Question 1 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesEasy
What is 20% of 30% of 50?
Official Correct Answer: D. 20% of 30% of 50 is calculated as (20/100) * (30/100) * 50 = 0.2 * 0.3 * 50 = 3. Therefore, the answer is D) 2.
Arithmetic Practice Hub (QA) • 877 Qs• Official Answer Keys
CAT Arithmetic Practice Questions & Drills
Comprehensive Practice Library Covering TSD, Time & Work, Percentages, Profit & Loss, Mixtures, and Averages with Step-by-Step Derivations
877 Total Questions
MCQ: 711 (+3 / -1)
TITA: 166 (0 Negative Penalty)
Core Formulas & Shortcut Matrix: Arithmetic
Percentage MultiplierFormula #1
Final = Initial × (1 ±)
Essential for successive profit, markup, and population changes.
Relative Speed (Opposite Direction)Formula #2
S_{rel} = S_1 + S_2
Use when bodies move towards each other; add speeds.
Relative Speed (Same Direction)Formula #3
S_{rel} = |S_1 - S_2|
Use when one body pursues another in the same direction.
Time and Work Unitary RuleFormula #4
\frac{1}{T_{total}} = + $
Equate total work to LCM of individual time units.
Exam Hall Traps & Speedbreakers to Avoid
- •Reversing percentage bases: A 25% increase followed by a 20% decrease returns to 100%, not a net 5% gain.
- •Average Speed Trap: Average speed is never the arithmetic mean (S1 + S2)/2; it is Total Distance / Total Time = 2*S1*S2 / (S1 + S2) for equal distances.
- •Units mismatch: Mixing km/h with m/s without converting (multiply by 5/18 or 18/5).
Bite-Sized Practice Sets (36 Modules Available)
Authentic CAT BlueprintSolve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.
20 QuestionsFree Pass
Set 01: Percentages
Difficulty: Easy
25 QuestionsFree Pass
Set 02: Ratio, Proportion & Variation
Difficulty: Easy
25 QuestionsPro Pass
Set 03: Time & Work
Difficulty: Easy
25 QuestionsPro Pass
Set 04: Time, Speed & Distance
Difficulty: Easy
15 QuestionsPro Pass
Set 05: Mixture & Alligation
Difficulty: Easy
25 QuestionsPro Pass
Set 06: Percentages
Difficulty: Hard
24 QuestionsPro Pass
Set 07: Time & Work
Difficulty: Hard
25 QuestionsPro Pass
Set 08: Profit & Loss
Difficulty: Moderate
24 QuestionsPro Pass
Set 09: Percentages
Difficulty: Easy
25 QuestionsPro Pass
Set 10: Time & Work
Difficulty: Easy
25 QuestionsPro Pass
Set 11: Profit & Loss
Difficulty: Hard
25 QuestionsPro Pass
Set 12: Simple & Compound Interest
Difficulty: Easy
25 QuestionsPro Pass
Set 13: Ratio, Proportion & Variation
Difficulty: Moderate
25 QuestionsPro Pass
Set 14: Time, Speed & Distance
Difficulty: Hard
25 QuestionsPro Pass
Set 15: Percentages
Difficulty: Easy
25 QuestionsPro Pass
Set 16: Time & Work
Difficulty: Hard
25 QuestionsPro Pass
Set 17: Mean
Difficulty: Easy
25 QuestionsPro Pass
Set 18: Ratio, Proportion & Variation
Difficulty: Moderate
25 QuestionsPro Pass
Set 19: Profit & Loss
Difficulty: Hard
25 QuestionsPro Pass
Set 20: Ratio, Proportion & Variation
Difficulty: Easy
25 QuestionsPro Pass
Set 21: Percentages
Difficulty: Moderate
25 QuestionsPro Pass
Set 22: Time & Work
Difficulty: Moderate
25 QuestionsPro Pass
Set 23: Mixture & Alligation
Difficulty: Hard
25 QuestionsPro Pass
Set 24: Time, Speed & Distance
Difficulty: Easy
25 QuestionsPro Pass
Set 25: Percentages
Difficulty: Easy
24 QuestionsPro Pass
Set 26: Simple & Compound Interest
Difficulty: Hard
25 QuestionsPro Pass
Set 27: Ratio, Proportion & Variation
Difficulty: Easy
25 QuestionsPro Pass
Set 28: Percentages
Difficulty: Moderate
25 QuestionsPro Pass
Set 29: Profit & Loss
Difficulty: Hard
25 QuestionsPro Pass
Set 30: Time, Speed & Distance
Difficulty: Easy
25 QuestionsPro Pass
Set 31: Percentages
Difficulty: Easy
25 QuestionsPro Pass
Set 32: Time & Work
Difficulty: Moderate
20 QuestionsPro Pass
Set 33: Mixture & Alligation
Difficulty: Hard
25 QuestionsPro Pass
Set 34: Time, Speed & Distance
Difficulty: Easy
25 QuestionsPro Pass
Set 35: Simple & Compound Interest
Difficulty: Hard
25 QuestionsPro Pass
Set 36: Ratio, Proportion & Variation
Difficulty: Easy
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Official Exam Questions & Explanations (25 of 877)
Sorted in official convenor sequenceQuestion 2 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossEasy
A shopkeeper sells an item for $120, making a profit of 20%. What was the cost price of the item?
