CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus

Percentages questions ask you to express a quantity as a part of 100, or to find the result when a quantity rises or falls by a given percent. They also sit inside many profit, data and mixture problems.

Tap Show answer, or open the detailed solution (free login). Page 1 of 10.

Start here: the repeating CAT PYQs

Study the percentage pattern in each CAT PYQ, then practise variations. The 15 selected families contain 55 of the 56 questions tagged Percentage multipliers in the reviewed set.

CAT Percentages Bible Top 10 PYQ Questions

Questions	CAT Area Covered
First 5 CAT Questions	48.21%
First 10 CAT Questions	82.14%
First 15 CAT Questions	98.21%

Importance of Percentages each year of CAT exam

CAT year	Total Percentages questions	First 6 examples	First 10 examples	First 15 examples	Outside these 15 families	Share of all Quant
2021	11	7	10	11	0	16.67%
2022	5	1	2	4	1	7.58%
2023	15	6	12	15	0	22.73%
2024	14	11	13	14	0	21.21%
2025	11	7	9	11	0	16.67%
Total	56	32	46	55	1	16.97%
Share of all 56	100%	57.14%	82.14%	98.21%	1.79%

Quick review for beginners and last day revision

Rule	Formula or what to do	Small example
Convert a percentage	p% = p/100	25% = 0.25 = 1/4
Increase or decrease	New = old × (1 ± p/100)	20% increase → ×1.20; 20% decrease → ×0.80.
Reverse a change	Old = new / multiplier	After a 20% discount price is 80 → marked price = 80/0.8 = 100.
Successive changes	Multiply the factors.	+20%, then −20% → 1.2 × 0.8 = 0.96, a 4% fall.
Profit and discount bases	SP = CP(1 + profit%); SP = MP(1 − discount%)	Profit is based on CP; discount is based on MP.
Simple interest	Interest = P × r × t / 100	At 5% simple interest, interest after 3 years = 0.15P.
Compound interest	Amount = P(1 + r/100)ⁿ	Half-yearly: use r/2 each half-year and double the number of periods.
Weighted percentage	Overall change = sum(group amount × group rate) / total amount	Weight salary changes by original salary totals.
Replacement	Original component remaining = initial amount × (1 − removed fraction)ⁿ	Two 10% replacements retain 0.9² = 81% of the original component.
Percentage points	Subtract percentages to compare rates; divide when finding relative change.	20% to 25% is +5 percentage points and a 25% relative increase.

10 Core CAT PYQ Questions

Study these first.

CAT PYQ 1: Repeated fractional replacement

Understand: After each replacement the old liquid left is multiplied by (1 minus the fraction removed). Repeat this for every step.

CAT 2021 Slot 2 · Quant

From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

CAT PYQ 2: Compound growth factors and equivalent simple interest

Understand: Yearly interest amounts grow by the same factor, so next year's interest is this year's squared divided by last year's.

CAT 2021 Slot 1 · Quant

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

CAT PYQ 4: Successive changes with unknown rates

Understand: Multiply the growth factors and set them equal to the final amount. Reject the root that breaks the given condition.

CAT 2021 Slot 2 · Quant

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

CAT PYQ 6: Percentages of groups and remaining shares

Understand: Turn each percentage into a count of its group. Equal counts give the ratio of the 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 7: Weighted sale revenue and overall profit

Understand: Find the average cost of the mixture, then the target selling price, and solve for the unknown price.

CAT 2021 Slot 2 · Quant

A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

CAT PYQ 8: Profit shares and successive trading transactions

Understand: A change in profit rate times an investment gives the change in profit. Use it to find each investment.

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 9: Percentage stocks constrained to integer counts

Understand: Write each percentage as a fraction of the total. Counts must be whole numbers, so the total must suit every denominator.

CAT 2023 Slot 3 · Quant

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

CAT PYQ 10: Component percentages after adding mixtures

Understand: Write the amount of the pure part before and after mixing. Equate it to the given percentage of the new total.

