30+ CAT Successive Discounts Questions Formula, Solved Qs & Free PDF

Quick Answer: CAT successive discounts questions test what happens when two or more discounts are applied one after another, with each discount acting on the price left after the previous one. Two successive discounts of a% and b% equal a single discount of (a + b - ab/100)%, which is always less than a + b. So 20% followed by 10% is a 28% discount, not 30%.

The fastest exam method is multiplicative: multiply the marked price by (1 - a/100) × (1 - b/100). In CAT 2026, expect this concept inside a profit-and-loss question involving markup on cost price rather than on its own. That is exactly where most aspirants lose the mark.

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Key Takeaways

• Successive discounts never add up. The shortfall from the simple sum is exactly ab/100 percentage points. You can compute it mentally.
• The multiplicative-factor method (0.8 × 0.9 = 0.72) beats the formula when three or more discounts appear. Learn both, but default to factors.
• Order does not matter. 20% then 10% gives the same price as 10% then 20%. Questions implying otherwise are testing whether you know this.
• Discount percentage sits on marked price. Profit percentage sits on cost price. Mixing the two bases is the commonest error in this topic.
• For a fixed sum of two discounts, the more unequal the split, the bigger the total discount. So 30% + 10% (37%) beats 20% + 20% (36%).
• Successive discounts, compound interest and depreciation run on one engine. Master it once and you cover parts of three CAT Quantitative Aptitude syllabus topics.
• QA carries 22 questions in 40 minutes. Eight were TITA in CAT 2025, with no negative marking, so verifiable arithmetic questions like these are among the safest attempts.

Table of Contents

What Are Successive Discounts In CAT 2026?

In CAT exam successive discount is a discount applied to an already-discounted price.

When a store advertises "40% off, plus an extra 10% off at checkout," the second 10% is not taken on the original tag price. It is taken on the 60% that remains. That single detail is the whole topic. It is also why the shopper saves 46% rather than 50%.

Worked Example: The ₹4,000 Jacket

Consider a jacket marked at ₹4,000 with successive discounts of 40% and 10%.

Step	Calculation	Amount
Marked Price (MP)	-	₹4,000
First discount (40%)	40% of 4,000	₹1,600
Price after first discount	4,000 - 1,600	₹2,400
Second discount (10%)	10% of 2,400	₹240
Selling Price (SP)	2,400 - 240	₹2,160
Total discount	4,000 - 2,160	₹1,840
Equivalent single discount	1,840 / 4,000	46%

The second discount was worth ₹240 instead of ₹400 because it operated on a smaller base. That ₹160 difference, as a percentage of MP, is 4%. And 4 is exactly (40 × 10)/100.

Why CAT Successive Discounts Questions Are Important

CAT successive discounts questions are one of the most practical and scoring topics in the Arithmetic section of CAT Quantitative Aptitude. While direct questions are rare, the concept is frequently embedded in Profit & Loss, Percentage, and Marked Price problems, making it an essential topic for CAT 2026 preparation.

A strong understanding of CAT successive discounts questions helps you:

• Solve Profit & Loss questions involving markups and multiple discounts.
• Build a solid foundation for Percentage-based Arithmetic.
• Improve speed using multiplication factors instead of lengthy calculations.
• Avoid common mistakes related to cost price and marked price.
• Master concepts that are equally useful in Compound Interest and Depreciation.

If you are aiming for a high percentile, practising Successive Discounts Questions for CAT should be a part of your regular Arithmetic revision. You can also download the CAT successive discounts questions PDF for offline practice and revision before the exam.

Download CAT Successive Discounts Questions PDF

Successive Discounts in the CAT 2026 Exam Pattern

As per the CAT exam pattern, the Quantitative Aptitude section carries 22 questions in 40 minutes. Each correct answer earns 3 marks and each incorrect MCQ costs 1 mark. In CAT 2025, the split was 14 MCQs and 8 TITA questions, where TITA carries no negative marking.

Within QA, the CAT Arithmetic syllabus has consistently been the largest contributor in recent years. That block covers percentages, profit and loss, ratios, averages, time and work, and time-speed-distance.

How CAT Frames the Question

• A profit and loss CAT question with markup over cost price
• A comparison question such as "Which store is cheaper?"
• A reverse question where the marked price or one of the discounts is unknown
• A layered price-change chain with an increase followed by discounts or tax added after discounts

Successive Discount Formula for CAT

Formula for Two Successive Discounts

For discounts of a% and b% applied successively, the equivalent single discount is:

D = a + b - (ab / 100)

Derivation: Take MP = 100.

