If you are preparing for a campus placement or an off-campus drive in India, the first hurdle is almost always the aptitude round. This guide brings together the most important aptitude questions for interview preparation across quantitative, logical reasoning, and verbal ability, and every single question here comes with a full step-by-step worked solution, not just a final answer. That is the difference that actually moves your score: understanding the method so you can solve a new variant under time pressure.
Companies like TCS, Infosys, Wipro, Cognizant, Accenture, and Capgemini use the aptitude test as an early filter. A strong aptitude score is what gets your resume in front of a human interviewer, so treat this round as the gateway to everything that follows. Clear it, and the next step is the technical and HR interview, which you can rehearse with the Goodspace AI Mock Interview so you are ready when a recruiter finally calls.
Work through the examples below with a pen and paper. Read the solution only after you attempt each one.
Aptitude Test Topics and Typical Weightage
Most placement aptitude sections in India follow a similar shape. The table below shows the topics and their typical share of questions, which helps you decide where to invest your study time. Exact splits vary by company and year, so treat these as planning guidance rather than fixed rules.
| Section | Topic | Typical weightage |
|---|---|---|
| Quantitative Aptitude | Percentages | 8-10% |
| Quantitative Aptitude | Profit and Loss | 6-8% |
| Quantitative Aptitude | Time and Work | 5-7% |
| Quantitative Aptitude | Time, Speed and Distance | 6-8% |
| Quantitative Aptitude | Ratio and Proportion | 4-6% |
| Quantitative Aptitude | Averages | 4-5% |
| Quantitative Aptitude | Simple and Compound Interest | 5-7% |
| Quantitative Aptitude | Permutations and Combinations | 3-5% |
| Quantitative Aptitude | Probability | 3-5% |
| Quantitative Aptitude | Number System | 6-8% |
| Logical Reasoning | Series, coding, blood relations, syllogisms, directions | 20-25% |
| Verbal Ability | Grammar, vocabulary, comprehension | 10-15% |
The clear takeaway is that quantitative aptitude carries the most weight, and within it, percentages, number system, and the arithmetic word-problem topics dominate. Let us solve them one by one.
Quantitative Aptitude Questions
Percentages
Q1. If 40% of a number is 240, what is 75% of the same number?
First find the number. If 40% equals 240, then 1% equals 240 divided by 40, which is 6. So the whole number (100%) is 6 times 100, that is 600. Now 75% of 600 is 0.75 times 600, which equals 450. Answer: 450.
Q2. The price of rice rises by 25%. By what percent must a family cut its consumption so that the monthly spend stays the same?
Use the reduction formula: required reduction percent equals rise divided by (100 plus rise), all times 100. That is 25 divided by 125, times 100, which equals 20%. So a 20% cut in consumption keeps the bill unchanged. Answer: 20%.
Q3. In an exam a student scores 30% and fails by 45 marks. Another student scores 45% and gets 30 marks more than the pass mark. Find the maximum marks.
Let the maximum marks be M and the pass mark be P. From the first student: 0.30M equals P minus 45. From the second: 0.45M equals P plus 30. Subtract the first equation from the second: 0.45M minus 0.30M equals 75, so 0.15M equals 75, giving M equals 500. Answer: 500 marks (and the pass mark is 0.30 times 500 plus 45, which is 195).
Q4. A town has 20,000 people. The population rises 10% in year one and falls 10% in year two. What is the final population?
Do not cancel the two 10% changes, because they act on different bases. After year one: 20,000 times 1.10 equals 22,000. After year two: 22,000 times 0.90 equals 19,800. Answer: 19,800. Notice the net effect is a 1% fall, which matches the shortcut for successive changes of plus x and minus x, giving a loss of (x squared)/100 percent.
Profit and Loss
Q5. An article costs 400 rupees and is sold for 500 rupees. Find the profit percent.
Profit equals 500 minus 400, which is 100. Profit percent equals profit divided by cost price times 100, that is 100 divided by 400 times 100, which equals 25%. Answer: 25%.
Q6. A man sells an item at a 10% loss. Had he sold it for 45 rupees more, he would have made a 5% profit. Find the cost price.
