Quantitative Aptitude: 20 Solved Questions for Campus Placements

Placement aptitude tests at TCS, Infosys, Wipro, and Capgemini draw quant questions from five topics: profit and loss, speed-distance-time, time and work, averages, and simple interest. The key is not rote formula memorisation. It is applying one formula per topic under time pressure. This article covers 20 solved questions, four per topic, using a consistent four-step approach: identify what is given, what is asked, which formula connects them, then substitute.

Every worked solution below follows that same structure. Read through one topic completely before moving to the next; the pattern recognition transfers across topics and is faster to build in one sitting than across separate sessions.

Why these five topics appear on every placement test

Placement selection tests are designed to be completed by a wide candidate pool within a fixed time window. They need questions that are solvable in under two minutes each, have a single correct answer, and differentiate on speed and accuracy rather than advanced mathematical knowledge. The five topics in this article sit at exactly that intersection: solvable with one formula, tierable by difficulty, and reliable discriminators between well-prepared and underprepared candidates.

The TCS National Qualifier Test Numerical Ability section runs 26 questions in 40 minutes. The AMCAT Quantitative Ability module covers the same topic clusters with a similar question structure. Across both, and across Infosys, Wipro, and Capgemini tests, these five topics account for the majority of numerical questions in every paper.

FACE Prep’s Campus Placement Evaluation Test benchmarks where you currently stand on the full placement syllabus, including quant. If you haven’t taken it yet, it gives you a percentile baseline before you start this practice set.

Profit and loss: 4 worked questions

The core formula is: Profit % = (Profit / Cost Price) × 100, where Profit = SP minus CP. Derived forms: SP = CP × (1 + P%/100) to find selling price, and CP = SP / (1 + P%/100) to find cost price when profit% is given. Loss problems use the same structure with subtraction.

• Q1: A product is bought for ₹500 and sold for ₹600. What is the profit percentage?

• Answer: Profit = ₹600 - ₹500 = ₹100. Profit % = (100/500) × 100 = 20%. (Option C in the original quiz)

• Q2: A shirt is sold for ₹840 at a 20% profit. What was the cost price?

• Answer: SP = CP × (1 + 20/100). So CP = 840 / 1.20 = ₹700.

• Q3: An item bought for ₹200 is sold at a 15% loss. Find the selling price.

• Answer: SP = CP × (1 - 15/100) = 200 × 0.85 = ₹170.

• Q4: A trader marks a product at ₹1,000, gives a 10% discount, and makes a 20% profit. What is the cost price?

• Answer: SP after discount = 1000 × 0.90 = ₹900. CP = SP / (1 + 20/100) = 900 / 1.20 = ₹750.

Time, speed, and distance: 4 worked questions

Core formula: Speed = Distance / Time. Rearranged: Distance = Speed × Time, and Time = Distance / Speed. For unit conversion: 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h. Relative speed problems add speeds (opposite directions) or subtract (same direction).

• Q1: A car travels 180 km in 3 hours. What is the average speed?

• Answer: Speed = Distance / Time = 180 / 3 = 60 km/h. (Option B in the original quiz)

• Q2: Two cars start from the same point in opposite directions at 40 km/h and 60 km/h. How far apart are they after 2 hours?

• Answer: Relative speed (opposite) = 40 + 60 = 100 km/h. Distance = 100 × 2 = 200 km.

• Q3: A train 300 metres long passes a stationary pole in 15 seconds. What is the train’s speed in km/h?

• Answer: Speed = 300/15 = 20 m/s. Convert: 20 × (18/5) = 72 km/h.

• Q4: Person A covers 300 km at 60 km/h. Person B covers the same 300 km at 75 km/h. How much time does B save compared to A?

• Answer: A’s time = 300/60 = 5 hours. B’s time = 300/75 = 4 hours. Time saved = 1 hour.

Time and work: 4 worked questions

Core formula: if a person completes a task in N days, their work rate is 1/N per day. Combined rate for A and B working together = 1/A + 1/B. Time taken together = 1 / (combined rate). This extends to three or more workers by adding a third rate.

