🔢 Quant

Arithmetic

Percentages, profit & loss, time-speed-distance, work & time, mixtures. Core of CAT Quant.

38%

of Quant

Why This Topic Matters

Total PYQs📊

124

of 1002 · 2021–2025

Years featured📅

5/5

of recent CAT years

% of Quant📈

~38%

of section questions

Est. hours⏱️

~45h

to master

9/22

2021

~9/22

2022

~9/22

2023

~8/22

2024

~8/22

2025

The biggest block in CAT Quant

Arithmetic is the largest area of CAT Quant — typically 8–10 of the 22 questions in a slot (38% of Quant). It also powers Data Interpretation. The sub-topics — percentages, profit & loss, interest, ratio–average–mixtures, time-speed-distance, time & work — each have their own page; this overview gives you the trends, the mental-math toolkit, and the MCQ shortcuts that cut across all of them.

What CAT 2021–2025 actually asked

Sub-skill	2021	2022	2023	2024	2025	Avg/slot
Time & Work	2.0	1.0	1.7	1.0	1.0	1.3
Time, Speed & Distance	1.0	1.3	1.3	1.0	1.7	1.3
Profit & Loss	1.7	0.7	1.3	1.0	1.0	1.1
Averages	1.0	2.0	0.7	1.0	0.7	1.1
Mixtures & Alligation	1.3	1.0	1.0	1.0	1.0	1.1
Simple & Compound Interest	0.7	1.0	0.7	1.0	1.0	0.9
Percentages	0.7	0.7	1.3	0.7	0.3	0.7
Ratio & Proportion	0.3	0.7	0.3	0.7	0.7	0.5

🎯PYQ Evidence

Every one of the eight arithmetic sub-skills appeared in every single year, 2021–2025. There is no "safe to skip" row in this table — CAT spreads ~25 arithmetic questions a year almost evenly across all eight. Contrast this with Modern Math (where probability appeared once in five years): arithmetic is where consistency is rewarded, and it's the densest supply of bankable easy-medium marks in Quant. Roughly a third of QA is TITA (no negative marking); difficulty splits about a third easy / medium / hard — bank the easy third first.

Mental-math toolkit

Fraction → percentage (recognise these instantly in DI and P&L):

Fraction	%	Fraction	%
1/2	50	1/8	12.5
1/3	33.3	1/9	11.1
1/4	25	1/11	9.1
1/6	16.7	1/12	8.3

Successive percentage changes of $a\%$ then $b\%$ combine to:

$a + b + \frac{ab}{100}\ \%$

Squaring numbers ending in 5: $(a5)^2 = a(a{+}1)\,|\,25$ . So $35^2 = (3\cdot4)\,|\,25 = 1225$ .

Product-constant rule: if price rises $x\%$ but spending is fixed, consumption must fall by $\dfrac{x}{100+x}\times100\%$ .

A worked example

✏️Worked Example

A shopkeeper marks goods 40% above cost and then offers a 25% discount. What is the profit percentage?

Treat it as two successive changes on the cost price: +40% (marking up), then −25% (discount):

$40 + (-25) + \frac{40\times(-25)}{100} = 40 - 25 - 10 = \mathbf{+5\%}$

Check directly: $\text{SP} = 0.75 \times 1.40 \times \text{CP} = 1.05\,\text{CP}$ → 5% profit. The successive-change formula got there with no fractions.

MCQ shortcuts (no shortcut for TITA)

CAT MCQs reward working backward and smart, not always solving forward:

Backsolving: plug the options into the condition; start from the middle value to halve your work.
Eliminate by estimation, parity, or units digit before computing exactly.
Smart numbers: for "base-independent" questions (answer is a %, ratio, or fraction), assume a clean base like 100; avoid 0 and 1.

These apply to MCQs only — TITA has no options to exploit, so solve those forward and cleanly.

⚠️CAT Trap

Percentage-of-what. The single most engineered arithmetic trap across recent papers: a percentage applied to the wrong base — a discount % on cost instead of marked price, an increase measured from the new value, "75% were unprofitable" read as "75% profitable." Before any percentage move, name the base out loud. The wrong-base value is almost always sitting among the options.

Watch this

2IIM's compilation of CAT arithmetic previous-year questions, worked end to end:

Where to go deeper

Each arithmetic sub-topic has its own page with formulas, diagrams, and practice: Time-Speed-Distance, Time & Work, Mixtures & Alligation, Interest & P&L, Averages & Ratio.

🎯PYQ Evidence

Arithmetic rewards one habit: name the unknown, then let one equation do the work. : write the two quantities as 13k and 9k so a single k captures all valid sizes, then the "after 21 move" condition cross-multiplies to 11k = 693, k = 63. : make the job a fixed LCM of person-hours (120 units), fix each rate (Renu 2, Seema 3 units/hr), and the day conditions collapse to one linear equation. : track only the acid, since removing 20% of a well-mixed 200 L removes 20% of the acid present while volume returns to 200 — step through the three swaps to land near 27%. The move is always the same: one variable or one tracked quantity turns the words into arithmetic.

Checklist

Know the fraction → % table cold
Use successive-change instead of chaining multipliers
Name the base before applying any percentage
On MCQs, consider backsolving / smart numbers first
Bank the easy third; don't over-invest in one hard word problem
Mind TITA vs MCQ — no negative marking on TITA, so always attempt

Sample Questions

52 practice questions

Easy

Joe buys 360 gallons of paint. During week 1 he uses 1/4 of all the paint. During week 2 he uses 1/5 of the remaining paint. How many gallons has Joe used?

Easy

3/4 of all married couples have more than one child. 2/5 of all married couples have more than 3 children. What fraction of all married couples have exactly 2 or 3 children?

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CAT PYQ Spotlight

Actual CAT questions on this topic

CAT 2025 · Slot 1

Hard

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 2024 · Slot 1

TITAHard

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

Your answer

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