After the first discount the price becomes:

100 - a

After the second discount:

(100 - a) × (1 - b/100)

Expanding gives:

100 - a - b + ab/100

Therefore, the total discount becomes:

a + b - ab/100

Formula for Three Successive Discounts

For three successive discounts of a%, b%, and c%, the equivalent single discount is:

D = a + b + c - (ab + bc + ca)/100 + (abc/10,000)

For example, if the discounts are 10%, 20%, and 30%:

D = 60 - (200 + 600 + 300)/100 + 6000/10000 = 49.6%

While the formula is useful to know, it becomes lengthy during the exam. The multiplicative-factor method is much faster and less prone to calculation errors.

The Multiplicative Factor Method

The fastest way to solve CAT successive discount questions is by using discount factors.

Selling Price = Marked Price × (1 - d₁/100) × (1 - d₂/100) × (1 - d₃/100)...

For example, if the discounts are 10%, 20%, and 30%:

Factor = 0.9 × 0.8 × 0.7 = 0.504

The customer pays 50.4% of the marked price.

Equivalent Discount = 49.6%.

This method immediately proves that the order of discounts never matters because multiplication is commutative.

Multiplication Factors Worth Memorising

Discount	Decimal Factor	Fraction
5%	0.95	19/20
6.25%	0.9375	15/16
10%	0.90	9/10
12.5%	0.875	7/8
16.67%	-	5/6
20%	0.80	4/5
25%	0.75	3/4
33.33%	-	2/3
37.5%	0.625	5/8
40%	0.60	3/5
50%	0.50	1/2

Using fractions instead of decimals often makes calculations significantly faster during the CAT exam.

Successive Discount Reference Table for CAT 2026

These combinations should become instant mental calculations.

Successive Discounts	Equivalent Single Discount
5% + 5%	9.75%
10% + 5%	14.5%
10% + 10%	19%
15% + 15%	27.75%
20% + 5%	24%
20% + 10%	28%
20% + 20%	36%
25% + 10%	32.5%
25% + 20%	40%
25% + 25%	43.75%
30% + 10%	37%
30% + 20%	44%
30% + 30%	51%
40% + 10%	46%
40% + 40%	64%
50% + 10%	55%
50% + 20%	60%
10% + 10% + 10%	27.1%
20% + 20% + 20%	48.8%

Notice that 30% + 10% gives a larger overall discount than 20% + 20%, even though both total 40 percentage points.

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Solved CAT Successive Discounts Questions: Level 1 (Foundation)

Q1. An article marked at ₹2,400 is sold after successive discounts of 20% and 15%. Find the selling price and the equivalent single discount.

Approach: Use multiplication factors.

SP = 2400 × 0.80 × 0.85

= 2400 × 0.68

SP = ₹1,632

The customer pays 68% of the marked price.

Equivalent Discount = 32%

Formula check:

20 + 15 - (20 × 15)/100

= 35 - 3

= 32%

Q2. Find the single discount equivalent to three successive discounts of 10% each.

Approach: Multiplication factors.

Factor = 0.9 × 0.9 × 0.9

= 0.729

Equivalent Discount

= 1 - 0.729

= 27.1%

Three successive 10% discounts are not equal to a 30% discount.

Q3. An item with a marked price of ₹5,000 sells for ₹3,375 after two successive discounts. If the first discount is 25%, find the second discount.

After the first discount:

5000 × 0.75 = ₹3750

Second factor = 3375 / 3750

= 0.90

Second Discount = 10%

Q4. Which is the better deal for a buyer: a flat 30% discount, or successive discounts of 20% and 12%?

Equivalent discount

= 20 + 12 - (20 × 12)/100

= 32 - 2.4

= 29.6%

Therefore, the flat 30% discount is slightly better.

Q5. After two successive discounts of 20% and 25%, an article sells for ₹1,800. Find its marked price.

Combined factor

= 0.80 × 0.75

= 0.60

Marked Price

= 1800 / 0.60

= ₹3,000

Successive Discounts Questions for CAT: Level 2 (Exam Level)

Q6. A shopkeeper marks his goods 45% above cost price and offers successive discounts of 10% and 10%. Find his profit percentage.

Assume Cost Price = ₹100.

Marked Price = ₹145.

Selling Price = 145 × 0.9 × 0.9

= ₹117.45

Profit = 17.45%

Q7. A trader allows two successive discounts of 20% and 10% and still earns a profit of 8%. By what percentage above cost price are his goods marked?

Assume Cost Price = ₹100.

Selling Price = ₹108.

MP × 0.80 × 0.90 = 108

MP × 0.72 = 108

MP = ₹150

Markup = 50%

Solved CAT Successive Discounts Questions: Level 1 (Foundation)

Q1. An article marked at ₹2,400 is sold after successive discounts of 20% and 15%. Find the selling price and the equivalent single discount.

Approach: Use factors because both answers are required.

