CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus – Page 7
All 32 Mixtures questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 9.
Refer to the passage above ↑
Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in bank A, ₹5,000 at 5.6% in bank B and the remaining amount at \(x\)% in bank C, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to 5% of the initial capital. If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been
Answer: B. 800
Solution — first steps
Step 1. Required annual income=.05×20000=1000.
Step 2. A contributes 8000×.055=440 and B contributes 5000×.056=280.
Step 2. A contributes 8000×.055=440 and B contributes 5000×.056=280.
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Refer to the passage above ↑
Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is
Answer: D. 22.5
Solution — first steps
Step 1. Order numbers a<b<c<d<e<f. Given a+b = 28 and e+f(56).
Step 2. As e<f and integers, e≤27.
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Refer to the passage above ↑
A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio
Answer: A. 1:1
Solution — first steps
Step 1. After the complete two-way transfer, each vessel again contains 500 cc.
Step 2. Let water in the milk glass be w. Its milk content is 500−w.
Step 2. Let water in the milk glass be w. Its milk content is 500−w.
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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.