CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 2
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 2 of 11.
Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After mixing well, an equal volume is taken out from B and poured into A. If the ratio of alcohol and water in A is 15:4, then the volume, in litres, initially taken out from A, is [TITA]
Answer: 16
Solution — first steps
Correct Answer: 16 Given vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. Assum x litres of alcohol from A is transferred to B After the first transfer (from A to B): Vessel A: 60 - x liters of alcohol, 60 liters of water.
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The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled by pipe A in 15 hours. If all pipes are used simultaneously to fill up this empty tank, the time, in minutes, taken to fill up the tank entirely tank completely is nearest to :
Answer: D. 73
Solution — first steps
Pipe A fills the tank in 15 hours. Pipe A's rate = 1/15 of the tank per hour.
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A glass is filled with milk. Two-thirds of its content is poured out and replaced with water.
If this process of pouring out two-thirds the content and replacing with water is repeated
three more times, then the final ratio of milk to water in the glass is:
If this process of pouring out two-thirds the content and replacing with water is repeated
three more times, then the final ratio of milk to water in the glass is:
Answer: D. 1 : 80
Solution — first steps
Step 1: Concept of Dilution and Replacement
When a fraction of a liquid is replaced repeatedly, the amount of the original liquid
left after \( n \) repetitions is given by:
\[
\text{Remaining Fraction of Original Liquid} = \left( 1 - \text{Fraction Replaced} \right)^n
\]
Step 2: Apply the formula
Fraction replaced = \( \frac{2}{3} \), so the remaining fraction = \( 1 - \frac{2}{3} = \frac{1}{3} \).
Number of repetitions, \( n = 4 \).
\[
\text{Fraction of Milk Remaining} = \left( \frac{1}{3} \right)^4 = \frac{1}{81}
\]
When a fraction of a liquid is replaced repeatedly, the amount of the original liquid
left after \( n \) repetitions is given by:
\[
\text{Remaining Fraction of Original Liquid} = \left( 1 - \text{Fraction Replaced} \right)^n
\]
Step 2: Apply the formula
Fraction replaced = \( \frac{2}{3} \), so the remaining fraction = \( 1 - \frac{2}{3} = \frac{1}{3} \).
Number of repetitions, \( n = 4 \).
\[
\text{Fraction of Milk Remaining} = \left( \frac{1}{3} \right)^4 = \frac{1}{81}
\]
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Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
Answer: 6
Solution — first steps
Step 1. Renu's total work is 15×4=60 Renu-hours, so her hourly rate is 1/60.
Step 2. Seema's total is 8×5=40 Seema-hours, so her hourly rate is 1/40.
Step 2. Seema's total is 8×5=40 Seema-hours, so her hourly rate is 1/40.
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In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
Answer: C. 13.26
Solution — first steps
Step 1. Represent September incomes as 8u,6u,5u.
Step 2. September rent is 15% of 8u plus 12% of 6u plus 18% of 5u =1.2u+0.72u+0.9u=2.82u.
Step 2. September rent is 15% of 8u plus 12% of 6u plus 18% of 5u =1.2u+0.72u+0.9u=2.82u.
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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.