Top 50 Aptitude Questions Asked in Placement Exams (with Solutions)

Meta Description: Master placement aptitude with 50 most-asked questions from TCS, Infosys, Wipro, Accenture. Detailed solutions with shortcuts. Download PDF included.

Aptitude tests are the first gateway to your dream job. Every major IT and core company—including TCS, Infosys, Wipro, Accenture, Cognizant, and HCL—includes an aptitude round that filters 60-70% of candidates. This comprehensive guide covers the 50 most frequently asked aptitude questions across all topics, with detailed solutions and shortcut tricks.

How to Use This Guide

Practice first: Try solving before checking the solution
Learn shortcuts: Note the time-saving techniques
Track patterns: Same concepts appear repeatedly
Time yourself: Aim for 1-1.5 minutes per question

Quantitative Aptitude Questions

Topic 1: Number System (Questions 1-5)

Q1. Find the unit digit of 2^67 × 3^45 × 7^23

Solution:

Unit digit of 2^67: Cycle of 2 is [2,4,8,6]. 67 mod 4 = 3. So 8.
Unit digit of 3^45: Cycle of 3 is [3,9,7,1]. 45 mod 4 = 1. So 3.
Unit digit of 7^23: Cycle of 7 is [7,9,3,1]. 23 mod 4 = 3. So 3.
Unit digit of 8 × 3 × 3 = 72 → 2

Q2. What is the remainder when 2^100 is divided by 3?

Solution: 2 ≡ -1 (mod 3)
2^100 ≡ (-1)^100 ≡ 1 (mod 3)

Q3. Find the HCF of 144 and 180.

Solution: 144 = 16 × 9 = 2^4 × 3^2
180 = 4 × 45 = 2^2 × 3^2 × 5

HCF = 2^2 × 3^2 = 36

Q4. Three bells toll at intervals of 12, 15, and 18 seconds. If they toll together at 8:00 AM, when will they toll together again?

Solution: LCM of 12, 15, 18: 12 = 2^2 × 3
15 = 3 × 5
18 = 2 × 3^2
LCM = 2^2 × 3^2 × 5 = 180 seconds = 3 minutes

Next together: 8:03 AM

Q5. The sum of two numbers is 45 and their difference is 15. Find their product.

Solution: x + y = 45
x - y = 15
Adding: 2x = 60 → x = 30, y = 15

Product = 30 × 15 = 450

Topic 2: Time & Work (Questions 6-10)

Q6. A can do a work in 15 days, B in 10 days. How long will they take working together?

Solution: A's rate = 1/15, B's rate = 1/10
Combined = 1/15 + 1/10 = (2+3)/30 = 5/30 = 1/6

Q7. A and B together complete work in 12 days. A alone takes 20 days. How long for B alone?

Solution: 1/A + 1/B = 1/12
1/20 + 1/B = 1/12
1/B = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30

Q8. 12 men complete work in 8 days. After 3 days, 4 men leave. How many more days to complete?

Solution: Total work = 12 × 8 = 96 man-days
Work done in 3 days = 12 × 3 = 36 man-days
Remaining = 60 man-days
Men left = 8
Days needed = 60/8 = 7.5 days

Q9. Pipe A fills tank in 6 hours, Pipe B empties in 8 hours. Both open. Time to fill?

Solution: Net rate = 1/6 - 1/8 = (4-3)/24 = 1/24

Q10. A is twice as good as B. Together they finish in 14 days. How long for A alone?

Solution: If B takes x days, A takes x/2 days
1/(x/2) + 1/x = 1/14
2/x + 1/x = 1/14
3/x = 1/14
x = 42 (B's time)

A's time = 42/2 = 21 days

Topic 3: Time, Speed & Distance (Questions 11-15)

Q11. A car travels 60 km at 30 km/hr and 60 km at 60 km/hr. Average speed?