At a 10% loss the selling price is 0.90 times cost. At a 5% profit it is 1.05 times cost. The gap between them is 45 rupees, so 1.05CP minus 0.90CP equals 45. That is 0.15CP equals 45, giving CP equals 300. Answer: 300 rupees.
Q7. Two articles are each sold for 990 rupees. On one there is a 10% profit and on the other a 10% loss. What is the overall result?
When the same selling price gives equal profit and loss percentages, the trader always makes a net loss. The loss percent equals (common percent squared) divided by 100, that is 10 squared over 100, which equals 1%. Answer: a 1% overall loss.
Q8. A shopkeeper marks his goods 20% above cost and then gives a 10% discount. What is his profit percent?
Take cost price as 100 for easy arithmetic. Marked price is 120. Discount of 10% on 120 is 12, so selling price is 108. Profit is 8 on a cost of 100, which is 8%. Answer: 8%.
Q9. A dishonest shopkeeper sells goods at cost price but uses a 900 gram weight for a kilogram. Find his gain percent.
He gives 900 grams but charges for 1000 grams, so his gain is on the missing 100 grams. Gain percent equals (error divided by true weight given) times 100, that is 100 divided by 900 times 100, which equals 11.11%. Answer: 11.11% (or 11 and 1/9 percent).
Time and Work
Q10. A finishes a job in 10 days and B in 15 days. How long together?
A does 1/10 of the work per day and B does 1/15. Together they do 1/10 plus 1/15. The common denominator is 30, giving 3/30 plus 2/30, which is 5/30, that is 1/6 per day. So together they take 6 days. Answer: 6 days.
Q11. A and B together finish a task in 12 days. A alone needs 20 days. How long does B alone take?
Combined rate is 1/12 per day. A's rate is 1/20. B's rate is 1/12 minus 1/20. The common denominator is 60, giving 5/60 minus 3/60, which is 2/60, that is 1/30. So B alone takes 30 days. Answer: 30 days.
Q12. If 6 men build a wall in 8 days, how long will 8 men take?
The total effort is 6 times 8, which is 48 man-days. With 8 men, the time is 48 divided by 8, which equals 6 days. Answer: 6 days. This is inverse proportion: more men, fewer days.
Q13. A is twice as efficient as B. Working together they finish in 18 days. How long would A take alone?
Let B do 1 unit of work per day, so A does 2 units. Together they do 3 units per day. In 18 days the total work is 3 times 18, which is 54 units. A alone does 2 units per day, so A needs 54 divided by 2, which equals 27 days. Answer: 27 days.
Time, Speed and Distance
Q14. A car covers 240 km in 4 hours. Find its speed.
Speed equals distance divided by time, that is 240 divided by 4, which equals 60 km/h. Answer: 60 km/h.
Q15. Convert 72 km/h into metres per second.
Multiply by 5/18 to go from km/h to m/s. So 72 times 5/18 equals 20 m/s. Answer: 20 m/s. Remember this conversion factor, it appears in almost every train problem.
Q16. A 150 metre long train runs at 90 km/h. How long does it take to pass a pole?
First convert speed: 90 times 5/18 equals 25 m/s. To pass a pole the train travels its own length, 150 metres. Time equals 150 divided by 25, which equals 6 seconds. Answer: 6 seconds.
Q17. Two trains, 120 m and 130 m long, move towards each other at 40 km/h and 50 km/h. How long to cross each other?
For opposite directions, add the speeds: 40 plus 50 equals 90 km/h, which is 90 times 5/18 equals 25 m/s. The total distance to clear is the sum of lengths, 120 plus 130 equals 250 metres. Time equals 250 divided by 25, which equals 10 seconds. Answer: 10 seconds.
Q18. A student walking at 5 km/h reaches college 10 minutes late, but at 6 km/h reaches 5 minutes early. Find the distance.
The difference in arrival times is 15 minutes, which is 1/4 hour. Let the distance be d. Time at 5 km/h minus time at 6 km/h equals 1/4, so d/5 minus d/6 equals 1/4. The left side is (6d minus 5d) over 30, which is d/30. So d/30 equals 1/4, giving d equals 7.5 km. Answer: 7.5 km.
