CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 3
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 3 of 11.
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
Answer: C. 6
Solution — first steps
Step 1. Let the term at bank A be n years. Its simple interest is 10000×0.05n=500n.
Step 2. The maturity deposited in B is 10000+500n.
Step 2. The maturity deposited in B is 10000+500n.
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A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
Answer: C. 3 : 5
Solution — first steps
Step 1: After adding 2 litres of water, the concentration of acid becomes 50%.
\( \frac{A}{A + W + 2} = \frac{1}{2} \)
\( \Rightarrow 2A = A + W + 2 \Rightarrow A = W + 2 \quad \text{(Equation 1)} \)
Step 2: Then, 15 litres of acid is added and acid becomes 80% of the solution:
\( \frac{A + 15}{A + W + 17} = \frac{4}{5} \)
\( \Rightarrow 5(A + 15) = 4(A + W + 17) \)
\( \Rightarrow 5A + 75 = 4A + 4W + 68 \)
\( \Rightarrow A = 4W - 7 \quad \text{(Equation 2)} \)
\( \frac{A}{A + W + 2} = \frac{1}{2} \)
\( \Rightarrow 2A = A + W + 2 \Rightarrow A = W + 2 \quad \text{(Equation 1)} \)
Step 2: Then, 15 litres of acid is added and acid becomes 80% of the solution:
\( \frac{A + 15}{A + W + 17} = \frac{4}{5} \)
\( \Rightarrow 5(A + 15) = 4(A + W + 17) \)
\( \Rightarrow 5A + 75 = 4A + 4W + 68 \)
\( \Rightarrow A = 4W - 7 \quad \text{(Equation 2)} \)
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Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
Answer: B. 3/10
Solution — first steps
Step 1. Use total work 60 units. Sam, Mohit and Ayna work at 3,6,2 units per day.
Step 2. The repeating three-day schedule completes 9,5,8 units respectively, totalling 22 per cycle.
Step 2. The repeating three-day schedule completes 9,5,8 units respectively, totalling 22 per cycle.
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Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
Answer: B. 7 : 9
Solution — first steps
Step 1. Total area is 20+30=50 hectares. Overall wheat:mustard=11:9, giving wheat=27.5 and mustard=22.5 hectares.
Step 2. Vimal has 30 hectares split 5:3, so wheat=18.75 and mustard=11.25.
Step 2. Vimal has 30 hectares split 5:3, so wheat=18.75 and mustard=11.25.
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Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that a 10% profit is made on object B, then the profit made on object A will be nearest to:
Answer: C. 47%
Solution — first steps
Given, Gita sold two objects and changed the selling price, resulting in a profit percentage on object A being approximately 47%.
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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.