Aptitude Questions and Answers for Placements: 100+ Ultimate Solved Problems (2026 Guide)

(A) ₹850 (B) ₹880 (C) ₹900 (D) ₹920

Solution: SP = CP × (1 + Profit%/100) = 750 × 1.20 = ₹900

Topic: Profit & Loss | Formula: SP = CP × (100 + P%) / 100

(A) 70 (B) 75 (C) 80 (D) 85

Solution: Speed = Distance / Time = 480 / 6 = 80 km/h

Topic: Speed-Distance by Time

(A) 152 (B) 158 (C) 162 (D) 168

Solution: 45% of 360 = (45/100) × 360 = 162

Shortcut: 10% of 360 = 36.

So 45% = 36 × 4 + 36 × 0.5 = 144 + 18 = 162

(A) 25 (B) 30 (C) 35 (D) 40

Solution: B’s rate = 1/12 − 1/20 = 5/60 − 3/60 = 2/60 = 1/30 B alone = 30 days

(A) 156 (B) 164 (C) 168 (D) 172

Solution: 7 parts out of 12 = (7/12) × 288 = 168

(A) ₹9,500 (B) ₹9,600 (C) ₹9,680 (D) ₹9,800

Solution: A = 8000 × (1.10)² = 8000 × 1.21 = ₹9,680

(A) 29 (B) 30 (C) 31 (D) 32

Solution: Total = 8 × 35 = 280. Remaining = 280 − 71 = 209.

New average = 209 / 7 = 29.86 ≈ 30

(A) 20 (B) 24 (C) 28 (D) 32

Solution: Net rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24 Time = 24 hours

(A) 18% (B) 19% (C) 20% (D) 22%

Solution: Let CP = 100. MP = 150. SP = 150 × 0.80 = 120. Profit% = 20%

(A) 15:20:22 (B) 15:20:24 (C) 12:20:24 (D) 15:18:24

Solution: a:b = 3:4 → ×5 → 15:20 b:c = 5:6 → ×4 → 20:24 a:b:c = 15:20:24

Want to improve speed in topics like percentages, ratios, and time & work? Practice more questions from our Quantitative Aptitude section.

(A) ₹3,000 (B) ₹3,100 (C) ₹3,240 (D) ₹3,500

Solution: SI = (P × R × T) / 100 = (12000 × 9 × 3) / 100 = ₹3,240

(A) 15 (B) 18 (C) 20 (D) 25

Solution: Numbers = 4x and 5x. LCM = 20x = 80 → x = 4. Larger = 5 × 4 = 20

(A) ₹95,000 (B) ₹98,000 (C) ₹1,00,000 (D) ₹1,05,000

Solution: 72250 = P × (0.85)² = P × 0.7225 → P = 72250/0.7225 = ₹1,00,000

(A) 28 sec (B) 29 sec (C) 30 sec (D) 32 sec

Solution: Speed = 60 km/h = 60 × 5/18 = 50/3 m/s Total distance = 200 + 300 = 500 m Time = 500 ÷ (50/3) = 30 seconds

(A) 120 (B) 132 (C) 144 (D) 156

Solution: LCM = Product / HCF = 1728 / 12 = 144

(A) 30 (B) 32 (C) 34 (D) 36

Solution: Boys = 48, Girls = 32. Boys above 90% = 48×50% = 24. Girls above 90% = 32×25% = 8. Total = 32

(A) 162 (B) 216 (C) 243 (D) 324

Solution: Each term × 3. 81 × 3 = 243

Topic: Geometric Progression series

(A) 35 (B) 40 (C) 45 (D) 50

Solution: Workers × Days = constant: 15 × 24 = W × 9 → W = 360/9 = 40 workers

(A) 15% (B) 18% (C) 20% (D) 25%

Solution: 2 hours = 120 minutes. (24/120) × 100 = 20%

(A) 2 km/h (B) 3 km/h (C) 4 km/h (D) 5 km/h

Solution: Upstream speed = 12 km/h. Downstream = 18 km/h. Current = (18 − 12)/2 = 3 km/h

(A) Beta Corp (B) Gamma Inc (C) Alpha Ltd (D) Delta Co

Solution: Alpha: (540−450)/450 × 100 = 20% Beta: 38/380 × 100 = 10% Gamma: 78/520 × 100 = 15% Delta: 29/290 × 100 = 10% Highest = Alpha Ltd at 20%

