CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 7
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 11.
Refer to the passage above ↑
Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals
Answer: 10
Solution — first steps
Step 1. Let polygon side counts be n and 2n.
Step 2. Interior angles are 180−360/n and 180−180/n.
Step 2. Interior angles are 180−360/n and 180−180/n.
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Refer to the passage above ↑
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
Answer: 6
Solution — first steps
Step 1. Time ratio 5: 8: 10 gives hourly work rates 8: 5: 4.
Step 2. Three workers together work 32 hours, so choose total work 32×17=544 units.
Step 2. Three workers together work 32 hours, so choose total work 32×17=544 units.
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Refer to the passage above ↑
In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was
Answer: D. 62800
Solution — first steps
Step 1. Of cast votes, candidate shares are 30%, 70%/6, 140%/6, 210%/6.
Step 2. The winner has 35% and runner-up 30%, a gap 5%.
Step 2. The winner has 35% and runner-up 30%, a gap 5%.
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Refer to the passage above ↑
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
Answer: D. 5:6
Solution — first steps
Step 1. Scale initial volumes to 2 syrup and 2 milk.
Step 2. Move 1 syrup to second vessel: second has 1 syrup, 2 milk.
Step 2. Move 1 syrup to second vessel: second has 1 syrup, 2 milk.
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Refer to the passage above ↑
Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
Answer: 20
Solution — first steps
Step 1. Annual interest as fraction of capital is(1/5)(.06)+(1/3)(.10)+(7/15)(.01).
Step 2. This is.012+.033333…+.004666…=.05.
Step 2. This is.012+.033333…+.004666…=.05.
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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 14 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Work rate ratios and individual contributions | 12 | CAT 2021 S1 Q19 | 12 | 20.69% |
| 2 | Mixture ratios replacement and dilution | 8 | CAT 2021 S1 Q11 | 20 | 34.48% |
| 3 | Income payroll and savings on a common scale | 5 | CAT 2021 S1 Q17 | 25 | 43.10% |
| 4 | Unit prices equivalent costs and trading ratios | 5 | CAT 2021 S1 Q3 | 30 | 51.72% |
| 5 | Speed time length and meeting ratios | 5 | CAT 2021 S2 Q5 | 35 | 60.34% |
| 6 | Investment shares interest and returns | 5 | CAT 2021 S2 Q8 | 40 | 68.97% |
| 7 | Subgroup counts with different percentages | 4 | CAT 2021 S2 Q7 | 44 | 75.86% |
| 8 | Geometric side angle and altitude ratios | 3 | CAT 2022 S2 Q1 | 47 | 81.03% |
| 9 | Stock and population ratios after transfers | 3 | CAT 2024 S1 Q1 | 50 | 86.21% |
| 10 | Allocate a conserved total among groups | 3 | CAT 2023 S2 Q16 | 53 | 91.38% |
| 11 | Integer multiplier and divisibility of ratios | 2 | CAT 2022 S1 Q8 | 55 | 94.83% |
| 12 | Price ratio with a product condition | 1 | CAT 2021 S3 Q17 | 56 | 96.55% |
| 13 | Recover group size ratio from averages | 1 | CAT 2022 S1 Q20 | 57 | 98.28% |
| 14 | Age ratios with a constant difference | 1 | CAT 2024 S2 Q22 | 58 | 100% |
Based on CAT Actual Quant Papers.