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

Variations

Same idea, extra twist.

CAT PYQ 12: Workforce and efficiency percentages

Understand: Work done is proportional to people times hours. Equate the work per person hour in both stages.

CAT 2022 Slot 3 · Quant

A group of \(N\) people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of \(N\) is

CAT PYQ 13: Simple interest rates and reinvestment

Understand: Equal interest means rate times time times principal is equal. Turn that into a ratio of the two parts.

CAT 2022 Slot 1 · Quant

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

CAT PYQ 15: Unit price percentage and quantity ratio

Understand: Weight ratio equals price ratio divided by unit price ratio.

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 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

A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to the customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

CAT 2025 Slot 1 · QuantMedium

In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was _____.

CAT 2025 Slot 1 · QuantMedium

At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

CAT 2025 Slot 1 · QuantHard

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of the resulting solution with water, and finally replaces 10% of this solution with acid, then 15% of the solution obtained with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

Frequently asked questions

Where can I find CAT percentage questions with solutions?

Every Percentages 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 15 CAT PYQs at the top, because they repeat the most.

Are there CAT percentage 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 percentage questions?

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

What are the CAT percentage previous year questions (PYQs)?

They are the real questions of the CAT Actual Quant Papers that are about percentages and percentage change: 56 questions, grouped into 15 repeating CAT PYQs, with the other questions listed after them in paper order.

Which percentage questions should I practise first for CAT?

Start with the first 6 CAT PYQs, which cover about 60% of the Percentages questions. Then do the first 10 (about 80%) and finally all 15 (about 98%).

How many Percentages questions came in CAT papers?

40 Percentages questions are on this page: 10 in CAT 2025, 14 in CAT 2024, 11 in CAT 2023, 3 in CAT 2022, 2 in CAT 2021. The same real question is shown once.

How difficult are CAT Percentages questions?

Of the 10 Percentages questions that carry a difficulty rating, 3 are Easy, 6 Medium and 1 Hard; the other 30 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 (2 sets here), so you never solve half of one. Questions that stand alone are shown five to a page.

Where can I practise more Percentages?

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 16 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Repeated fractional replacement	6	CAT 2021 S2 Q4	6	10.71%
2	Compound growth factors and equivalent simple interest	6	CAT 2021 S1 Q10	12	21.43%
3	Cost marked price discount and free item multipliers	5	CAT 2024 S1 Q21	17	30.36%
4	Successive percentage changes with unknown rates	5	CAT 2021 S2 Q18	22	39.29%
5	Weighted subgroup payroll or investment growth	5	CAT 2023 S2 Q8	27	48.21%
6	Percentages of groups and remaining shares	5	CAT 2021 S2 Q7	32	57.14%
7	Weighted sale revenue and overall profit	4	CAT 2021 S2 Q22	36	64.29%
8	Profit shares and successive trading transactions	4	CAT 2021 S2 Q8	40	71.43%
9	Percentage stocks constrained to integer counts	3	CAT 2023 S3 Q14	43	76.79%
10	Component percentages after adding mixtures	3	CAT 2021 S3 Q1	46	82.14%
11	Compound balances after repayments	2	CAT 2023 S2 Q12	48	85.71%
12	Workforce and efficiency percentages	2	CAT 2022 S3 Q16	50	89.29%
13	Simple interest rates and reinvestment	2	CAT 2022 S1 Q16	52	92.86%
14	Percentage changes in speed or angle	2	CAT 2025 S3 Q16	54	96.43%
15	Unit price percentage and quantity ratio	1	CAT 2021 S1 Q3	55	98.21%
16	Reciprocal day growth factors	1	CAT 2022 S2 Q7	56	100%

Based on CAT Actual Quant Papers.

CAT Percentages Bible Top 10 Must Solve Percentages Questions covering 80% of Syllabus

Start here: the repeating CAT PYQs

10 Core CAT PYQ Questions

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Variations

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Frequently asked questions