(A) 458 (B) 462 (C) 465.2 (D) 470

Solution: Total = 540+418+598+319+451 = 2,326 Average = 2326/5 = ₹465.2 Crore

(A) 4.1 (B) 4.0 (C) 4.12 (D) 4.5

Solution: 598 Crore = 59,800 Lakhs. Per employee = 59800/1450 = ₹41.24 Lakhs ≈ 4.12 (in ₹10L units)

(A) 5,300 (B) 5,430 (C) 5,500 (D) 5,600

Solution: 1200+950+1450+780+1050 = 5,430

(A) ₹455 Cr (B) ₹456 Cr (C) ₹459.8 Cr (D) ₹462 Cr

Solution: Growth % = 10%. 2024 = 418 × 1.10 = ₹459.8 Crore

(A) 18 (B) 19 (C) 20 (D) 22

Solution: 40% of 50 = ₹20 Crore

(A) 13 (B) 13.5 (C) 14.5 (D) 15

Solution: (15+14)% of 50 = 29% of 50 = ₹14.5 Crore

(A) 3.5 (B) 4.5 (C) 5 (D) 5.5

Solution: Infrastructure = 20% = 10 Cr. Miscellaneous = 11% = 5.5 Cr. Difference = 10 − 5.5 = ₹4.5 Crore

(A) 18% (B) 19% (C) 20% (D) 21%

Solution: New R&D = 14 × 1.5 = 21%. New total = 100% + 7% = 107%. R&D % = 21/107 × 100 ≈ 19.6% ≈ 20%

(A) 1/4 (B) 1/3 (C) 2/5 (D) 2/7

Solution: Non-salary = 60%. Infrastructure = 20%. Fraction = 20/60 = 1/3

(A) Mar (B) Apr (C) May (D) Jun

Solution: Feb: +30 (+25%). Mar: −20. Apr: +50 (+38.5%). May: +20 (+11%). Jun: −30. Highest growth = April (+38.5%)

(Note: If question asks absolute growth, April wins with +50)

(A) 152 (B) 155 (C) 158.33 (D) 162

Solution: Total = 120+150+130+180+200+170 = 950 Average = 950/6 = ₹158.33 Lakhs

(A) 80% (B) 82% (C) 85% (D) 88%

Solution: Peak = May = 200. June = 170. (170/200) × 100 = 85%

(A) 60% (B) 66.67% (C) 70% (D) 75%

Solution: (200−120)/120 × 100 = 80/120 × 100 = 66.67%

(A) 130 (B) 140 (C) 150 (D) 160

Solution: Apr=180 → May=+20 → Jun=−30. Net trend: May added 20, Jun lost 30. Average change = (20−30)/2 = −5. July ≈ 170−30 = 140 Lakhs

(Using the declining pattern: Apr→May +20, May→Jun −30, so Jun→Jul pattern suggests ~140)

(A) 40 (B) 42 (C) 42 (D) 44

Solution: Differences: 4, 6, 8, 10, 12. Next term = 30 + 12 = 42

(A) Uncle (B) Father (C) Grandfather (D) Brother

Solution: A → father of B → B is the sister of C → C is the mother of D. A is the father of C’s sibling. C is A’s child. D is A’s grandchild. A is the grandfather of D.

(A) FSBSFS (B) FSBSFT (C) FSBSFS (D) FTBSFS

Solution: Each letter +1: E→F, R→S, A→B, S→T, E→F, R→S → FSBSFS

(Correction: E+1=F, R+1=S, A+1=B, S+1=T, E+1=F, R+1=S = FSBTFS)

Correct coding: FSBTFS

(A) Only I follows (B) Only II follows (C) Neither follows (D) Both follow

Solution: “Some flowers are red” doesn’t guarantee roses (a subset of flowers) are red. Neither conclusion follows definitively. → Neither follows

(A) 5 km East (B) 3 km East (C) 3 km West (D) 5 km West

Solution: 5N → 3E → 5S. He is back at the original latitude, 3 km East of the start. Distance = 3 km East

(A) D (B) E (C) C is 2nd, D/E/F fill position 1 — (D) Cannot determine

Solution: A = position 3. B = position 5. C = position 2. Positions 1, 4, and 6 are filled by D, E, and F in some order. Cannot determine who is at the extreme left without more constraints.

