Arithmetic Reasoning Questions: Guide with Answers & Tips

Below you’ll find a wide range of arithmetic ability questions and answers, each accompanied by clear solutions and explanations. These arithmetic reasoning examples cover various topics and difficulty levels, helping you understand both the methods and logic required to solve similar problems.

1. What is the smallest number divisible by 12, 15, and 20?
Solution:
Find the least common multiple (LCM) of 12, 15, and 20.
12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5
LCM = 2² × 3 × 5 = 60
Explanation: The LCM is the smallest number divisible by all the given numbers.

2. What is the remainder when 38 is divided by 7?
Solution:
38 ÷ 7 = 5 remainder 3, since 7 × 5 = 35 and 38 - 35 = 3.
Explanation: Divide and subtract to get the remainder.

3. What is 35% of 200?
Solution:
0.35 × 200 = 70
Explanation: Convert percent to decimal and multiply.

4. If a product costs $120 and is marked up by 25%, what is the new price?
Solution:
25% of 120 = 30; 120 + 30 = $150
Explanation: Add the percentage increase to the original price.

5. Divide 180 in the ratio 4:5.
Solution:
The sum of the ratio parts is 4 + 5 = 9.
First part: (4/9) × 180 = 80
Second part: (5/9) × 180 = 100
Explanation: Divide the total into parts based on the given ratio.

6. If 6 pens cost $54, how much do 11 pens cost?
Solution:
Cost of 1 pen = $54 ÷ 6 = $9
Cost of 11 pens = 11 × $9 = $99
Explanation: Find the unit price and multiply by the required quantity.

7. Find the average of 12, 17, 23, 28, 30.
Solution:
Sum = 12 + 17 + 23 + 28 + 30 = 110
Average = 110 ÷ 5 = 22
Explanation: Average is the sum divided by the number of items.

8. The average of four numbers is 45. If one number is 55, what is the sum of the other three?
Solution:
Total sum = 45 × 4 = 180
Sum of other three = 180 - 55 = 125
Explanation: Find the total using the average, then subtract the known value.

9. An item bought for $80 is sold for $100. What is the profit percentage?
Solution:
Profit = $100 - $80 = $20
Profit percentage = (20 ÷ 80) × 100 = 25%
Explanation: Profit percentage is (Profit ÷ Cost Price) × 100.

10. A product is marked $250 and sold at 10% discount. What is the selling price?
Solution:
10% of $250 = $25
Selling price = $250 - $25 = $225
Explanation: Subtract the discount from the marked price.

11. Find the simple interest on $1,000 at 6% per annum for 5 years.
Solution:
SI = (1000 × 6 × 5) ÷ 100 = $300
Explanation: Use the formula SI = Principal × Rate × Time ÷ 100.

12. What is the total amount after 3 years if $2,500 is invested at 4% p.a.?
Solution:
SI = (2500 × 4 × 3) ÷ 100 = $300
Total amount = $2,500 + $300 = $2,800
Explanation: Add the interest to the principal.

13. Find the compound interest on $2,000 at 5% for 2 years.
Solution:
Amount = 2000 × (1.05)² = 2000 × 1.1025 = $2,205
Compound interest = $2,205 - $2,000 = $205
Explanation: Use the compound interest formula: Amount = Principal × (1 + Rate/100)ⁿ.

14. $1,000 at 8% compound interest for 3 years.
Solution:
Amount = 1000 × (1.08)³ ≈ 1000 × 1.2597 = $1,259.71
Compound interest = $1,259.71 - $1,000 = $259.71
Explanation: Apply the compound interest formula for n years.

15. A train covers 360 km in 6 hours. What is its speed?
Solution:
Speed = 360 ÷ 6 = 60 km/h
Explanation: Speed equals distance divided by time.

16. How long to cover 150 km at 50 km/h?
Solution:
Time = 150 ÷ 50 = 3 hours
Explanation: Time equals distance divided by speed.

17. If A can do a job in 8 days and B in 12 days, how long together?
Solution:
A’s rate = 1/8; B’s rate = 1/12
Combined rate = 1/8 + 1/12 = (3 + 2) / 24 = 5/24
Time = 24 ÷ 5 = 4.8 days
Explanation: Add rates and take the reciprocal for total time.

18. Six workers finish a job in 9 days. How many days for 3 workers?
Solution:
Total work = 6 × 9 = 54 worker-days
Time for 3 workers = 54 ÷ 3 = 18 days
Explanation: Divide total work by the number of workers.

19. The sum of ages of A and B is 50. If A is 8 years older than B, how old is A?
Solution:
A + B = 50; A = B + 8
(B + 8) + B = 50 → 2B = 42 → B = 21
A = 21 + 8 = 29
Explanation: Set up equations and solve for the unknowns.

