Problem Solving Interview Questions India 2026: Aptitude, Logical Reasoning, and Case Studies

Quantitative aptitude for Indian tech company assessments:

1. Time and Work: Formula: if A completes in 'a' days and B in 'b' days, together they complete in ab/(a+b) days. Extension: A can do a job in 8 days, B in 12 days. Together: (8x12)/(8+12) = 96/20 = 4.8 days. With efficiency variation: if A is 1.5x as efficient as B, and together they complete in 6 days, find each person's rate individually.

2. Time, Speed, and Distance: Distance = Speed x Time. Relative speed: objects moving in the same direction: |S1 - S2|; opposite directions: S1 + S2. Train and platform problems: distance covered = length of train + length of platform.

3. Percentages: Successive percentage change: original x (1 + p/100) x (1 + q/100). A 20% increase followed by a 20% decrease gives a net result of 1.2 x 0.8 = 0.96 (4% net decrease).

4. Profit, Loss, and Discount: Profit% = (Profit/Cost Price) x 100. Discount is always on Marked Price. Successive discounts d1 and d2: net discount = d1 + d2 - (d1 x d2)/100.

5. Number Series: Arithmetic progression (constant difference), geometric progression (constant ratio), alternating series (odd positions follow one pattern, even positions another), Fibonacci-style (each term is the sum of the previous two).

Logical reasoning for Indian aptitude tests:

1. Syllogisms: Method: draw a Venn diagram for each statement. 'All A are B' means circle A is completely inside circle B. 'Some A are C' means circles A and C overlap. Common mistakes: 'All A are B, All B are C' does imply 'All A are C' (transitivity holds). 'All A are B, Some B are C' does NOT imply 'Some A are C' (the B's that are also C might not be the same B's that are A).

2. Blood Relations: Draw a family tree. Start with the person mentioned first; add relationships one step at a time. Common phrasing: 'A is the mother of B's wife' means A is B's mother-in-law.

3. Seating Arrangements: Circular: (n-1)! arrangements for n people in a circle (fix one person, arrange the rest). Linear: n! arrangements. Conditional: 'A and B must sit together' = treat A and B as one unit: (n-1)! arrangements, then multiply by 2! for A and B's internal arrangement.

4. Coding-Decoding: Caesar cipher: each letter is shifted by a fixed number. 'A = 1, Z = 26' mapping. Position reversal: A=Z, B=Y. Identify the pattern from 1-2 examples before applying.

5. Data Interpretation: Calculate row and column totals first. Identify the question type before reading the data: percentage change, ratio, finding the largest or smallest value. Use estimation to eliminate options before precise calculation.

Guesstimate framework (used in PM, consulting, and strategy interviews):

1. Clarify the question before starting: 'Are we estimating the number of active users in India or the total number of downloads?'

1. State your approach first: 'I will estimate this using a top-down approach starting from India's population, then filtering by relevant segments.'

1. Use round numbers; acknowledge approximations openly.

4. Sample guesstimate: 'Estimate the number of people ordering food delivery in India on a typical weekday.' - India population: 1.4 billion - Urban population (35%): 490 million - Working-age urban adults (60%): 294 million - Smartphone users in this group (75%): 220 million - Food delivery app users (40%): 88 million - Daily active orderers on a weekday (7%): ~6 million - Sanity check: Swiggy + Zomato combined do 5-8 million orders per day. Estimate looks reasonable.

5. Alternative guesstimate: 'Estimate the number of Uber/Ola rides per day in Bangalore.' - Bangalore metro population: ~10 million - Working-age adults (60%): 6 million - Own vehicle or use public transport primarily (80%): 4.8 million - Regular ride-sharing users (20%): 1.2 million - Average rides per user per week (2 rides): 2.4 million rides per week - Per day: 2.4M / 7 = ~340K rides per day

Case study structure (used in PM, strategy, and consulting firm interviews):

1. Understand the problem (5 minutes): ask clarifying questions before diving in. 'What is the primary goal of the business? Revenue? Market share? Customer retention?' Do not solve the wrong problem.

1. Structure your approach (2 minutes): state the framework you will use before applying it. 'I will use a customer journey framework: acquisition, activation, engagement, retention, and revenue.'

1. Diagnose (10 minutes): use the framework to identify where the problem lies. 'The data shows that our activation rate is 40% but the industry average is 60%. The issue is in the activation stage.'

1. Generate solutions (5 minutes): 3-5 specific, prioritised solutions. 'Option 1: improve the onboarding flow (high impact, medium effort). Option 2: add social proof elements to the trial signup page (medium impact, low effort). Option 3: add a personalisation quiz at signup to improve relevance (high impact, high effort).'

1. Recommend with trade-offs (3 minutes): pick one recommendation and explain why. 'I recommend Option 2 as the immediate action because it has the highest ROI ratio, and Option 1 as the Q2 initiative once we have the data from the Option 2 experiment.'

1. Measure success (2 minutes): 'We will measure success by the 7-day activation rate (completing the first meaningful action). Baseline: 40%. Target: 55% within 30 days of the change.'

Aptitude test preparation strategy (4 weeks):

Week 1: Quantitative foundations (2 hours per day):

• Time-Work, Time-Speed-Distance, Percentages, Number Series
• Resource: RS Aggarwal Quantitative Aptitude (focus on these 4 chapters)
• Daily: solve 30 problems with a timer; target 1 problem per minute

Week 2: Logical reasoning (2 hours per day):

• Syllogisms, Blood Relations, Seating Arrangements, Coding-Decoding
• Resource: RS Aggarwal Verbal and Non-Verbal Reasoning, IndiaBIX logical reasoning section

Week 3: Data Interpretation and advanced topics (2 hours per day):

• Reading bar charts, line graphs, pie charts, and tables under time pressure
• Probability, Permutations and Combinations, Simple and Compound Interest
• Resource: IndiaBIX Data Interpretation section

Week 4: Mock tests and company-specific preparation:

• Full-length timed mock tests for your target company (PrepInsta has company-specific mocks)
• Identify your 3 weakest topic areas and drill them
• Previous year question papers: the pattern repeats significantly each year

Speed strategy: aptitude tests have fixed time per section (typically 25-30 questions in 25-35 minutes: approximately 1 question per minute). Easy questions should take 10-15 seconds; medium 30-40 seconds; hard 60-90 seconds. Flag and skip if a question takes more than 90 seconds on your first pass; return after completing the easier ones.