Solution: Total distance = 120 km
Time 1 = 60/30 = 2 hrs
Time 2 = 60/60 = 1 hr
Total time = 3 hrs

Average speed = 120/3 = 40 km/hr

Q12. A train 150m long crosses a pole in 9 seconds. Speed in km/hr?

Solution: Speed = 150/9 = 50/3 m/s
In km/hr: (50/3) × (18/5) = 60 km/hr

Q13. Two trains 200m and 300m long approach each other at 40 km/hr and 50 km/hr. Crossing time?

Solution: Relative speed = 40 + 50 = 90 km/hr = 90 × (5/18) = 25 m/s
Total distance = 200 + 300 = 500m
Time = 500/25 = 20 seconds

Q14. A man rows at 6 km/hr in still water. Against current (2 km/hr), time for 12 km?

Solution: Upstream speed = 6 - 2 = 4 km/hr
Time = 12/4 = 3 hours

Q15. A person walks at 5/6 of usual speed and is 15 minutes late. Usual time?

Solution: Speed ratio: New/Usual = 5/6
Time ratio: New/Usual = 6/5

Difference = 6/5 - 1 = 1/5 of usual time = 15 minutes
Usual time = 15 × 5 = 75 minutes = 1 hr 15 min

Topic 4: Profit & Loss (Questions 16-20)

Q16. Cost price = ₹400, Selling price = ₹500. Profit %?

Solution: Profit = 100
Profit % = (100/400) × 100 = 25%

Q17. An article sold at 20% loss. If SP increases by ₹100, profit is 5%. Find CP.

Solution: Let CP = x
Original SP = 0.8x
New SP = 0.8x + 100 = 1.05x
100 = 0.25x
x = ₹400

Q18. A shopkeeper marks 50% above CP and gives 20% discount. Profit %?

Solution: CP = 100, MP = 150
SP = 150 × 0.8 = 120
Profit = 20%

Q19. Two articles sold at same price. One at 20% profit, other at 20% loss. Net result?

Solution: When SP is same and profit% = loss%, there is ALWAYS an overall loss.

Loss % = (Common %)²/100 = 20²/100 = 4% loss

Q20. If CP of 20 articles = SP of 16 articles, profit %?

Solution: CP of 20 = SP of 16
CP/SP = 16/20 = 4/5

If CP = 4, SP = 5
Profit = 1
Profit % = (1/4) × 100 = 25%

Topic 5: Percentage & Ratio (Questions 21-25)

Q21. If A's income is 20% more than B's, B's income is less than A's by?

Solution: Let B = 100, A = 120
Difference = 20
% less = (20/120) × 100 = 16.67%

Q22. Population increases 10% yearly. After 2 years, increase %?

Solution: Effective increase = 10 + 10 + (10×10)/100 = 21%

Q23. If 20% of A = 30% of B, then A:B = ?

Solution: 0.20A = 0.30B
A/B = 0.30/0.20 = 3/2

A:B = 3:2

Q24. Divide ₹4500 in ratio 2:3:4

Solution: Total parts = 2+3+4 = 9
1 part = ₹500
Shares: ₹1000, ₹1500, ₹2000

Q25. If A:B = 2:3 and B:C = 4:5, then A:C = ?

Solution: A:B = 2:3 = 8:12
B:C = 4:5 = 12:15
A:C = 8:15

Logical Reasoning Questions

Topic 6: Number Series (Questions 26-30)

Q26. 3, 8, 15, 24, 35, ?

Solution: Pattern: 1×3, 2×4, 3×5, 4×6, 5×7, 6×8 = 48

Q27. 2, 5, 11, 23, 47, ?

Solution: Pattern: ×2+1: 2×2+1=5, 5×2+1=11... 47×2+1 = 95

Q28. 64, 32, 48, 120, ?, 840

Solution: Pattern: ÷2, ×1.5, ×2.5, ×3.5... 120 × 3.5 = 420

Q29. 1, 4, 27, 256, ?