Ratio and Proportion
Q19. Divide 600 rupees between two people in the ratio 2 to 3.
Total parts equal 2 plus 3, which is 5. One part is 600 divided by 5, which is 120. So the shares are 2 times 120 equals 240, and 3 times 120 equals 360. Answer: 240 and 360.
Q20. If a to b is 2 to 3 and b to c is 4 to 5, find a to b to c.
Make b the same in both ratios. In the first, b is 3; in the second, b is 4. Their LCM is 12. Scale the first ratio by 4 to get a to b equals 8 to 12. Scale the second by 3 to get b to c equals 12 to 15. Combine: a to b to c equals 8 to 12 to 15. Answer: 8:12:15.
Q21. Two numbers are in the ratio 3 to 5 and their sum is 64. Find the numbers.
Total parts equal 3 plus 5, which is 8. One part is 64 divided by 8, which is 8. The numbers are 3 times 8 equals 24, and 5 times 8 equals 40. Answer: 24 and 40.
Q22. The present ages of A and B are in the ratio 4 to 5. After 5 years the ratio becomes 5 to 6. Find their present ages.
Let the present ages be 4x and 5x. After 5 years they are 4x plus 5 and 5x plus 5, and this ratio is 5 to 6. Cross multiply: 6 times (4x plus 5) equals 5 times (5x plus 5). That gives 24x plus 30 equals 25x plus 25, so x equals 5. Present ages are 4 times 5 equals 20, and 5 times 5 equals 25. Answer: 20 and 25 years.
Averages
Q23. Find the average of the first five natural numbers.
Sum equals 1 plus 2 plus 3 plus 4 plus 5, which is 15. Average equals 15 divided by 5, which equals 3. Answer: 3.
Q24. The average of 10 numbers is 45. If one number, 25, is removed, what is the new average?
The total of all 10 numbers is 10 times 45, which is 450. Removing 25 leaves 425 spread over 9 numbers. New average equals 425 divided by 9, which is 47.22 (approximately). Answer: about 47.22.
Q25. The average age of 30 students is 12 years. When the teacher's age is added, the average becomes 13. Find the teacher's age.
Total age of students is 30 times 12, which is 360. With the teacher there are 31 people averaging 13, so the new total is 31 times 13, which is 403. The teacher's age is 403 minus 360, which equals 43 years. Answer: 43 years.
Q26. The average of four consecutive even numbers is 15. Find the largest of them.
Let the numbers be x, x plus 2, x plus 4, and x plus 6. Their average is x plus 3, which equals 15, so x equals 12. The numbers are 12, 14, 16, and 18. The largest is 18. Answer: 18.
Simple and Compound Interest
Q27. Find the simple interest on 5,000 rupees at 8% per annum for 3 years.
Simple interest equals principal times rate times time divided by 100. That is 5000 times 8 times 3 divided by 100, which equals 1,200 rupees. Answer: 1,200 rupees.
Q28. At what simple interest rate will a sum double in 8 years?
For the amount to double, the interest earned must equal the principal itself. So P equals P times r times 8 divided by 100. Cancel P from both sides: 1 equals 8r divided by 100, giving r equals 12.5%. Answer: 12.5% per annum.
Q29. Find the compound interest on 10,000 rupees at 10% per annum for 2 years.
The amount equals principal times (1 plus rate/100) raised to the number of years. That is 10000 times (1.1) squared, which is 10000 times 1.21, equal to 12,100. Compound interest is 12,100 minus 10,000, which equals 2,100 rupees. Answer: 2,100 rupees.
Q30. The difference between compound and simple interest on a sum at 10% per annum for 2 years is 50 rupees. Find the sum.
For 2 years the difference equals principal times (rate/100) squared. So 50 equals P times (0.1) squared, which is 0.01P. Therefore P equals 50 divided by 0.01, which equals 5,000 rupees. Answer: 5,000 rupees.
Permutations and Combinations
Q31. In how many ways can the letters of the word APPLE be arranged?