(A) 36 (B) 64 (C) None, all perfect squares (D) 100

Solution: 25=5², 36=6², 49=7², 64=8², 81=9², 100=10², 121=11² All are perfect squares, No odd one out

(Check question: if asking for odd number among these, answer is 25, 49, 81, 121 are odd; 36, 64, 100 are even. Odd one out among even = 64 as 8² where 8=2³)

(A) EDRPNI (B) ECPFNI (C) ECPFNG (D) EDRFNH

Solution: F+2=H, R+3=U, I+2=K, E+2=G… Pattern: each letter +2. C+2=E, A+2=C, N+2=P, D+2=F, L+2=N, E+2=G → ECPFNG

(A) Only I (B) Only II (C) Both (D) Neither

Solution: The statement doesn’t say non-exercisers have poor mental health — I does not follow. II directly follows from the statement. Only II follows.

(A) Uncle (B) Brother (C) Cousin (D) Father

Solution: Neha’s grandfather’s only son = Neha’s father. Father’s son = Neha’s brother.

(A) 18 (B) 21 (C) 24 (D) 26

Solution: Fibonacci series: each term = the sum of the previous two. 8+13 = 21

(A) 120° (B) 125° (C) 130° (D) 135°

Solution: Minute hand at 40 min = 240°. Hour hand at 3:40 = (3×30) + (40×0.5) = 90 + 20 = 110°. Angle = 240 − 110 = 130°

(A) Knowledge (B) Books (C) School (D) Students

Solution: A doctor works in a hospital. A teacher works in a school.

(A) Friday (B) Saturday (C) Sunday (D) Monday

Solution: Jan has 31 days (31−1=30 days after Jan 1). Feb 2025 = 28 days (non-leap). Total days from Jan 1 to Mar 1 = 31 + 28 = 59 days. 59 mod 7 = 3 days. Wed + 3 = Saturday

(A) B (B) C (C) D (D) E

Solution: Circular: E–A–D and C–B–E. Arrangement: D–A–E–B–C (circular). Opposite to A (position 2) = position 5 = C

(in a 5-person circle, position opposite = position +2 or −2)

(A) 24 (B) 25 (C) 26 (D) 27

Solution: Rank from bottom = (Total − Rank from top) + 1 = 40 − 15 + 1 = 26

(A) A is cause, B is effect (B) B is cause, A is effect (C) A is cause, B is effect (D) Both are independent

Solution: Flooding causes evacuation. A is the cause, B is the effect.

(A) EU (B) EV (C) EW (D) FV

Solution: First letter: A, B, C, D, E (ascending). Second letter: Z, Y, X, W, V (descending). Next = EV

(A) Yellow-Green-Red-Blue (B) Yellow-Green-Red-Blue (C) Green-Yellow-Red-Blue (D) Yellow-Red-Green-Blue

Solution: Yellow > Green > Red > Blue. Order: Yellow–Green–Red–Blue

(A) I alone sufficient (B) II alone sufficient (C) Both together sufficient (D) Neither sufficient

Solution: Divisible by 6 requires divisibility by both 2 and 3. Both statements together are sufficient.

Logical reasoning is heavily tested in companies like TCS and Infosys. Practice more in our Logical Reasoning question bank.

(A) Dog (B) Rabbit (C) Horse (D) Bear

Solution: A cat has paws. A horse has hooves. Answer: Horse

(A) Publisher (B) Editor (C) Author (D) Reader

Solution: A composer creates a symphony. An author creates a novel. Answer: Author

(A) Rose (B) Lily (C) Lotus (D) Mango

Solution: Rose, Lily, Lotus, Tulip are all flowers. Mango is a fruit. Mango is the odd one out.

(A) Cricket (B) Hockey (C) Chess (D) Tennis

Solution: Cricket, Football, Hockey, and Tennis are outdoor sports. Chess is an indoor board game. Chess is the odd one out.

(A) Only I is implicit (B) Only II is implicit (C) Only I is implicit (D) Both are implicit

Solution: The advice implies people need to drink more, assuming they currently don’t. Assumption I is valid. Assumption II is not necessarily implied. Only I is implicit.

(A) Conclusion follows (B) Conclusion does not follow (C) Cannot say (D) Partially follows

Solution: “All birds can fly” is factually incorrect (ostriches are a known exception). The conclusion does not follow from real-world knowledge, even if logically it might from the statement alone. In standard verbal reasoning, the conclusion does not follow (as the major premise is false).

