Deloitte Aptitude Test Questions and Answers: Worked Examples

Deloitte’s aptitude section runs 35 minutes and covers 14 topics from number systems to permutations. It’s the first filter in Deloitte India’s campus recruitment for freshers, placed before the coding test and case study rounds. The full recruitment process breakdown is worth reading before the test; this article focuses on the aptitude section specifically.

What the Deloitte Aptitude Test Pattern Looks Like

Parameter	Detail
Duration	35 minutes
Format	Multiple-choice (MCQ)
Difficulty	Easy to moderate
Topics covered	14 quantitative and logical areas
Calculator	Not permitted

The test draws from high-school mathematics plus applied reasoning. Most questions are direct formula applications at moderate speed. Fluency with core formulas matters more than depth: 35 minutes for roughly 20 to 30 questions leaves under two minutes per item.

Topics the Test Covers

Deloitte’s aptitude section draws from these 14 areas. For topic-level weightages and past-question distributions, see the section-wise syllabus.

• Number Systems — divisibility rules, prime numbers, LCM and HCF
• Averages — weighted averages, effect of adding or removing a value
• Percentages — profit and loss percentages, percentage change calculations
• Simple Interest and Compound Interest — applying SI and CI formulas
• Time, Speed, and Distance — trains, boats, relative speed problems
• Geometry — area, volume, basic properties of standard shapes
• Coordinate Geometry — distance formula, slope, midpoint
• Logarithms — log properties, solving exponential equations
• Quadratic Equations — discriminant, roots, factoring
• Probability — classical probability, mutually exclusive events
• Permutation and Combination — arrangements and selections
• Time and Work — work-rate problems with multiple workers
• Alligation — mixture problems and ratio blending
• Miscellaneous — number series, data sufficiency, basic logic

The highest-frequency areas in campus placement drives are Time and Work, Ratio and Proportion, Profit and Loss, Probability, and Permutation and Combination. If preparation time is limited, cover these first.

10 Practice Questions with Worked Solutions

Each solution below is verified from first principles. Four questions (Q3, Q5, Q7, Q10) have corrected answers; the widely circulated legacy versions contained arithmetic errors that have been fixed.

Q1: Number Series

• Question: Find the next number in the series: 2, 6, 12, 20, 30, ___
• Step 1: Compute successive differences: 6 minus 2 = 4, 12 minus 6 = 6, 20 minus 12 = 8, 30 minus 20 = 10.
• Step 2: Each difference increases by 2. Next difference = 12.
• Step 3: 30 plus 12 = 42.
• Answer: 42

Q2: Profit and Loss

• Question: A person buys a product for Rs. 500 and sells it for Rs. 600. What is the profit percentage?
• Step 1: Profit = Selling Price minus Cost Price = 600 minus 500 = 100.
• Step 2: Profit% = (Profit / Cost Price) multiplied by 100 = (100 / 500) multiplied by 100 = 20%.
• Answer: 20%

Q3: Time and Work (corrected)

• Question: A can complete a job in 5 days. B can complete the same job in 10 days. How long do they take working together?
• Step 1: A’s rate = 1/5 of the job per day. B’s rate = 1/10 of the job per day.
• Step 2: Combined rate = 1/5 plus 1/10 = 2/10 plus 1/10 = 3/10 of the job per day.
• Step 3: Time = 1 divided by (3/10) = 10/3 days.
• Step 4: The fractional part is 1/3 of a day. 1/3 multiplied by 24 = 8 hours. Total time = 3 days 8 hours.
• Answer: 3 days 8 hours.
• Correction note: The widely copied version of this question states “3 days 4 hours.” That is incorrect. 10/3 days = 3.333… days, and 0.333 multiplied by 24 = 8 hours, not 4.

Q4: Simple Interest

• Question: A sum amounts to Rs. 9,000 in 2 years at simple interest of 10% per annum. What is the principal?
• Step 1: Amount = Principal plus SI = P plus (P multiplied by R multiplied by T / 100) = P(1 plus 0.20) = 1.2P.
• Step 2: 1.2P = 9,000, so P = 9,000 / 1.2 = 7,500.
• Answer: Rs. 7,500

Q5: Permutation and Combination (corrected)

• Question: In how many ways can the letters of the word LEADER be arranged?
• Step 1: List each letter and its count: L(1), E(2), A(1), D(1), R(1). Total = 6 letters, with E appearing twice.
• Step 2: Distinct arrangements = 6! / 2! = 720 / 2 = 360.
• Answer: 360 distinct arrangements.
• Correction note: The widely circulated version of this solution claims LEADER contains two L’s and gives 180 (= 720 / 4). LEADER contains one L. The denominator is 2! for the repeated E only, giving 360.

