CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus – Page 2
All 40 Percentages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 2 of 10.
A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is
Answer: A. 5 : 8
Solution — first steps
Correct answer A) 5 : 8 Suppose total = 100. Person Basis of Calculation Amount Received Pinu 20% of total 20 Remaining after Pinu 100 − 20 80 Meena 40% of remaining (40% of 80) 32 Seema 20% less than Pinu → 80% of 20 16 Total given so far 20 + 32 + 16 68 Rinu Remaining → 100 − 68 32 So Pinu got 20, Rinu got 32 thus ratio = 20 : 32 = 5 : 8
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An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, as a percentage, at which the profit percentage would be equal to the rate of discount, is nearest to
Answer: D. 14
Solution — first steps
Correct Answer D) 14 Given: CP = 1650, MP = 2200 Condition: profit % = discount % Discount % SP = MP × (1 − d) Profit (SP − 1650) Profit % Match? A.
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A loan of Rs 1000 is fully repaid by two instalments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is _____
Answer: C. 8
Solution — first steps
Correct Answer is c) 8% Let the annual rate of interest be r%. The present value of the two instalments must equal the loan amount.
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The monthly sales of a product from January to April were 120, 135, 150 and 165 units respectively. The cost per unit of the product was Rs 240 per unit and a fixed marked price was used for the product in all the four months. However, 20%, 10% and 5% discount on the marked price was offered in January, February, March respectively while no discount were given in April.If the total profit from January to April was Rs 138825, then the marked price (in Rs) is equal to, say:
Answer: B. 525
Solution — first steps
Correct Answer: 2 Given: Units sold: January (120), February (135), March (150), April (165) Cost per unit: Rs 240 Discounts: 20% (January), 10% (February), 5% (March), 0% (April) Total profit: Rs 138,825 Let M be the marked price. 5M + 165M = 525M Total Cost = (120 + 135 + 150 + 165) × 240 = 136800 Profit = Revenue - Cost 138825 = 525M - 136800 525M = 275625 M = 275625 / 525 = 525 The marked price M = Rs 525, so the correct answer is Option 2.
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The average salary of 5 managers and 25 engineers in a company is Rs 60000. If each of the manager receive 20% hike in the salary while the salary of the engineer remains unchanged , the average salary of all 30 employees increased by 5%.The average salary, of engineer , in rs , is :
Answer: B. 54000
Solution — first steps
05 = 63,000 Total salary after the hike: 30 × 63,000 = 1,890,000 Before hike: 5M + 25E = 1,800,000 After hike: 6M + 25E = 1,890,000 Solve for M (manager's salary): (6M + 25E) - (5M + 25E) = 1,890,000 - 1,800,000 M = 90,000 Solve for E (engineer's salary): 5 × 90,000 + 25E = 1,800,000 450,000 + 25E = 1,800,000 25E = 1,350,000 Thus E = 54,000
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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.