20. Five years ago, the ratio of ages of P and Q was 2:3. Now, it is 3:4. What are their present ages?
Solution:
Let 5 years ago: P = 2x, Q = 3x
Now: P = 2x + 5, Q = 3x + 5
(2x + 5)/(3x + 5) = 3/4
Cross-multiplied: 4(2x + 5) = 3(3x + 5) → 8x + 20 = 9x + 15 → x = 5
P now = 2×5 + 5 = 15; Q now = 3×5 + 5 = 20
Explanation: Use ratios and set up an equation.

21. Area of a rectangle with length 10 m, width 7 m?
Solution:
Area = 10 × 7 = 70 m²
Explanation: Area equals length times width.

22. Perimeter of a square with side 9 cm?
Solution:
Perimeter = 4 × 9 = 36 cm
Explanation: Perimeter is four times the side length.

23. Solve: 3x + 7 = 28
Solution:
3x = 28 - 7 = 21
x = 21 ÷ 3 = 7
Explanation: Rearrange the equation and solve for x.

24. If x + y = 20 and x - y = 8, what is x?
Solution:
Add: (x + y) + (x - y) = 20 + 8 = 28
2x = 28 → x = 14
Explanation: Add equations to eliminate y.

25. Probability of getting a head when tossing a coin?
Solution:
There are 2 outcomes; 1 is head.
Probability = 1/2
Explanation: Probability is favorable outcomes divided by total outcomes.

26. A bag has 3 red, 4 blue balls. Probability of red?
Solution:
Total balls = 3 + 4 = 7
Probability = 3/7
Explanation: Divide the number of red balls by total balls.

27. How many ways to arrange 4 books?
Solution:
Number of arrangements = 4! = 24
Explanation: The factorial of the number of items gives the arrangements.

28. Ways to select 2 out of 6 items?
Solution:
Number of ways = 6C2 = 6! / (2! × 4!) = 15
Explanation: Use the combination formula.

29. If a bar graph shows 30, 40, 50 units, what is the total?
Solution:
Total = 30 + 40 + 50 = 120
Explanation: Add all the values together.

30. A pie chart shows 40% for a category out of 250 people. How many is that?
Solution:
Number = 0.4 × 250 = 100
Explanation: Multiply the percentage by the total.

31. Next number: 7, 14, 28, 56, _?
Solution:
Pattern: Each number is multiplied by 2.
Next: 56 × 2 = 112
Explanation: Identify and continue the sequence.

32. Fill in the blank: 4, 9, 16, 25, _
Solution:
These are squares: 2², 3², 4², 5², next is 6² = 36
Explanation: Sequence of perfect squares.

33. 3L of 20% alcohol mixed with 2L of 50%. What’s the concentration?
Solution:
Total alcohol = (3 × 20) + (2 × 50) = 60 + 100 = 160
Total volume = 3 + 2 = 5L
Concentration = 160 ÷ 5 = 32%
Explanation: Use the weighted average formula.

34. Add water to 5L of 40% solution to make it 25%. How much water?
Solution:
(5 × 0.4) / (5 + x) = 0.25
2 / (5 + x) = 0.25
2 = 0.25 × (5 + x) → 2 = 1.25 + 0.25x → 0.75 = 0.25x → x = 3
Explanation: Set up and solve the equation for x.

35. If 4 workers earn $320 in 5 days, what do 6 workers earn in 3 days?
Solution:
Total earned per worker per day = $320 ÷ (4 × 5) = $16
6 workers × 3 days × $16 = $288
Explanation: Find per worker, per day wage and scale up.

36. If 8 workers finish a job in 12 days, how many days for 4 workers?
Solution:
Total work = 8 × 12 = 96 worker-days
Time for 4 workers = 96 ÷ 4 = 24 days
Explanation: Divide total work by number of workers.

37. A $400 item is sold at 10% then 5% discount. Final price?
Solution:
First discount: 400 × 0.9 = 360
Second discount: 360 × 0.95 = 342
Explanation: Apply discounts successively.

38. Marked price $500, sold for $400. What is the discount %?
Solution:
Discount = $500 - $400 = $100
Discount percent = (100 ÷ 500) × 100 = 20%
Explanation: Discount percentage is calculated as (Discount ÷ Marked Price) × 100.

39. What is the simple interest on $2,000 at 7% per annum for 3 years?
Solution:
SI = (2000 × 7 × 3)/100 = $420
Explanation: Use the formula SI = Principal × Rate × Time ÷ 100.

40. Find the compound interest on $1,200 at 5% per annum for 2 years.
Solution:
Amount = 1200 × (1.05)² = 1200 × 1.1025 = $1,323
Compound Interest = $1,323 - $1,200 = $123
Explanation: Apply the compound interest formula: Amount = Principal × (1 + Rate/100)ⁿ.