APPLE has 5 letters with the letter P repeated twice. The count is 5 factorial divided by 2 factorial, that is 120 divided by 2, which equals 60. Answer: 60 ways.
Q32. In how many ways can 3 students be selected from a group of 10?
Order does not matter, so use combinations. C(10,3) equals 10 factorial divided by (3 factorial times 7 factorial), which simplifies to (10 times 9 times 8) divided by (3 times 2 times 1), that is 720 divided by 6, which equals 120. Answer: 120 ways.
Q33. How many 3-digit numbers can be formed from the digits 1 to 9 with no digit repeated?
The hundreds place has 9 choices. The tens place then has 8 remaining choices. The units place has 7 left. Multiply: 9 times 8 times 7, which equals 504. Answer: 504 numbers.
Q34. In how many ways can the letters of the word LEADER be arranged?
LEADER has 6 letters with E repeated twice. The count is 6 factorial divided by 2 factorial, that is 720 divided by 2, which equals 360. Answer: 360 ways.
Probability
Q35. A fair die is rolled. What is the probability of getting an even number?
Even outcomes are 2, 4, and 6, so 3 favourable outcomes out of 6 total. Probability equals 3 divided by 6, which is 1/2. Answer: 1/2.
Q36. A bag has 5 red and 3 blue balls. One ball is drawn at random. Find the probability that it is red.
Total balls equal 5 plus 3, which is 8. Favourable red outcomes are 5. Probability equals 5 divided by 8. Answer: 5/8.
Q37. Two dice are thrown together. What is the probability that the sum is 7?
The pairs that add to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which is 6 outcomes. Total outcomes are 6 times 6, which is 36. Probability equals 6 divided by 36, which is 1/6. Answer: 1/6.
Q38. A card is drawn from a standard 52-card deck. Find the probability that it is a king.
There are 4 kings in 52 cards. Probability equals 4 divided by 52, which simplifies to 1/13. Answer: 1/13.
Number System
Q39. Find the unit digit of 7 raised to the power 105.
The unit digit of powers of 7 cycles through 7, 9, 3, 1 and then repeats every 4 powers. Divide the exponent 105 by 4, which leaves a remainder of 1. A remainder of 1 points to the first digit in the cycle, which is 7. Answer: unit digit is 7.
Q40. Find the sum of the first 50 natural numbers.
Use the formula n times (n plus 1) divided by 2. That is 50 times 51 divided by 2, which equals 2550 divided by 2, that is 1,275. Answer: 1,275.
Q41. Find the LCM and HCF of 12 and 18.
Write 12 as 2 squared times 3, and 18 as 2 times 3 squared. HCF takes the lowest powers common to both: 2 times 3, which equals 6. LCM takes the highest powers: 2 squared times 3 squared, which equals 36. Answer: HCF is 6 and LCM is 36.
Q42. Show that 1001 is divisible by 7, 11, and 13.
Factorise: 1001 equals 7 times 143, and 143 equals 11 times 13. So 1001 equals 7 times 11 times 13. Since each of these is a factor, 1001 is divisible by all three. Answer: 1001 equals 7 times 11 times 13. This is a handy identity for many number system questions.
Logical Reasoning Questions
Number and Letter Series
Q43. Find the next term: 2, 6, 12, 20, 30, ?
Look at the differences: 6 minus 2 is 4, 12 minus 6 is 6, 20 minus 12 is 8, 30 minus 20 is 10. The differences rise by 2 each time, so the next difference is 12. Add it to 30 to get 42. Answer: 42.
Q44. Find the next term: 3, 9, 27, 81, ?
Each term is the previous term multiplied by 3. So the next is 81 times 3, which equals 243. Answer: 243.
Q45. Find the next term: 1, 4, 9, 16, 25, ?
These are perfect squares: 1 squared, 2 squared, 3 squared, 4 squared, 5 squared. The next is 6 squared, which equals 36. Answer: 36.
Q46. Find the next term: 5, 11, 23, 47, ?
Each term is the previous one times 2 plus 1. Check: 5 times 2 plus 1 is 11, 11 times 2 plus 1 is 23, 23 times 2 plus 1 is 47. So the next is 47 times 2 plus 1, which equals 95. Answer: 95.