SP = 2,400 × 0.80 × 0.85 = 2,400 × 0.68 = ₹1,632

The customer pays 68% of the marked price, so the equivalent discount is 32%.

Formula Check:

20 + 15 − (20 × 15)/100 = 35 − 3 = 32%

Q2. Find the single discount equivalent to three successive discounts of 10% each.

Approach: Factor method.

0.9 × 0.9 × 0.9 = 0.729

Equivalent Discount = 1 − 0.729 = 27.1%

Q3. An item with a marked price of ₹5,000 sells for ₹3,375 after two successive discounts. If the first discount is 25%, find the second.

Solution:

After first discount:

₹5,000 × 0.75 = ₹3,750

Second factor:

3375 ÷ 3750 = 0.90

Second Discount = 10%

Q4. Which is the better deal: Flat 30% discount or successive discounts of 20% and 12%?

Equivalent discount:

20 + 12 − (20 × 12)/100

= 32 − 2.4

= 29.6%

Winner: Flat 30% discount.

Q5. After successive discounts of 20% and 25%, an article sells for ₹1,800. Find the marked price.

Combined factor:

0.80 × 0.75 = 0.60

Marked Price = 1800 ÷ 0.60 = ₹3,000

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Successive Discounts Questions for CAT: Level 2 (Exam Level)

Q6. A shopkeeper marks goods 45% above cost and offers discounts of 10% and 10%. Find the profit percentage.

Assume CP = 100

MP = 145

SP = 145 × 0.9 × 0.9

= 145 × 0.81

= 117.45

Profit = 17.45%

Q7. A trader allows successive discounts of 20% and 10% and still earns 8% profit. Find the markup.

Assume CP = 100

SP = 108

MP × 0.8 × 0.9 = 108

MP × 0.72 = 108

MP = 150

Markup = 50%

Q8. Two successive discounts, where the second is twice the first, equal a single discount of 28%. Find both discounts.

Let first discount = d

Second discount = 2d

(1 − d)(1 − 2d) = 0.72

2d² − 3d + 0.28 = 0

d = 10%

Therefore discounts are:

• 10%
• 20%

Q9. A product's list price increases by 25%, then receives discounts of 10% and 20%. Find the net change.

Net factor:

1.25 × 0.90 × 0.80 = 0.90

Final price is 10% below the original list price.

Q10. A dealer buys an article at a 30% discount and sells it at a 5% discount on the same list price. Find profit percentage.

Assume List Price = 100

CP = 70

SP = 95

Profit = (95 − 70)/70 × 100

= 25/70 × 100

= 35.71%

Q11. Two stores offer different discounts on an ₹8,000 article.

Store A: 25% + 15%

Factor = 0.75 × 0.85 = 0.6375

SP = ₹5,100

Store B: 30% + 10%

Factor = 0.70 × 0.90 = 0.63

SP = ₹5,040

Store B is cheaper by ₹60.

How to Solve CAT Successive Discounts Questions Step by Step

Most CAT successive discounts questions follow a predictable pattern. Once you learn the correct approach, these questions become some of the quickest marks in the QA section.

Step 1: Identify the marked price

Read the question carefully and determine whether the given price is the Marked Price (MP), Cost Price (CP), or Selling Price (SP).

Step 2: Convert discounts into multiplication factors

Instead of subtracting percentages repeatedly, use factors.

• 10% discount = × 0.90 
• 20% discount = × 0.80
• 25% discount = × 0.75
• 40% discount = × 0.60

Step 3: Multiply the factors

For successive discounts of 20% and 10%:

Selling Price = MP × 0.80 × 0.90

= MP × 0.72

Therefore, the equivalent discount is 28%.

Step 4: Find the required quantity

Depending on the question, calculate:

• Selling Price
• Marked Price
• Profit Percentage
• Equivalent Discount
• Unknown Discount

Step 5: Verify your answer

Whenever possible, multiply the factors again to ensure your calculations are correct. This simple verification method reduces silly mistakes in CAT successive discounts questions.

For additional practice, solve more Successive Discounts Questions for CAT and revise regularly using the CAT successive discounts questions PDF.

CAT Successive Discounts Question Shortcut Tricks

Learning a few shortcut techniques can help you solve CAT successive discounts questions much faster during the exam.

Shortcut 1: Use the Equivalent Discount Formula

For two successive discounts of a% and b%:

Equivalent Discount = a + b − (ab/100)

Example:

20% and 10%

= 20 + 10 − (20 × 10)/100

= 30 − 2

= 28%

Shortcut 2: Use Multiplication Factors

Instead of remembering formulas, simply multiply the remaining value.

Example:

25% and 20%

= 0.75 × 0.80

= 0.60

Equivalent discount = 40%

This is the fastest method for solving CAT successive discounts questions involving multiple discounts.