Official Correct Answer: A. Let the cost price be $x. Since the shopkeeper makes a 20\% profit, the selling price is 1.2x. Given the selling price is $120, we have 1.2x = 120. Solving for x, we get x = 120 / 1.2 = 100. Therefore, the cost price is A) $100.
Question 3 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesModerate
If 40% of a number is 120, what is 60% of the number?
Official Correct Answer: A. Let the number be x. Then, 40% of x is 120, which gives 0.4x = 120. Solving for x, we get x = 120 / 0.4 = 300. Now, 60% of 300 is 0.6 * 300 = 180. Therefore, the answer is A) 180.
Question 4 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossModerate
A retailer sells a product at a 20% discount and still makes a 10% profit. If the marked price is $200, what is the cost price of the product?
Official Correct Answer: B. Let the cost price be $x. The retailer sells the product at 20\% discount on the marked price, which is $200. So, the selling price is 0.8 * 200 = 160. Since the retailer makes a 10% profit, we have 1.1x = 160. Solving for x, we get x = 160 / 1.1 = 145.45, approximately $145. Therefore, the closest option is B) $150.
Question 5 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesHard
If 30% of a number is 120, and another 20% of the same number is 80, what is the original number?
Official Correct Answer: A. Let the number be x. Then, 30% of x is 120, which gives 0.3x = 120. Solving for x, we get x = 120 / 0.3 = 400. We can verify this by checking that 20% of 400 is indeed 80. Therefore, the answer is A) 400.
Question 6 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossHard
A wholesaler sells an item at a 15% discount and makes a 20% profit. If the marked price is $250, what is the cost price of the item?
Official Correct Answer: A. Let the cost price be $x. The wholesaler sells the item at a 15\% discount on the marked price, which is $250. So, the selling price is 0.85 * 250 = 212.50. Since the wholesaler makes a 20% profit, we have 1.2x = 212.50. Solving for x, we get x = 212.50 / 1.2 = 177.08, approximately $180. Therefore, the closest option is A) $200.
Question 7 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesEasy
If 25% of a number is 15, what is 40% of the same number?
TITA Answer:
Official Correct Answer: 24. Let the number be x. Then, 25% of x is 15, which gives 0.25x = 15. Solving for x, we get x = 15 / 0.25 = 60. Now, 40% of 60 is 0.4 * 60 = 24. Therefore, the answer is 24.
Question 8 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossEasy
If the cost price of a product is $100 and it is sold for $120, what is the profit percentage?
TITA Answer:
Official Correct Answer: 20. The profit is $120 - 100 = 20. The profit percentage is (20 / 100) * 100 = 20%. Therefore, the answer is 20.
Question 9 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesModerate
If 15% of a number is 45, what is 10% of the same number?
Official Correct Answer: A. Let the number be x. Then, 15% of x is 45, which gives 0.15x = 45. Solving for x, we get x = 45 / 0.15 = 300. Now, 10% of 300 is 0.1 * 300 = 30. Therefore, the answer is A) 30.
Question 10 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossModerate
A shopkeeper sells an item at a 25% discount and still makes a 25% profit. If the marked price is $200, what is the cost price of the item?
Official Correct Answer: A. Let the cost price be $x. The shopkeeper sells the item at a 25\% discount on the marked price, which is $200. So, the selling price is 0.75 * 200 = 150. Since the shopkeeper makes a 25% profit, we have 1.25x = 150. Solving for x, we get x = 150 / 1.25 = 120. Therefore, the answer is A) $150.
Question 11 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesHard
If 35% of a number is 70, what is 20% of the same number?
Official Correct Answer: A. Let the number be x. Then, 35% of x is 70, which gives 0.35x = 70. Solving for x, we get x = 70 / 0.35 = 200. Now, 20% of 200 is 0.2 * 200 = 40. Therefore, the answer is A) 40.
Question 12 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossHard
A retailer sells a product at a 30% discount and still makes a 20% profit. If the marked price is $250, what is the cost price of the item?
Official Correct Answer: A. Let the cost price be $x. The retailer sells the product at a 30\% discount on the marked price, which is $250. So, the selling price is 0.7 * 250 = 175. Since the retailer makes a 20% profit, we have 1.2x = 175. Solving for x, we get x = 175 / 1.2 = 145.83, approximately $146. Therefore, the closest option is A) $175.
Question 13 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesEasy
If 20% of a number is 100, what is 50% of the same number?
TITA Answer:
Official Correct Answer: 250. Let the number be x. Then, 20% of x is 100, which gives 0.2x = 100. Solving for x, we get x = 100 / 0.2 = 500. Now, 50% of 500 is 0.5 * 500 = 250. Therefore, the answer is 250.