Blood Relations
Q47. Pointing to a photograph, a man says, "She is the daughter of my grandfather's only son." How is she related to the man?
His grandfather's only son is the man's own father. The daughter of his father is his sister. Answer: she is his sister.
Q48. A is B's brother, C is A's mother, D is C's father, E is D's mother. How is A related to D?
C is A's mother, and D is C's father, so D is A's mother's father, that is A's maternal grandfather. Therefore A is D's grandson. Answer: A is the grandson of D.
Q49. Pointing to a man, a woman says, "His mother is the only daughter of my mother." How is the woman related to the man?
The only daughter of the woman's mother is the woman herself, assuming she is that daughter. So the man's mother is the woman. Answer: she is his mother.
Coding and Decoding
Q50. If CAT is coded as DBU, how is DOG coded?
Each letter is shifted forward by one place in the alphabet: C to D, A to B, T to U. Apply the same shift to DOG: D to E, O to P, G to H. Answer: EPH.
Q51. If TEACHER is written as VGCEJGT, how is CHILDREN written in that code?
Compare TEACHER and VGCEJGT letter by letter: T to V is plus 2, E to G is plus 2, and so on. Each letter moves forward by 2 places. Apply plus 2 to CHILDREN: C to E, H to J, I to K, L to N, D to F, R to T, E to G, N to P. Answer: EJKNFTGP.
Q52. If APPLE is coded as ELPPA, how is MANGO coded?
The code simply reverses the word. Reverse MANGO to get OGNAM. Answer: OGNAM.
Syllogisms
Q53. Statements: All cats are animals. All animals are living things. What follows?
If every cat is an animal, and every animal is a living thing, then every cat must be a living thing. The conclusion "All cats are living things" is valid. Answer: All cats are living things.
Q54. Statements: Some pens are books. All books are papers. Which conclusions follow?
Since some pens are books and all books are papers, those pens that are books must also be papers. So "Some pens are papers" is valid. It also follows that "Some papers are pens," because that is the same overlap stated in reverse. Answer: both "Some pens are papers" and "Some papers are pens" are valid.
Q55. Statements: All roses are flowers. Some flowers fade quickly. Does "Some roses fade quickly" follow?
The flowers that fade quickly are not guaranteed to be the roses. The overlap could lie entirely among non-rose flowers. So the conclusion does not necessarily follow. Answer: it does not follow.
Direction Sense
Q56. A man walks 5 km North, turns right and walks 3 km, then turns right and walks 5 km. How far and in which direction is he from the start?
Turning right from North faces East, so he walks 3 km East. Turning right again faces South, so he walks 5 km South, which cancels the initial 5 km North. He is left 3 km to the East of the start. Answer: 3 km East.
Q57. A man walks 10 m South, turns left and walks 5 m, turns left and walks 10 m, then turns right and walks 5 m. How far is he from the start?
South 10 m, then left faces East for 5 m, then left faces North for 10 m which cancels the South leg, then right faces East again for 5 m. His eastward legs add to 5 plus 5, which is 10 m, and the north-south motion cancels out. Answer: 10 m East of the start.
Q58. The sun rises in the east. In the early morning, in which direction does the shadow of a pole fall?
Since the sun is in the east in the morning, shadows point away from it, that is towards the west. Answer: west.
Verbal Ability Questions
Verbal ability is a smaller section but easy marks if your basics are sound. Here are quick examples.
Q59. Choose the synonym of "Abundant."
Abundant means present in large quantity. The closest synonym is "plentiful." Answer: plentiful.
Q60. Choose the antonym of "Benevolent."
Benevolent means kind and well-meaning. Its opposite is "malevolent," meaning wishing harm. Answer: malevolent.
Q61. Fill in the blank: "He is senior ____ me."
With the word "senior," English uses the preposition "to," not "than." The correct sentence is "He is senior to me." Answer: to.
Q62. One-word substitution: a person who cannot read or write.
The single word for this is "illiterate." Answer: illiterate.
Q63. Correct the sentence: "Each of the students have submitted the form."
The subject "each" is singular, so the verb must be singular. The correct form is "Each of the students has submitted the form." Answer: replace "have" with "has."