(A) Cars (B) Planes (C) Ships (D) Trains

Solution: A bouquet is a collection of flowers. A fleet is a collection of ships. Ships

(A) A is effect, B is cause (B) A is cause, B is effect (C) Both are independent (D) Both are effects of another cause

Solution: Lower interest rates directly lead to more home loan applications. A is cause, B is effect.

(A) January (B) March (C) June (D) August

Solution: January, March, August, and October all have 31 days. June has 30 days — odd one out.

(A) Inference definitely follows (B) Inference probably follows (C) Inference does not follow (D) Inference is irrelevant

Solution: The study shows a correlation, not exclusivity. The inference is too absolute. Inference does not follow.

(A) Sewing (B) Thread (C) Cloth (D) Tailor

Solution: A hammer drives a nail. Scissors cut cloth. Cloth

(A) Mobile phones are expensive. (B) Studies show a 25% improvement in grades when phones are banned. (C) Students use phones for music. (D) Teachers also use phones.

Solution: Only (B) provides direct evidence supporting the argument. B strengthens the argument.

(A) Brave (B) Confident (C) Timid (D) Strong

Solution: Optimist and Pessimist are antonyms. Bold’s antonym is Timid.

(A) Only I follows (B) Only II follows (C) Only I follows (D) Both follow

Solution: An inquiry is appropriate before any action. Dismissal without investigation is improper. Only Course of Action I follow.

(A) Sun (B) Stars (C) Lens (D) Sky

Solution: A microscope is used to observe bacteria. A telescope is used to observe stars.

(A) Hexagon inside Square (B) Hexagon inside Square (C) Circle inside Triangle (D) Pentagon inside Triangle

Solution: The inner shape gains one side with each step: Circle(0)→Triangle(3)→Pentagon(5)→Hexagon(6). Answer: Hexagon inside Square

Solution: The figure with dots placed outside the shape is the odd one out — all others have the symbol inside.

(A) DRAOB (B) DAORB (C) The reversed horizontal version

Solution: Mirror image reverses left-right. Each letter is individually mirrored and the order is reversed. BOARD in mirror = ᗺOARᗡ (each letter flipped horizontally)

(A) 1 (B) 2 (C) 3 (D) 4

Solution: One fold → one punch creates 2 holes when unfolded.

Solution: Apply Latin square logic: identify which shape is missing from that row AND that column. The answer is whichever shape appears in neither the row nor the column already.

(A) 2 (B) 3 (C) 4 (D) 5

Solution: Pattern: dots increase by 1 reading left-to-right, top-to-bottom. Bottom-right = 4 dots

Solution: Trace each option’s outline within the complex figure. The correct answer is the one whose exact shape (without rotation or scaling) can be found as a part of the complex figure.

(A) 3 (B) 5 (C) 6 (D) 8

Solution: Individual (3) + pairs (2 adjacent) + whole (1) = 6 triangles

Solution: Water image = vertical flip (top becomes bottom). The letter K flipped vertically is the correct answer.
(Select option with K flipped on its horizontal axis)

Solution: Map each face of the net to its position on the cube. The face directly opposite is the one at the end of the same column as the top face in the cross pattern.

(A) △△△△□□□□ (B) △△△△□□□□ (C) △△△□□□□ (D) △△△△□□□

Solution: Each step adds one more of each shape. Step 4 = 4 triangles + 4 squares.

(A) Pentagon outside Pentagon (B) Small rhombus inside large circle (C) Small rhombus inside large rhombus (D) Two separate pentagons

Solution: The pattern is: same shape, small inside large. The next should follow the same rule: a small rhombus inside a large rhombus.

(A) submitted (B) submitted (C) submits (D) will submitted

Correct: “submitted” — Past tense consistent with “before the deadline.”

(A) Silent (B) Confused (C) Articulate (D) Hesitant

Solution: Eloquent means fluent and persuasive in speech. Synonym: Articulate

(A) Kind (B) Generous (C) Malevolent (D) Honest

Solution: Benevolent = kind and generous. Antonym: Malevolent (cruel, harmful)

(A) No error (B) “have” should be “has” (C) “neither” should be “both” (D) “their” should be “his”

Solution: “Neither” is singular and takes a singular verb. Correct: “Neither of the students has submitted…”

(A) She (B) doesn’t (C) know (D) play

Solution: Third-person singular (she) requires “doesn’t,” not “don’t.” Error: don’t