Question 14 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesEasy
A store owner increases the price of an item by 20% and then offers a 10% discount. What is the net percentage change in the price of the item?
A
8% (B) 9% (C) 10% (D) 12%
Official Correct Answer: A. Let the original price be $100. After a 20\% increase, the price becomes $120. A 10% discount on $120 is $12. So, the final price is $108. The net percentage change is $8$ (final price - original price) / 100 (original price) * 100 = 8%.
Question 15 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossEasy
A shopkeeper bought a radio for $250 and sold it for $300. What is the profit percentage?
A
15% (B) 18% (C) 20% (D) 25%
Official Correct Answer: D. The profit is $300 - 250 = 50. The profit percentage is $50 / 250 * 100 = 20%.
Question 16 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesModerate
If 40% of a number is 140, what is 60% of the number?
A
210 (B) 220 (C) 230 (D) 240
Official Correct Answer: A. 40% of the number is 140, so the number is $140 / 0.40 = 350$. Therefore, 60% of the number is $350 * 0.60 = 210$.
Question 17 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossModerate
A dealer sells a bicycle for $1200 and incurs a loss of 20\%. At what price should he have sold it to gain a 20\% profit?
A
$1800 (B) $1900 (C) $2000 (D) $2100
Official Correct Answer: A. The cost price of the bicycle is $1200 / 0.80 = 1500. To gain a 20\% profit, the selling price should be $1500 * 1.20 = 1800.
Question 18 of 877
ThinkCAT Practice SetQAArithmetic • PercentagesEasy
A company's sales increased by 10% from the previous year. If the sales in the previous year were $1200, what are the sales this year?
TITA Answer:
Official Correct Answer: 1320.00. Sales increased by 10%, so the current year's sales are $1200 * 1.10 = 1320$.
Question 19 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossEasy
If a shopkeeper sells a book for $120 and makes a 20% profit, what is the cost price of the book?
TITA Answer:
Official Correct Answer: 100.00. A 20% profit means the selling price is 120% of the cost price. So, $120 = 1.20 * \text{cost price}$. Solving, $\text{cost price} = 120 / 1.20 = 100$.
Question 20 of 877
ThinkCAT Practice SetQAArithmetic • Profit & LossModerate
A company sells a product at a 15% discount and still makes a 25% profit. What was the original marked price if the selling price is $170?
A
$200 (B) $220 (C) $240 (D) $260
Official Correct Answer: C. Let the original marked price be $x$. A 15% discount means the selling price is 85% of the marked price. So, $0.85x = 170$. Solving, $x = 170 / 0.85 = 200$. The cost price is 75% of the marked price, so $0.75x = 150$. Therefore, the original marked price is $240$.
Question 21 of 877
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationEasy
The ratio of the incomes of A and B is 5:3. If the income of A is $7500, what is the income of B?
Official Correct Answer: A. Given ratio is 5:3. If A's income is $7500, then B's income is calculated as (7500 * 3) / 5 = 4500.
Question 22 of 877
ThinkCAT Practice SetQAArithmetic • Simple & Compound InterestEasy
An amount of $1200 is invested at a simple interest rate of 5% per annum. How much will it be worth after 3 years?
Official Correct Answer: A. Simple interest = (1200 * 5 * 3) / 100 = 180. Total amount = 1200 + 180 = 1380.
Question 23 of 877
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationModerate
If the ratio of A to B is 4:7 and the ratio of B to C is 5:3, what is the ratio of A to C?
Official Correct Answer: A. The ratio of A to B is 4:7 and B to C is 5:3. To find the ratio of A to C, we need to equate the B terms, so the combined ratio is 20:21.
Question 24 of 877
ThinkCAT Practice SetQAArithmetic • Simple & Compound InterestModerate
What is the compound interest on $1000 for 2 years at 5% per annum, compounded annually?
Official Correct Answer: A. CI = P(1 + r/100)^t - P = 1000(1 + 5/100)^2 - 1000 = 102.50.
Question 25 of 877
ThinkCAT Practice SetQAArithmetic • Ratio, Proportion & VariationHard
If the ratio of the ages of A, B, and C is 2:3:4, and the sum of their ages is 126 years, what is the age of A?
Official Correct Answer: B. The sum of the ratios is 2+3+4=9. A's age is (2/9) * 126 = 28 / 3 = 24 years.
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Frequently Asked Questions about CAT Arithmetic Practice Questions & Drills
How many Arithmetic practice questions are in this collection?
This repository contains 877 curated CAT Arithmetic practice questions organized by subtopic and difficulty (Easy, Moderate, Hard).
What is the historical weightage of Arithmetic in the CAT exam?
8 to 10 Questions in QA Section (~35–45% of QA weightage). Excelling in Arithmetic is critical for securing a 99.0+ percentile.
Are these practice questions accompanied by past year CAT questions?
Yes! You can explore verified official past year questions for this section in our dedicated CAT Arithmetic Previous Year Questions (2017–2025) archive.
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