CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% of Syllabus

Ratios questions ask you to compare quantities as a ratio, split a total in a given ratio, or follow how a ratio changes when something is added, removed or transferred. CAT hides them inside work, mixture, speed, interest and percentage problems.

Tap Show answer, or open the detailed solution (free login). Page 1 of 11.

Start here: the repeating CAT PYQs

Study the ratio pattern in each CAT PYQ, then practise variations. The 14 selected families contain 58 of the 58 questions tagged Ratios and allocation in the reviewed set.

CAT Ratios Bible Top 10 PYQ Questions

Questions	CAT Area Covered
First 5 CAT Questions	60.34%
First 10 CAT Questions	91.38%
All 14 CAT Questions	100%

Importance of Ratios each year of CAT exam

CAT year	Total Ratios questions	First 6 examples	First 10 examples	All 14 examples	Outside these 14 families	Share of all Quant
2021	13	10	12	13	0	19.70%
2022	15	8	13	15	0	22.73%
2023	12	10	11	12	0	18.18%
2024	9	6	8	9	0	13.64%
2025	9	6	9	9	0	13.64%
Total	58	40	53	58	0	17.58%
Share of all 58	100%	68.97%	91.38%	100%	0%

Quick review for beginners and last day revision

Rule	Formula or what to do	Small example
Common multiplier	A : B = m : n → A = mk, B = nk	A : B = 2 : 3 and A + B = 50 → k = 10.
Part of a total	A = mT/(m + n); B = nT/(m + n)	Split 80 in 3 : 5 → 30 and 50.
Known difference	A − B = (m − n)k	A : B = 5 : 3 and A − B = 12 → k = 6.
Connect two ratios	Scale the shared quantity to the same value.	A : B = 2 : 3, B : C = 4 : 5 → A : B : C = 8 : 12 : 15.
Transfer	After t moves from A to B: (A − t)/(B + t) = new ratio.	Total A + B stays unchanged during a transfer.
Income and savings	Income − expenditure = savings	Choose expenditure values that fit every linked ratio.
Inverse relation	For fixed work or distance, time is inversely proportional to rate or speed.	Speed ratio 2 : 3 → time ratio 3 : 2.
Weighted average	Combined average = (n₁a₁ + n₂a₂)/(n₁ + n₂)	Do not average two group averages unless group sizes are equal.
Contribution and pay	Share of payment = individual work / total work × total payment	Work contribution = rate × time worked.
Mixture ratio	Track each component amount before finding the final ratio.	A half-transfer moves half of every component in a uniform mixture.

10 Core CAT PYQ Questions

Study these first.

CAT PYQ 1: Work rate ratios and contributions

Understand: Rate × time = work. Fix the total work, then find who does how much.

CAT 2021 Slot 1 · Quant

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

CAT PYQ 2: Mixture replacement and dilution

Understand: Treat the old and new liquid as amounts. Track the quantity of one component through each step.

CAT 2021 Slot 1 · Quant

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is

CAT PYQ 3: Income, payroll and savings

Understand: Bring every ratio to one common scale, then use income − spending = savings.

CAT 2021 Slot 1 · Quant

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

CAT PYQ 4: Unit prices and trading ratios

Understand: Compare price per unit. Equal totals let you set one ratio equal to another.

CAT 2021 Slot 1 · Quant

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

CAT PYQ 6: Investment shares and returns

Understand: Split in the ratio of money put in × time. Percentage changes shift the shares.

CAT 2021 Slot 2 · Quant

Anil, Bobby, and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu's share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is

CAT PYQ 7: Subgroups with different percentages

Understand: Split the total into groups, apply each group’s percentage, then add back.

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 8: Geometry side, angle and altitude ratios

Understand: Turn the side or angle ratio into a length ratio, then use the formula.

CAT 2022 Slot 2 · Quant

In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC = 45° and ∠ABC = θ, then AD/BE equals

CAT PYQ 9: Stock and population ratios after transfers

Understand: Write the ratio before and after the transfer. The total stays fixed.

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 10: Allocate a conserved total

Understand: The total is conserved. Share it in a ratio and test whole-number cases.

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

Variations

Same idea, extra twist.

CAT PYQ 11: Integer multiplier and divisibility

Understand: Write the ratio as k times the parts. k must be a whole number.

CAT 2022 Slot 1 · Quant

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

CAT PYQ 12: Price ratio with a product condition

Understand: Write the ratio, then use the product condition to fix the size of each part.

CAT 2021 Slot 3 · Quant

A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is

CAT PYQ 13: Group size ratio from averages

Understand: Average × count = total. The ratio of group sizes comes from the changed average.

CAT 2022 Slot 1 · Quant

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

CAT PYQ 14: Age ratios

Understand: The age difference never changes. Use it to link the two ratios.

CAT 2024 Slot 2 · Quant

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

CAT 2025 Slot 1 · QuantEasy

Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was _____

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 · QuantMedium

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone 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]

Frequently asked questions

Where can I find CAT ratio questions with solutions?

Every Ratios 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 14 CAT PYQs at the top, because they repeat the most.

Are there CAT ratio 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 ratio and proportion questions?

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

What are the CAT ratio and proportion previous year questions (PYQs)?

They are the real questions of the CAT Actual Quant Papers that are about ratios and allocation: 58 questions, grouped into 14 repeating CAT PYQs, with the other questions listed after them in paper order.

Which ratio and proportion questions should I practise first for CAT?

Start with the first 6 CAT PYQs, which cover about 70% of the Ratios questions. Then do the first 10 (about 90%) and finally all 14 (all of them).

How many Ratios questions came in CAT papers?

40 Ratios questions are on this page: 7 in CAT 2025, 7 in CAT 2024, 10 in CAT 2023, 12 in CAT 2022, 4 in CAT 2021. The same real question is shown once.

How difficult are CAT Ratios questions?

Of the 6 Ratios questions that carry a difficulty rating, 3 are Easy, 3 Medium and 0 Hard; the other 34 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 Ratios?

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 14 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Work rate ratios and individual contributions	12	CAT 2021 S1 Q19	12	20.69%
2	Mixture ratios replacement and dilution	8	CAT 2021 S1 Q11	20	34.48%
3	Income payroll and savings on a common scale	5	CAT 2021 S1 Q17	25	43.10%
4	Unit prices equivalent costs and trading ratios	5	CAT 2021 S1 Q3	30	51.72%
5	Speed time length and meeting ratios	5	CAT 2021 S2 Q5	35	60.34%
6	Investment shares interest and returns	5	CAT 2021 S2 Q8	40	68.97%
7	Subgroup counts with different percentages	4	CAT 2021 S2 Q7	44	75.86%
8	Geometric side angle and altitude ratios	3	CAT 2022 S2 Q1	47	81.03%
9	Stock and population ratios after transfers	3	CAT 2024 S1 Q1	50	86.21%
10	Allocate a conserved total among groups	3	CAT 2023 S2 Q16	53	91.38%
11	Integer multiplier and divisibility of ratios	2	CAT 2022 S1 Q8	55	94.83%
12	Price ratio with a product condition	1	CAT 2021 S3 Q17	56	96.55%
13	Recover group size ratio from averages	1	CAT 2022 S1 Q20	57	98.28%
14	Age ratios with a constant difference	1	CAT 2024 S2 Q22	58	100%

Based on CAT Actual Quant Papers.

CAT Ratios Bible Top 10 Must Solve Ratios Questions covering 90% 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