CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 5
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 5 of 11.
A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
Answer: B. 15.5%
Solution — first steps
Step 1. For every Rs100 paid, the merchant receives 105 cm of cloth.
Step 2. After 5% discount, a billed metre sells for 110×0.95=Rs104.50, but only 95 cm is delivered.
Step 2. After 5% discount, a billed metre sells for 110×0.95=Rs104.50, but only 95 cm is delivered.
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A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is
Answer: A. \(3(3-\sqrt{5})\)
Solution — first steps
Step 1. Let distance be D and stream speed v. Boat1 has downstream speed D/2 and upstream speed D/3, so v=(D/2−D/3)/2=D/12.
Step 2. For boat2 with still-water speed w, write z=w/D>1/12. The six-hour round trip gives1/(z−1/12)+1/(z+1/12)=6.
Step 2. For boat2 with still-water speed w, write z=w/D>1/12. The six-hour round trip gives1/(z−1/12)+1/(z+1/12)=6.
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The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is
Answer: 42
Solution — first steps
Step 1. Let weekly collections be A=3k and B=4k.
Step 2. A's five-week total 15k is divisible by 7, so k is divisible by 7.
Step 2. A's five-week total 15k is divisible by 7, so k is divisible by 7.
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Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
Answer: 36
Solution — first steps
Step 1. Let Gautam and Suhani's usual daily rates be g and s. Then g+s=1/20.
Step 2. The compensation statement gives 0.6g+1.5s=g+s.
Step 2. The compensation statement gives 0.6g+1.5s=g+s.
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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.