CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus – Page 3
All 32 Mixtures questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 3 of 9.
A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was
Answer: B. 95000
Solution — first steps
Step 1. Convert each reported average bonus into a total bonus for that employee block.
Step 2. First 30 total =30×their average; last 30 total =30×their average.
Step 2. First 30 total =30×their average; last 30 total =30×their average.
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The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is _____
Answer: 70
Solution — first steps
Sum = 84. Let numbers a Solve → b=25, a+c=59 (c-10)-(a+7)=64 → c-a=81 Add: 2c=140 → c=70 Answer: 70
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Rajesh owns 20 hectares, Vimal owns 30 hectares with wheat and mustard in 5:3 ratio. Total wheat:mustard is 11:9. Find Rajesh's ratio.
Answer: 7:9
Solution — first steps
5 → ratio 19:21 → closest 7:9
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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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Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is
Answer: C. 31.25%
Solution — first steps
Option 3
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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 12 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Compare or recover totals from changing averages | 9 | CAT 2021 S1 Q16 | 9 | 20.45% |
| 2 | Conservation of mixture components | 7 | CAT 2021 S3 Q1 | 16 | 36.36% |
| 3 | Weighted money price or payroll totals | 5 | CAT 2021 S1 Q7 | 21 | 47.73% |
| 4 | Partition a population or vote total | 5 | CAT 2021 S2 Q7 | 26 | 59.09% |
| 5 | Completed work plus remaining work | 4 | CAT 2021 S2 Q6 | 30 | 68.18% |
| 6 | Stocks conserved through transfers sales or allocation | 4 | CAT 2024 S1 Q1 | 34 | 77.27% |
| 7 | Fixed score total with ordered integer constraints | 3 | CAT 2021 S3 Q7 | 37 | 84.09% |
| 8 | Money shared from a fixed total | 2 | CAT 2023 S2 Q16 | 39 | 88.64% |
| 9 | Cash flow across alternative sales or resale | 2 | CAT 2021 S1 Q9 | 41 | 93.18% |
| 10 | Loan payments minus initial principal | 1 | CAT 2023 S2 Q12 | 42 | 95.45% |
| 11 | Reverse successive sales from the final stock | 1 | CAT 2024 S1 Q13 | 43 | 97.73% |
| 12 | Portfolio count and total value | 1 | CAT 2025 S1 Q20 | 44 | 100% |
Based on CAT Actual Quant Papers.