CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus – Page 6
All 32 Mixtures questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 6 of 9.
Refer to the passage above ↑
Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
Answer: D. 20
Solution — first steps
Step 1. Total marks 190. To minimize Amit, maximize the other four as 50, 49, 48, 32.
Step 2. This gives minimum 11 and meets exactly three scores above 32.
Step 2. This gives minimum 11 and meets exactly three scores above 32.
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Refer to the passage above ↑
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
Answer: 6
Solution — first steps
Step 1. Time ratio 5: 8: 10 gives hourly work rates 8: 5: 4.
Step 2. Three workers together work 32 hours, so choose total work 32×17=544 units.
Step 2. Three workers together work 32 hours, so choose total work 32×17=544 units.
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Refer to the passage above ↑
Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be
Answer: A. 4400
Solution — first steps
Step 1. Target annual saving 12×550=6600.
Step 2. First nine months save 9×500=4500.
Step 2. First nine months save 9×500=4500.
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Refer to the passage above ↑
In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was
Answer: D. 62800
Solution — first steps
Step 1. Of cast votes, candidate shares are 30%, 70%/6, 140%/6, 210%/6.
Step 2. The winner has 35% and runner-up 30%, a gap 5%.
Step 2. The winner has 35% and runner-up 30%, a gap 5%.
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Refer to the passage above ↑
The average of a non-decreasing sequence of N numbers a1, a2, ..., aN is 300. If a1 is replaced by 6a1, the new average becomes 400. Then, the number of possible values of a1 is
Answer: 14
Solution — first steps
Step 1. Original sum 300N. Replacing a = 1 by 6a1 increases sum by 5a1.
Step 2. The average rises 100, so 5a1=100N and a = 1=20N.
Step 2. The average rises 100, so 5a1=100N and a = 1=20N.
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Refer to the passage above ↑
There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
Answer: D. 5:6
Solution — first steps
Step 1. Scale initial volumes to 2 syrup and 2 milk.
Step 2. Move 1 syrup to second vessel: second has 1 syrup, 2 milk.
Step 2. Move 1 syrup to second vessel: second has 1 syrup, 2 milk.
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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.