7 Must-Solve TCS Aptitude Questions (2026) with Full Solutions

TCS NQT aptitude practice resolves to six recurring topic clusters: number systems, TSD, profit and loss, percentages, mensuration, and ratio-proportion.

This article works through one verified question per cluster (seven total), with every step derived from scratch. Where the original legacy article had arithmetic errors, the correct working is shown.

Why These Six Clusters Appear Across TCS Tracks

TCS recruits engineering freshers through three tracks, and your NQT percentile determines which one you qualify for. The TCS NQT official page has the current eligibility criteria; the track CTC bands from the FACE Prep 2026 audit are:

Track	CTC Band	NQT Expectation
TCS Ninja	₹3.5 to 3.9 LPA	Baseline aptitude plus basic coding
TCS Digital	₹7.0 to 7.5 LPA	Higher NQT cutoff plus advanced technical
TCS Prime	₹9.0 to 11.0 LPA	Top NQT percentile plus AI/data project review

The Numerical Ability sub-section of the NQT draws from a fixed question bank. Six topic clusters appear in past TCS NQT aptitude questions with the highest consistency: number systems, time-speed-distance, profit and loss, percentages, mensuration, and ratio-proportion. Drilling all six takes less time than trying to predict which two or three to skip.

Number Systems

HCF and LCM

The core property: for any two integers, their product equals HCF multiplied by LCM. One formula covers a wide range of question types.

• Question: The LCM of two numbers is 48 and their HCF is 8. One number is 16. Find the other.
• Step 1: Product of the two numbers = HCF x LCM = 8 x 48 = 384.
• Step 2: Other number = 384 / 16 = 24.
• Check: HCF(16, 24) = 8 and LCM(16, 24) = 48; both confirmed.
• Answer: 24.

Divisibility

For divisibility by 9, the digit-sum rule handles most questions directly: a number is divisible by 9 if and only if its digit sum is divisible by 9.

• Question: What is the smallest positive integer to add to 99,998 so the result is divisible by 9?
• Step 1: Digit sum of 99,998 = 9 + 9 + 9 + 9 + 8 = 44.
• Step 2: 44 divided by 9 gives quotient 4 remainder 8. Current remainder is 8.
• Step 3: Shortfall to next multiple of 9 = 9 minus 8 = 1.
• Check: 99,999 divided by 9 = 11,111 exactly.
• Answer: Add 1.

Time, Speed, and Distance

Train-crossing questions are the dominant TSD form in TCS NQT aptitude. The template: total crossing distance equals the sum of both train lengths; relative speed equals the sum of their speeds when they run towards each other, and the difference when they run in the same direction.

• Question: Two trains of lengths 120 m and 80 m run towards each other at 42 km/h and 30 km/h. How many seconds do they take to cross each other?
• Step 1: Total crossing distance = 120 + 80 = 200 m.
• Step 2: Relative speed = 42 + 30 = 72 km/h. Convert to m/s: 72 x (5/18) = 20 m/s.
• Step 3: Time = 200 / 20 = 10 seconds.
• Answer: 10 seconds.

The conversion factor 5/18 (equivalently, divide km/h by 3.6) is worth memorising for TCS NQT. See previous TCS aptitude questions for more TSD worked examples.

Profit, Loss, and Successive Discounts

Successive discounts are not additive. The formula for net effective discount with two successive discounts x% and y%: effective percentage = x + y minus (x times y) divided by 100.

• Note: Applying 20% then 10% gives 28% effective, not 30%. The worked example below confirms this.
• Question: An item is marked at ₹5,000. A shopkeeper applies successive discounts of 20% and 10%. Find the selling price and the net effective discount.
• Step 1: After 20% discount: ₹5,000 x 0.80 = ₹4,000.
• Step 2: After 10% discount: ₹4,000 x 0.90 = ₹3,600.
• Step 3 (formula check): Effective discount = 20 + 10 minus (20 x 10)/100 = 30 minus 2 = 28%.
• Check: (₹5,000 minus ₹3,600) / ₹5,000 x 100 = 28%. Both routes agree.
• Answer: Selling price ₹3,600; effective discount 28%.

Percentages

Percentage-on-percentage questions catch students who add or subtract raw percentages. The correct approach multiplies the decimal factors.

• Question: A value increases by 20% and then decreases by 15%. What is the net percentage change?
• Step 1: Multiply the factors: 1.20 x 0.85 = 1.02.
• Step 2: Net change = (1.02 minus 1) x 100 = +2%.
• Shortcut check: Formula gives 20 + (minus 15) + (20 x minus 15)/100 = 5 minus 3 = 2% increase.
• Answer: 2% net increase.

The formula generalises: if a value changes by +a% then by +b% (positive or negative), net change % = a + b + (a x b)/100.

Mensuration

Cylinder and cuboid problems appear regularly in TCS NQT Numerical Ability sets. For cylinders, two formulas cover most questions: CSA = 2 x pi x r x h; TSA = 2 x pi x r x (r + h).

• Question: A cylinder has radius 7 cm and height 10 cm. Find the curved surface area and total surface area. Use pi = 22/7.
• Step 1: CSA = 2 x (22/7) x 7 x 10 = 2 x 22 x 10 = 440 sq cm.
• Step 2: TSA = 2 x (22/7) x 7 x (10 + 7) = 2 x 22 x 17 = 748 sq cm.
• Check: TSA minus CSA = 748 minus 440 = 308 = 2 x (22/7) x 49 = 308. Consistent.
• Answer: CSA = 440 sq cm; TSA = 748 sq cm.

Ratio and Proportion

Ratio questions in TCS NQT are usually direct: a total is split according to a given ratio, and the question asks for one person’s share. The method is always the same: find the total parts, divide, multiply.

• Question: A, B, and C invest in a business in the ratio 2:3:5. The total profit at year-end is ₹90,000. Find each person’s share.
• Step 1: Total ratio parts = 2 + 3 + 5 = 10.
• Step 2: A’s share = (2/10) x ₹90,000 = ₹18,000.
• Step 3: B’s share = (3/10) x ₹90,000 = ₹27,000.
• Step 4: C’s share = (5/10) x ₹90,000 = ₹45,000.
• Check: ₹18,000 + ₹27,000 + ₹45,000 = ₹90,000.
• Answer: A gets ₹18,000, B gets ₹27,000, C gets ₹45,000.

For more ratio and proportion practice alongside the TCS Ninja questions and pattern, the Ninja-track paper typically has two to three ratio questions per set.

After the Aptitude Gate: the Prime Track

The ratio-proportion and number-systems questions above are standard Ninja-track territory. The Prime track (see CTC table above) additionally requires AI project work, as of March 2026. TCS CHRO Sudeep Kunnumal stated at the AI Impact Summit that 60% of FY26 fresher hires are AI-skilled, up from 10 to 15% three years ago, with Prime and Digital cadre volume up 50% in one year.

Aptitude clears the NQT gate. AI project work determines which side of the Ninja-to-Prime gap you land on. TinkerLLM is a self-paced LLM playground at ₹299 for students who want to start building with AI before their placement window.