41. If 80% of a number is 64, what is the number?
Solution:
Let x be the number.
0.8x = 64 ⇒ x = 64 ÷ 0.8 = 80
Explanation: Rearrange the equation to solve for the original number.

42. If A:B = 3:4 and B:C = 2:5, what is A:B:C?
Solution:
A:B = 3:4; B:C = 2:5
To make B common, multiply A:B by 2 (get 6:8), and B:C by 4 (get 8:20).
So, A:B:C = 6:8:20
Explanation: Equalize the middle term (B) and combine the ratios.

43. A car travels 180 km in 3 hours. What is its speed?
Solution:
Speed = Distance ÷ Time = 180 ÷ 3 = 60 km/h
Explanation: Use the basic speed formula.

44. If speed is 72 km/h, time is 2.5 hours, what is the distance?
Solution:
Distance = Speed × Time = 72 × 2.5 = 180 km
Answer: 180 km
Explanation: Multiply speed by time.

45. A is thrice as old as B. If A is 27, what is B’s age?
Solution:
B = 27 ÷ 3 = 9
Answer: 9
Explanation: Divide A’s age by 3.

46. What is the next number in the series: 5, 10, 20, 40, _?
Solution:
Each term doubles: 40 × 2 = 80
Explanation: Identify and apply the pattern.

47. What is the probability of drawing a king from a standard deck of 52 cards?
Solution:
There are 4 kings in a deck. Probability = 4 ÷ 52 = 1 ÷ 13
Explanation: Probability = Favorable outcomes ÷ Total outcomes.

48. A pie chart shows 30% for a group out of 600. How many is that?
Solution:
0.3 × 600 = 180
Explanation: Multiply the percentage by the total.

49. What is the area of a circle with radius 10 cm (π = 3.14)?
Solution:
Area = πr² = 3.14 × 10 × 10 = 314 cm²
Explanation: Use the area formula for a circle.

50. Find the simple interest on $2,400 at 5% per annum for 4 years.
Solution:
SI = (2400 × 5 × 4) ÷ 100 = $480
Explanation: Use the simple interest formula.

Quick Note: Practicing a variety of arithmetic and reasoning problems is the most effective way to build speed and accuracy for any test.

Success in arithmetic aptitude and logical reasoning is not just about knowing formulas—it’s about applying the right approach:

1. Read Carefully: Understand what is being asked before jumping into calculations.
2. Identify Data: Extract and organize all given numbers and relationships.
3. Formulate Equations: Translate word problems into mathematical equations.
4. Work Systematically: Break complex problems into smaller, manageable steps.
5. Check Units: Ensure consistency in units (distance, time, currency).
6. Estimate and Eliminate: Use estimation to rule out clearly incorrect options.
7. Practice Time Management: Don’t spend too long on any one question; move on and return if time permits.
8. Review Your Work: Double-check calculations and ensure your answer makes sense in context.

To support your preparation and practice, many platforms and educational websites offer free and paid downloadable resources focused on arithmetic reasoning questions. These resources typically include:

1. Comprehensive Question Banks: Collections of arithmetic reasoning questions with varying difficulty levels, covering all key topics such as percentages, ratios, time and work, and more.
2. Solved Examples and Explanations: Step-by-step solutions to help you understand the logic and methods behind each answer.
3. Practice Worksheets: Printable worksheets for self-assessment, timed practice, or group study sessions.
4. Previous Years’ Exam Papers: Real exam questions from competitive exams like SSC, UPSC, banking, and more, often with answer keys and solutions.
5. Topic-wise PDF Booklets: Focused booklets dedicated to specific areas such as profit and loss, averages, or data interpretation.

Quick Recap: Downloadable resources can streamline your preparation and give you access to a wide variety of arithmetic reasoning practice problems

Arithmetic reasoning questions are more than just math—they challenge your logical thinking, analytical skills, and ability to apply knowledge in practical scenarios. With consistent practice, a clear understanding of concepts, and smart test-taking strategies, you can significantly boost your performance in any exam or assessment.

Why It Matters

Strong arithmetic and reasoning skills are foundational for academic achievement, career advancement, and making informed decisions in everyday life. Developing these abilities empowers you to approach challenges with clarity and confidence.

Practical Advice for Learners

• Set aside regular time for arithmetic reasoning practice tests and review.
• Focus on understanding concepts, not just memorizing formulas.
• Use downloadable PDFs and online tests for varied practice.
• Review mistakes carefully to avoid repeating them.
• Simulate exam conditions to improve speed and accuracy.
• Stay positive—consistent practice leads to measurable progress.