CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 8
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 8 of 11.
Refer to the passage above ↑
Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be
Answer: B. 12
Solution — first steps
Step 1. Use port O, with ships on rays at 60°. At the special time slower distance to O is 24−8=16.
Step 2. Let faster distance to O be z<16. A right angle cannot occur at O, and must be at the faster ship, so z=16 cos 60°=8.
Step 2. Let faster distance to O be z<16. A right angle cannot occur at O, and must be at the faster ship, so z=16 cos 60°=8.
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Refer to the passage above ↑
Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is
Answer: 11
Solution — first steps
Step 1. Choose total work 120 units. Bob rate 3, Alex 6, Cole 2.
Step 2. Three-day pair outputs are 9, 5, 8, total 22.
Step 2. Three-day pair outputs are 9, 5, 8, total 22.
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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.