(A) To eat quickly (B) To cause pain (C) To endure a painful situation (D) To argue aggressively

Solution: “Bite the bullet” means to endure a difficult situation with courage. To endure a painful situation

(A) QRPS (B) QPRS (C) PQRS (D) QRSP

Solution: Logical order: Q (intro) → P (how they help) → R (threat) → S (consequence). Q-P-R-S

(A) High cost (B) Slow adoption (C) Job displacement and data privacy (D) Poor accuracy

Solution: The passage explicitly states: “concerns about job displacement and data privacy remain significant.” Answer: C

(A) Healthcare and Education (B) Finance and Law (C) Healthcare, Finance, and Education (D) All industries worldwide

Solution: The passage mentions healthcare, finance, and education specifically. C

(A) discovery (B) discovery (C) invention (D) creation

Solution: Electrons already exist, they are discovered, not invented. Answer: Discovery

(A) He is (B) student who was (C) selected (D) No error

Solution: “One of the students” is plural. Should be: “one of the students who were selected.” Error in “student who was.”

(A) Talkative (B) Fluent (C) Concise (D) Elaborate

Solution: Verbose means using too many words. Antonym = Concise (brief and clear).

(A) harmful (B) possible (C) fatal (D) complete

Solution: Classic Winston Churchill quote. The correct word is fatal — failure is not fatal (does not permanently end you).

(A) No improvement (B) Despite his illness (C) Despite for his illness (D) In spite his illness

Solution: “Despite” does not take “of.” Correct: “Despite his illness, he attended the meeting.”

(A) Permanent (B) Strong (C) Transient (D) Beautiful

Solution: Ephemeral = lasting for a very short time. Synonym: Transient

(A) QRSP (B) QSPR (C) QSPR (D) QPRS

Solution: Q (event) → S (immediate result: homelessness) → P (government response: emergency declared) → R (relief action). Q-S-P-R

(A) Outgoing (B) Talkative (C) Reserved (D) Honest

Solution: Gregarious = very sociable (synonyms). Reticent = not inclined to speak freely. Synonym: Reserved

(A) “The committee have reached their decision.” (B) “Each of the players are ready.” (C) “The jury has delivered its verdict.” (D) “Neither the manager nor the staff was present.”

Solution: (A) Collective noun “committee” in formal English takes singular verb — but in British English, plural is acceptable. However, (C) is unambiguously correct: “jury” + singular “has” + singular “its.” C is correct.

Pattern: 26 questions | 40 minutes | No negative marking

Focus Areas: Number Systems, Blood Relations, Coding Patterns, Time & Work

Sample TCS Question:

A company hired 15 workers. After 3 months, 5 quit and were replaced by 8 new workers. What percentage increase in workforce occurred?

Answer: Original = 15. Final = 15 − 5 + 8 = 18. Increase = (18−15)/15 × 100 = 20%

Pattern: 10 questions | 35 minutes (Reasoning), 10 questions | 25 minutes (Quant)

Focus Areas: Puzzles, Data Sufficiency, Logical Deduction

Sample Infosys Question:

Five friends sit in a row. A sits to the left of B. C sits to the right of B. D sits to the left of A. E sits between C and the right end. Who sits in the middle?

Answer: The order is D–A–B–C–E. B sits in the middle.

Pattern: 16 questions | 16 minutes (Online Aptitude)

Focus Areas: Percentages, Profit/Loss, Averages, Simple/Compound Interest

Sample Wipro Question:

The average of 5 consecutive odd numbers is 31. What is the largest number?

Answer: Numbers: 27, 29, 31, 33, 35. Largest = 35

If 6 men can build a wall in 12 days, how many men are needed to build it in 4 days?

“This is a work-rate inverse proportion problem.” Men × Days = Constant → 6 × 12 = M × 4 → M = 18 men

A shopkeeper marks a product 40% above the cost price and gives a 20% discount. What is the net profit percentage?

“Mark up then discount, net effect calculation.” Let CP = 100. MP = 140. SP = 140 × 0.8 = 112. Profit = 12%. Net profit = 12%

In how many ways can the letters of the word “LEVEL” be arranged?

“Permutation with repeated letters.” Total = 5!/2!×2! = 120/4 = 30 ways

A bag contains 4 red, 5 blue, and 3 green balls. One ball is drawn at random. What is the probability that it is not red?

“Not red = blue + green.” P(not red) = (5+3)/12 = 8/12 = 2/3