CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus – Page 9
All 32 Mixtures questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 9 of 9.
Refer to the passage above ↑
The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is
Answer: B. 68.75
Solution — first steps
Step 1. Set 1970 population 100. Let male M and female 100−M.
Step 2. 1980 total 125 gives 1.4M+1.2(100−M)=125, so M = 25 and female 75.
Step 2. 1980 total 125 gives 1.4M+1.2(100−M)=125, so M = 25 and female 75.
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Refer to the passage above ↑
Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for ₹ 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is
Answer: 3000
Solution — first steps
Step 1. In six days Anil completes 6/12=1/2 and Barun 6/16=3/8.
Step 2. Chandu completes 1−1/2−3/8=1/8.
Step 2. Chandu completes 1−1/2−3/8=1/8.
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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.