
Solution — first steps
Step 1. Let G be girls and B=250−G be boys. The bounds give 110≤G≤150.
Step 2. Because every student chooses at least one activity, inclusion–exclusion fixes the overlap: both=0.2B+0.4G.
Step 2. Because every student chooses at least one activity, inclusion–exclusion fixes the overlap: both=0.2B+0.4G.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
Answer: 30
Solution — first steps
Step 1. Let initial water be W litres; initial milk is 300−W.
Step 2. The withdrawal is 2W litres, leaving the milk multiplied by (300−2W)/300.
Step 2. The withdrawal is 2W litres, leaving the milk multiplied by (300−2W)/300.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
Answer: B. 10
Solution — first steps
Step 1. A 10% discount saves 15 rupees, so marked price M=15/0.1=150.
Step 2. The marked price represents 20% profit on cost C, so 1.2C=150.
Step 2. The marked price represents 20% profit on cost C, so 1.2C=150.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that a 10% profit is made on object B, then the profit made on object A will be nearest to:
Answer: C. 47%
Solution — first steps
Given, Gita sold two objects and changed the selling price, resulting in a profit percentage on object A being approximately 47%.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
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.