Shortcut 3: Memorise Common Discount Pairs

Some combinations appear repeatedly in exams.

Successive Discounts	Equivalent Discount
10% + 10%	19%
20% + 10%	28%
20% + 20%	36%
25% + 20%	40%
30% + 10%	37%
40% + 10%	46%
50% + 20%	60%

Shortcut 4: Never Add Discounts Directly

20% + 10% is not 30%.

Always calculate the second discount on the reduced price.

Shortcut 5: Remember the Base

• Discount is always calculated on Marked Price.
• Profit is always calculated on Cost Price.

Confusing these two bases is the most common mistake in Successive Discounts Questions for CAT.

Previous Year CAT Successive Discounts Questions

Although direct CAT successive discounts questions do not appear every year, the concept has consistently been tested through mixed Arithmetic questions involving Profit & Loss, Marked Price, and Percentages. Instead of asking only for the equivalent discount, CAT generally combines successive discounts with one or more additional concepts.

Some of the most common previous-year patterns include:

• A shopkeeper marks an article above the cost price and offers two successive discounts before asking you to calculate the final profit percentage.
• Comparison-based questions where two stores offer different discount combinations and you must identify the better deal.
• Reverse questions in which the selling price is given after successive discounts and you need to determine the marked price or an unknown discount.
• Composite Arithmetic questions involving markup, discount, GST, or tax in the same calculation.

The best way to prepare for these questions is by solving Successive Discounts Questions for CAT from previous CAT papers and topic-wise practice sets. Rather than memorising formulas alone, focus on identifying the correct multiplication factors and applying them quickly under time pressure.

For structured revision, download the CAT successive discounts questions PDF, which contains solved examples, previous-year style questions, shortcut techniques, and practice exercises to strengthen your preparation. By consistently practising CAT successive discounts questions, you will improve both your calculation speed and your accuracy in the Arithmetic section.

Successive Discounts in XAT, SNAP, NMAT, CMAT and MAT

The concept is common across MBA entrances in the 2026-27 cycle, but the testing style differs. These exams should not be prepared for interchangeably. A fuller breakdown sits in CAT vs XAT vs SNAP vs NMAT.

• CAT - Quantitative Aptitude. Typically embedded in composite profit-and-loss questions rather than asked directly. Calculation is moderate, and the difficulty lies in the setup.
• XAT - Quantitative Ability and Data Interpretation. XAT has historically favoured somewhat more calculation-intensive and occasionally trickier arithmetic framing than CAT. It also carries a separate Decision Making section that CAT does not have.
• SNAP - Quantitative, Data Interpretation and Data Sufficiency. Less time per question puts a higher premium on the reference table and mental factors than on elaborate setups.
• NMAT - Quantitative Skills. A larger question count and a sectional structure that rewards steady speed on standard forms.
• CMAT and MAT - Quantitative Techniques. Generally more direct, formula-application framing.

The practical implication is worth stating plainly. The concept transfers fully across all five exams. The practice strategy does not. So drill the topic once for concept, then re-practise it inside each exam's own sectional format and timing. Confirm current section names, question counts and timings against each exam's official 2026 notification before finalising a plan.

Your Next Step for CAT 2026

Topic practice builds mechanics. It cannot reproduce the two conditions that make CAT difficult: mixed-topic sequencing and a 40-minute clock. Twenty discount questions in a row build a pattern recognition that evaporates the moment the same question turns up as question 14, sandwiched between a Geometry problem and a quadratic.

So use this sequence. Finish the practice set above. Download the PDF and drill it to reliability. Then move straight to a timed sectional mock test for CAT on Arithmetic. Afterwards, read your own paper properly, because how to analyse CAT mock tests explains how to separate a concept gap from a setup error. That distinction is what actually moves a percentile.

Topic-level practice establishes the skill. Sectional and full-length testing converts it into a score.

Conclusion

CAT successive discounts questions are among the highest ROI topics in Arithmetic because the underlying concept is simple, repeatable, and directly applicable to several other chapters like compound interest, depreciation, and percentage change. Rather than memorising formulas alone, focus on understanding the multiplicative-factor approach while practicing CAT sample papers, the distinction between cost price and marked price, and the sequence in which discounts are applied.

With regular practice, these questions can become some of the quickest marks in the Quantitative Aptitude section. Master the factor method, revise the reference table, avoid the common mistakes discussed above, and solve enough mixed Arithmetic questions to recognise the pattern instantly in the exam.

Finally, don't stop at theory. Attempt sectional tests, analyse every mistake, and revisit this topic during your final revision cycle. Consistency in practice is what converts a concept into a percentile-boosting strength on CAT 2026.