Q6: Probability

• Question: A box contains 5 red balls, 7 green balls, and 3 blue balls. One ball is drawn at random. What is the probability of drawing a green ball?
• Step 1: Total balls = 5 plus 7 plus 3 = 15.
• Step 2: P(green) = 7 / 15.
• Answer: 7/15

Q7: Ages (problem replaced — original was inconsistent)

• Question: A father is currently 3 times his son’s age. In 12 years, the father will be twice the son’s age. Find their present ages.
• Step 1: Let son’s present age = S. Then father’s present age = 3S.
• Step 2: In 12 years: father’s age = 3S plus 12, son’s age = S plus 12.
• Step 3: Condition: 3S plus 12 = 2(S plus 12) = 2S plus 24.
• Step 4: 3S minus 2S = 24 minus 12. So S = 12. Father = 3 multiplied by 12 = 36.
• Verification: In 12 years: son = 24, father = 48. 48 = 2 multiplied by 24. Confirmed.
• Answer: Son = 12 years, Father = 36 years.
• Replacement note: The original legacy problem (sum of ages = 60, in 10 years father = twice son’s age) has no integer solution. Solving it correctly gives son = 50/3, which is not a whole number. The legacy answer of son = 20, father = 40 fails direct verification. The problem above is a structurally equivalent replacement with a clean integer solution.

Q8: Average

• Question: The average of 5 consecutive even numbers is 30. What are the numbers?
• Step 1: In any arithmetic sequence, the average equals the middle term. Middle number = 30.
• Step 2: The 5 consecutive even numbers centred at 30 are: 30 minus 4, 30 minus 2, 30, 30 plus 2, 30 plus 4.
• Answer: 26, 28, 30, 32, 34.

Q9: Speed, Distance, and Time

• Question: A train travels at 60 km/h. How long does it take to cover 120 km?
• Step 1: Time = Distance / Speed = 120 / 60.
• Answer: 2 hours.

Q10: Ratio and Proportion (corrected)

• Question: The ratio of the ages of A and B is 3:5. Five years ago, the ratio was 4:7. Find their present ages.
• Step 1: Let A = 3k and B = 5k.
• Step 2: Five years ago: A = 3k minus 5, B = 5k minus 5. Set up: (3k minus 5) / (5k minus 5) = 4/7.
• Step 3: Cross-multiply: 7(3k minus 5) = 4(5k minus 5), which gives 21k minus 35 = 20k minus 20.
• Step 4: 21k minus 20k = minus 20 plus 35, so k = 15.
• Step 5: A = 3 multiplied by 15 = 45. B = 5 multiplied by 15 = 75.
• Verification: Five years ago: A = 40, B = 70. Ratio = 40:70 = 4:7. Confirmed.
• Answer: A is 45 years old, B is 75 years old.
• Correction note: The widely circulated version gives k = 10, producing ages 30 and 50. Checking: five years ago that gives 25:45 = 5:9, not 4:7. The cross-multiplication was expanded incorrectly in the legacy solution.

Where Students Drop Marks

Four error patterns appear across the questions above and are worth pre-empting before the test.

• Permutation — miscounting repeated letters. LEADER contains one L, not two. Write out each distinct letter with its count before applying the formula. That three-second check is the difference between 360 and 180.

• Time and Work — fraction-to-hours conversion. When combined time is 10/3 days, the fractional part is 1/3 of a day: 1/3 multiplied by 24 = 8 hours. The legacy version of Q3 stated “3 days 4 hours,” which is off by four hours on a single conversion.

• Ages — applying the time offset to only one side. “In N years, father = 2 times son’s age” means both ages increase by N. The correct equation is (father plus N) = 2(son plus N). Dropping N from one side shifts the answer incorrectly.

• Ratio and Proportion — skipping expansion steps. 7(3k minus 5) = 4(5k minus 5) must be expanded fully before collecting terms: 21k minus 35 = 20k minus 20. Students who skip the expansion step often combine signs incorrectly. Write each side out before moving terms.

For logical reasoning practice questions in the same test session, the same careful step-by-step habit reduces errors in deduction and sequence problems.

A Three-Week Preparation Plan

Three weeks of focused daily practice is sufficient for most students targeting Deloitte’s moderate-difficulty aptitude section. The plan below works in 45-minute sessions.

Week	Focus	Daily task
Week 1	High-frequency quantitative topics	Time and Work, Ratio and Proportion, Profit and Loss — 15 questions each, then review wrong answers
Week 2	Remaining quantitative topics	Probability, Permutation and Combination, Simple and Compound Interest, Number Series — 10 questions each
Week 3	Weak-area consolidation plus timed mocks	Three full 35-minute timed practice sessions; review every incorrect answer

For additional drill questions beyond the 10 above, IndiaBIX’s aptitude section organises problems by topic, which makes it easy to target specific gaps. Work through topic sets rather than random questions. Topic sets make pattern gaps visible faster.

The Deloitte placement papers collection has further worked examples across aptitude and reasoning categories, useful for Week 3 mock variety.

The logical pattern tested in Q1 (spotting the rule in a number series and projecting it forward) and Q10 (holding two simultaneous ratio constraints and solving) is the same cognitive move used when auditing AI outputs for reasoning consistency. That skill is increasingly relevant in tech consulting roles. TinkerLLM at ₹499 is where most students begin that transition; one weekend is enough to get through the core modules.