Solution: Pattern: 1^1, 2^2, 3^3, 4^4, 5^5 = 3125

Q30. 5, 11, 23, 47, 95, ?

Solution: Pattern: ×2+1... 95×2+1 = 191

Topic 7: Coding-Decoding (Questions 31-33)

Q31. If TEACHER is coded as VGCEJGT, how is CHILDREN coded?

Solution: Each letter +2: C→E, H→J, I→K, L→N, D→F, R→T, E→G, N→P

Q32. In a code, FLOWER = 36, GARDEN = 49. What is FOREST?

Solution: Pattern: Number of letters²: 6²=36, 7²=49, 6²=36

Topic 8: Blood Relations (Questions 34-36)

Q34. Pointing to a photo, a woman says, "His mother is my mother's only daughter." Relation?

Solution: My mother's only daughter = me (woman). So "his mother is me" → He is my son.

Q35. A is B's sister, C is B's mother, D is C's father, E is D's mother. How is A related to D?

Solution: D is C's father, C is B's mother → D is B's grandfather. A is B's sister → A is D's granddaughter.

Topic 9: Direction Sense (Questions 37-38)

Q37. A walks 10m North, turns right walks 20m, turns right walks 10m. How far from start?

Solution: Forms a U-shape. 20m South from start point.

Q38. Facing North, I turn 135° clockwise, then 45° anticlockwise. Final direction?

Solution: 135° clockwise = South-East. 45° anticlockwise from SE = South

Topic 10: Syllogism (Questions 39-40)

Q39. Statements: All pens are books. Some books are pencils. Conclusions: I. Some pens are pencils. II. Some pencils are books.

Solution: Only II follows. Answer: Only II

Q40. Statements: No dog is cat. All cats are mice. Conclusions: I. No dog is mouse. II. Some mice are cats.

Solution: Only II follows. Answer: Only II

Verbal Ability Questions

Topic 11: Grammar (Questions 41-43)

Q41. Neither of the boys _______ passed.

Q42. The committee _______ divided in opinion.

Q43. One of my friends _______ a doctor.

Topic 12: Synonyms/Antonyms (Questions 44-46)

Q44. Synonym of "PRUDENT":

Q45. Antonym of "VANQUISH":

Q46. Synonym of "UBIQUITOUS":

Topic 13: Sentence Correction (Questions 47-48)

Q47. "He is senior than me." Correct:

Q48. "The furniture are new." Correct:

Topic 14: Reading Comprehension Tips (Questions 49-50)

Q49-50. General RC Strategy:

Read questions first
Skim passage for main idea
Locate specific details
Eliminate wrong options
Never use outside knowledge

Quick Reference: Important Formulas

Quantitative

Speed: Distance/Time
Profit %: (Profit/CP) × 100
SI: (P×R×T)/100
CI: P[(1+r/100)^t - 1]
Work: M1×D1 = M2×D2

Logical

Permutation: nPr = n!/(n-r)!
Combination: nCr = n!/[r!(n-r)!]
Probability: Favorable/Total

Frequently Asked Questions (FAQ)

Q1: How many aptitude questions are asked in placement tests?

A: Usually 20-30 questions in 30-45 minutes depending on company.

Q2: Is calculator allowed?

A: Most companies provide on-screen calculator. Practice mental math anyway.

Q3: What is the difficulty level?

A: Mostly moderate. Focus on accuracy over speed.

Q4: Is there negative marking?

A: Most IT companies (TCS, Infosys, Wipro) have no negative marking.

Q5: How to improve aptitude speed?

A: Practice 20-30 questions daily. Learn shortcuts. Take timed tests.

Conclusion

Master these 50 questions and their underlying concepts, and you'll be prepared for 80% of aptitude questions in any placement test. Remember: Consistency beats intensity. Practice daily, track your progress, and focus on weak areas.

Download this guide as PDF and start practicing today! 📚

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Last Updated: March 2026