How to Prepare for Aptitude Rounds (TCS, Infosys, Wipro, Cognizant Style)
The aptitude round at most Indian recruiters is a timed, multiple-choice test, often with sectional cut-offs and, at some companies, negative marking. Here is a practical preparation plan.
Master the arithmetic core first. Percentages, ratio and proportion, profit and loss, averages, and time-based problems reuse the same underlying ideas. Once you are fluent with these, a large share of the paper becomes routine.
Build speed with shortcuts. Learn the standard formulas that save time: the successive percentage change formula, the equal profit-and-loss loss formula of (x squared)/100, the km/h to m/s factor of 5/18, and the compound-versus-simple interest difference of P times (r/100) squared for 2 years. Recognising which shortcut applies is half the battle.
Practise with a timer. TCS and Cognizant tests reward speed as much as accuracy. Solve full sections in the allotted time so you learn to skip and return rather than getting stuck on a single hard question.
Respect sectional cut-offs. Infosys and Wipro often require you to clear each section separately, so you cannot let a weak topic sink you. Give your weakest area extra revision rather than over-polishing your strengths.
Watch out for negative marking. Where wrong answers cost you, do not blind-guess. Eliminate obviously wrong options first, and only then attempt a reasoned guess.
Revise mental math daily. Knowing tables up to 20, squares up to 30, cubes up to 15, and common fractions as percentages removes seconds from every calculation, and those seconds add up across a full paper.
Clearing aptitude is only the first gate. Once your score gets you shortlisted, the technical and HR interview decides the offer, and that is a different skill entirely. Rehearse it in advance with the Goodspace AI Mock Interview, which lets you practise real interview questions and get feedback before you sit in front of an actual panel, so the round after aptitude does not catch you off guard.
Quick Tips and Shortcuts to Remember
- To find x% of a number, and the reverse, learn to move flexibly between fraction and percentage forms. For example, 12.5% equals 1/8, and 16.66% equals 1/6.
- For successive percentage changes of a% then b%, the net change equals a plus b plus (a times b)/100.
- In work problems, think in terms of units of work per day rather than fractions; it keeps the arithmetic clean.
- For train and boat problems, always convert speeds to m/s before touching the numbers.
- In series questions, first check for differences, then ratios, then squares or cubes, in that order.
- In blood relation and direction questions, draw a small diagram; it prevents careless errors.
Frequently Asked Questions
How many aptitude questions should I practise before a placement drive?
There is no fixed number, but consistent daily practice matters more than volume. Solving 15 to 20 fresh questions a day across topics for a few weeks, and reviewing your mistakes each time, builds far more reliable speed than cramming hundreds in one sitting.
Is negative marking common in company aptitude tests?
It varies. Some companies apply negative marking and some do not, and the policy can change year to year. Always read the instructions on the test screen carefully before you start, and adjust your guessing strategy to match.
Which topic carries the most weight in aptitude rounds?
Quantitative aptitude usually dominates, and within it the arithmetic word-problem topics such as percentages, profit and loss, time and work, and number system tend to appear most often. Logical reasoning is the next largest block.
How long does a typical placement aptitude test last?
Most run between 30 and 90 minutes depending on the company and the number of sections. Because time is tight, practising under a timer is essential so you learn to pace yourself and skip strategically.
Are a calculator or rough sheets allowed?
Online proctored tests usually provide an on-screen rough space or ask you to keep blank paper handy, and most do not allow a physical calculator. This is why strong mental math and shortcuts are so valuable.
What comes after I clear the aptitude round?
Clearing aptitude typically moves you to the technical interview and then the HR interview. Since these judge your communication and problem explanation, not just your answers, it helps to rehearse them beforehand. Practising with a structured mock interview builds the confidence to perform when a real recruiter is watching.
Final Word
Aptitude preparation rewards method over memorisation. Every question in this guide came with a full worked solution precisely because understanding the steps lets you handle any new variant on test day. Work through these regularly, master the shortcuts, and time yourself. Clear the aptitude gate, then turn your attention to the interview that decides the offer, and go in prepared.
