CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus – Page 6
All 40 Ratios questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 6 of 11.
Refer to the passage above ↑
Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
Answer: A. 1680
Solution — first steps
Step 1. Let total cost C and marked price per kg M. Planned revenue 24M=C+1752.
Step 2. Actual revenue 4M+20(0.8M)=20M=C+744.
Step 2. Actual revenue 4M+20(0.8M)=20M=C+744.
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Refer to the passage above ↑
A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is
Answer: D. 1 : 7
Solution — first steps
Step 1. Take 2 units of original mixture: 1 lemon and 1 syrup.
Step 2. Add 6 units pure syrup to make original-mixture: added-syrup=1: 3.
Step 2. Add 6 units pure syrup to make original-mixture: added-syrup=1: 3.
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Refer to the passage above ↑
Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
Answer: A. 37.5%
Solution — first steps
Step 1. Let investments be u, v.
Step 2. Equal interest gives 0.15×4u=0.12×3v, so 0.6u=0.36v.
Step 2. Equal interest gives 0.15×4u=0.12×3v, so 0.6u=0.36v.
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Refer to the passage above ↑
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
Answer: B. 15
Solution — first steps
Step 1. Let meeting occur t minutes after departure and B total journey time T.
Step 2. At meeting, fractions of distance satisfy t/10+t/T=1.
Step 2. At meeting, fractions of distance satisfy t/10+t/T=1.
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Refer to the passage above ↑
In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
Answer: 43200
Solution — first steps
Step 1. Literate males 3600 and females 5400 from ratio 2: 3.
Step 2. Let illiterate males 4t and females 3t.
Step 2. Let illiterate males 4t and females 3t.
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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.