CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus – Page 8
All 40 Percentages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 8 of 10.
Refer to the passage above ↑
Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is
Answer: 160
Solution — first steps
Step 1. Let juice cost j and syrup 0.8j per kg. Total cost=208j.
Step 2. Revenue from separate sales=10×0.8j×1.1+20×j×1.2=32.8j.
Step 2. Revenue from separate sales=10×0.8j×1.1+20×j×1.2=32.8j.
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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.