CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus – Page 2
All 32 Mixtures questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 2 of 9.
Teams A, B, and C consist of five, eight, and ten members, respectively such that the members within each team is equally productive. Working separately teams A , B and C can complete certain job in 40 hours , 50 hours and 4 hours respectively Two members from team A, three members from team B, and one member from team C together starts the work and the member from team C left the work after 23 hours. The number of additional member(s) required from team B , that would be required to replace the member from team C , to finish the job in next one hour is :
Answer: B. 2
Solution — first steps
5 On solving x = 2 Thus option 2 is the answer
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Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After mixing well, an equal volume is taken out from B and poured into A. If the ratio of alcohol and water in A is 15:4, then the volume, in litres, initially taken out from A, is [TITA]
Answer: 16
Solution — first steps
Correct Answer: 16 Given vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. Assum x litres of alcohol from A is transferred to B After the first transfer (from A to B): Vessel A: 60 - x liters of alcohol, 60 liters of water.
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In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
Answer: C. 13.26
Solution — first steps
Step 1. Represent September incomes as 8u,6u,5u.
Step 2. September rent is 15% of 8u plus 12% of 6u plus 18% of 5u =1.2u+0.72u+0.9u=2.82u.
Step 2. September rent is 15% of 8u plus 12% of 6u plus 18% of 5u =1.2u+0.72u+0.9u=2.82u.
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There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is
Answer: 15
Solution — first steps
Step 1. Let the four numbers be a,b,c,d.
Step 2. Average of the first two is one more than the first: (a+b)/2=a+1, so b=a+2.
Step 2. Average of the first two is one more than the first: (a+b)/2=a+1, so b=a+2.
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A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
Answer: C. 3 : 5
Solution — first steps
Step 1: After adding 2 litres of water, the concentration of acid becomes 50%.
\( \frac{A}{A + W + 2} = \frac{1}{2} \)
\( \Rightarrow 2A = A + W + 2 \Rightarrow A = W + 2 \quad \text{(Equation 1)} \)
Step 2: Then, 15 litres of acid is added and acid becomes 80% of the solution:
\( \frac{A + 15}{A + W + 17} = \frac{4}{5} \)
\( \Rightarrow 5(A + 15) = 4(A + W + 17) \)
\( \Rightarrow 5A + 75 = 4A + 4W + 68 \)
\( \Rightarrow A = 4W - 7 \quad \text{(Equation 2)} \)
\( \frac{A}{A + W + 2} = \frac{1}{2} \)
\( \Rightarrow 2A = A + W + 2 \Rightarrow A = W + 2 \quad \text{(Equation 1)} \)
Step 2: Then, 15 litres of acid is added and acid becomes 80% of the solution:
\( \frac{A + 15}{A + W + 17} = \frac{4}{5} \)
\( \Rightarrow 5(A + 15) = 4(A + W + 17) \)
\( \Rightarrow 5A + 75 = 4A + 4W + 68 \)
\( \Rightarrow A = 4W - 7 \quad \text{(Equation 2)} \)
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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.