CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus

Every real CAT question on this chapter from the past papers we have, newest year first. Passages and data sets stay together on one page.

Tap Show answer, or open the detailed solution (free login). Page 1 of 9.

Start here: the repeating CAT PYQs

Study the mixtures and totals pattern in each CAT PYQ, then practise variations. The 12 selected families contain 44 of the 44 questions tagged Conservation / totals in the reviewed set.

CAT Mixtures and Totals Bible Top 10 PYQ Questions

Questions	CAT Area Covered
First 5 CAT Questions	68.18%
First 10 CAT Questions	95.45%
All 12 CAT Questions	100%

Importance of Mixtures and Totals each year of CAT exam

CAT year	Total Mixtures and Totals questions	First 6 examples	First 10 examples	All 12 examples	Outside these 12 families	Share of all Quant
2021	11	9	11	11	0	16.67%
2022	12	10	12	12	0	18.18%
2023	5	2	5	5	0	7.58%
2024	8	7	7	8	0	12.12%
2025	8	6	7	8	0	12.12%
Total	44	34	42	44	0	13.33%
Share of all 44	100%	77.27%	95.45%	100%	0%

Quick review for beginners and last day revision

Rule	Formula or what to do	Small example
Partition a total	Total = sum of nonoverlapping parts.	N = boys + girls
Average into total	Total = number × average	Eight days averaging 63 means total 504.
Compare overlapping totals	Subtract shared portions to isolate the changed entries.	Total days 1–9 minus total days 2–9 gives day 1.
Transfer	Moving items between groups preserves their combined total.	A becomes A − t; B becomes B + t.
Mixture component	Track component amount and total mixture separately.	Acid = concentration × volume.
Work already done	Total job = completed work + remaining work.	If A did 2/5 and B did 1/6, C did 1 − 2/5 − 1/6.
Money and stock	Closing amount = opening amount + additions − removals.	Track sales proceeds separately from stock quantities.
Cash profit	Net profit = total receipts − total payments.	A resale history needs every purchase and sale.
Weighted total	Total payroll or value = sum(count × unit amount).	Five managers at m and 25 engineers at e → 5m + 25e.
Avoid double counting	Overlapping groups must be partitioned or adjusted before summing.	Use inclusion–exclusion when a person belongs to more than one group.

10 Core CAT PYQ Questions

Study these first.

CAT PYQ 1: Compare or recover totals from changing averages

Understand: Average × count = total. Call one hospital n and the other n + 21, then solve the equation from the average difference.

CAT 2021 Slot 1 · Quant

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

CAT PYQ 2: Conservation of mixture components

Understand: Track the amount of silver and the total weight separately in each mixture.

CAT 2021 Slot 3 · Quant

If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is

CAT PYQ 3: Weighted money price or payroll totals

Understand: Take a convenient fixed spend, find the kg bought each month, then divide total spend by total kg.

CAT 2021 Slot 1 · Quant

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

CAT PYQ 4: Partition a population or vote total

Understand: Split the total into two groups. Equal metallic counts give the ratio of the two groups.

CAT 2021 Slot 2 · Quant

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

CAT PYQ 5: Completed work plus remaining work

Understand: Total job = work done by each person. The last person did 1 minus the others, and pay follows work done.

CAT 2021 Slot 2 · Quant

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

CAT PYQ 6: Stocks conserved through transfers sales or allocation

Understand: Write the starting stock in the given ratio, apply each sale, then use the new ratio.

CAT 2024 Slot 1 · Quant

A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is

CAT PYQ 7: Fixed score total with ordered integer constraints

Understand: Total = mean × number. To raise the toppers, keep the other scores as low as allowed.

CAT 2021 Slot 3 · Quant

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

CAT PYQ 8: Money shared from a fixed total

Understand: The total is fixed. Write what each person gets and use the condition to bound n.

CAT 2023 Slot 2 · Quant

If a certain amount of money is divided equally among \(n\) persons, each one receives Rs 352 . However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330 . Then, the maximum possible value of \(n\) is

CAT PYQ 9: Cash flow across alternative sales or resale

Understand: A change in the selling price changes the profit by a known amount. That tells how many pens remain.

CAT 2021 Slot 1 · Quant

Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

Variations

Same idea, extra twist.

CAT PYQ 12: Portfolio count and total value

Understand: Let the shares of one stock be x, the other is 20 − x, then use the total value to find x.

CAT 2025 Slot 1 · QuantEasy

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is _______

CAT 2025 Slot 1 · QuantMedium

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

CAT 2025 Slot 2 · QuantEasy

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

CAT 2025 Slot 2 · QuantEasy

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is ____

CAT 2025 Slot 3 · Quant

The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins to be further shifted from box A to box B to make this ratio 1:1 is:
[TITA]

CAT 2025 Slot 3 · QuantMedium

The average salary of 5 managers and 25 engineers in a company is Rs 60000. If each of the manager receive 20% hike in the salary while the salary of the engineer remains unchanged , the average salary of all 30 employees increased by 5%.The average salary, of engineer , in rs , is :

Frequently asked questions

Where can I find CAT mixtures and totals questions with solutions?

Every Mixtures and Totals question on this page is a real CAT question from the CAT Actual Quant Papers. Tap Show answer for the answer; the detailed step-by-step solution opens after a free login. Start with the 12 CAT PYQs at the top, because they repeat the most.

Are there CAT mixtures and totals questions with answers?

Yes. Every question has its answer one tap away, free for everyone: pick an option and press Submit, or tap Show answer.

Is there a PDF of CAT mixtures and totals questions?

Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Mixtures and Totals Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT mixtures and totals questions. All the CAT Mixtures and Totals questions are also on this page to read online, with answers and, after a free login, detailed solutions.

What are the CAT mixtures and totals previous year questions (PYQs)?

They are the real questions of the CAT Actual Quant Papers that are about mixtures and totals: 44 questions, grouped into 12 repeating CAT PYQs, with the other questions listed after them in paper order.

Which mixtures and totals questions should I practise first for CAT?

Start with the first 6 CAT PYQs, which cover about 80% of the Mixtures and Totals questions. Then do the first 10 (about 100%) and finally all 12 (all of them).

How many Mixtures questions came in CAT papers?

32 Mixtures questions are on this page: 7 in CAT 2025, 7 in CAT 2024, 3 in CAT 2023, 12 in CAT 2022, 3 in CAT 2021. The same real question is shown once.

How difficult are CAT Mixtures questions?

Of the 6 Mixtures questions that carry a difficulty rating, 2 are Easy, 3 Medium and 1 Hard; the other 26 are not rated yet.

Are the solutions free?

The question and its answer are free for everyone. The detailed Cetking solution opens after a free login with your mobile number (OTP).

How is a set shown on this page?

Each passage or data set gets one page with all its questions together (4 sets here), so you never solve half of one. Questions that stand alone are shown five to a page.

Where can I practise more Mixtures?

Open all CAT papers and topics for every paper, or the Cetking Arena to practise.

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.

CAT Mixtures and Totals Bible Top 10 Must Solve Mixtures and Totals Questions covering 100% of Syllabus

Start here: the repeating CAT PYQs

10 Core CAT PYQ Questions

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Variations

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Frequently asked questions