For a broader set of time and work problems, including pipe-and-cistern and efficiency variants, see the full treatment in time and work problems in detail.

• Q1: A completes a task in 12 days, B in 18 days. How many days will they take together?

• Answer: Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time = 36/5 = 7.2 days. (≈ 7 days 5 hours; among the answer choices, the intended answer is 7.2 days)

• Q2: A alone finishes a task in 15 days. A and B together finish it in 10 days. How long does B take alone?

• Answer: Rate of B = Rate(A+B) - Rate(A) = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. B alone: 30 days.

• Q3: 8 workers can finish a project in 12 days. How many workers are needed to finish it in 8 days?

• Answer: Total work = 8 × 12 = 96 worker-days. Workers needed = 96 / 8 = 12 workers.

• Q4: Pipe A fills a tank in 4 hours. Pipe B empties it in 12 hours. With both open, how long to fill the tank?

• Answer: Net fill rate = 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6 per hour. Time = 6 hours.

Averages: 4 worked questions

Core formula: Average = Sum / Count, so Sum = Average × Count. For problems involving a removed or added element, compute both sums and find the difference. Weighted average problems specify the count in each group separately.

• Q1: The average of 7 numbers is 48. When one number is removed, the average of the remaining 6 becomes 47. What is the removed number?

• Answer: Sum of 7 = 48 × 7 = 336. Sum of 6 = 47 × 6 = 282. Removed number = 336 - 282 = 54. (Option D in the original quiz)

• Q2: The average of 5 numbers is 32. A sixth number is added and the average becomes 30. What is the sixth number?

• Answer: Sum of 5 = 32 × 5 = 160. Sum of 6 = 30 × 6 = 180. Sixth number = 180 - 160 = 20.

• Q3: A class has 15 boys with an average score of 60 and 15 girls with an average score of 70. What is the overall class average?

• Answer: Total marks = (15 × 60) + (15 × 70) = 900 + 1,050 = 1,950. Total students = 30. Average = 1,950 / 30 = 65.

• Q4: The average of 10 numbers is 50. Each number is increased by 5. What is the new average?

• Answer: Every element shifts up by 5, so the average also shifts by 5. New average = 50 + 5 = 55. (No need to recompute the sum.)

Simple interest and compound interest: 4 worked questions

Simple interest formula: SI = (P × R × T) / 100, where P is principal, R is annual rate in percent, T is time in years. Amount = P + SI. For compound interest: CI = P × (1 + R/100)^T minus P. When T equals 1 year and compounding is annual, SI and CI are equal. For T greater than 1, CI exceeds SI.

• Q1: ₹5,000 is invested at 4% simple interest for 2 years. What is the interest earned?

• Answer: SI = (5000 × 4 × 2) / 100 = 40,000 / 100 = ₹400. (Option A in the original quiz)

• Q2: ₹8,000 is invested at 5% per annum compound interest for 3 years. Find the compound interest.

• Answer: A = 8000 × (1.05)^3 = 8000 × 1.157625 = ₹9,261. CI = 9,261 - 8,000 = ₹1,261.

• Q3: The simple interest on a sum of ₹2,000 for 3 years is ₹360. What is the rate of interest?

• Answer: R = (SI × 100) / (P × T) = (360 × 100) / (2000 × 3) = 36,000 / 6,000 = 6% per annum.

• Q4: At what annual rate of simple interest will a sum double in 10 years?

• Answer: For the sum to double, SI = P. So P = (P × R × 10) / 100. This gives R × 10 = 100, so R = 10% per annum.

Time strategy for a timed aptitude paper

Four habits that separate good quant scores from average ones in placement tests.

Allocate 90 seconds per question and move on. For a 26-question numerical section with 40 minutes, that leaves roughly 4 minutes for review. Flag any question that exceeds your time budget and return to it at the end. Getting stuck on one question costs you two or three others.

Use elimination before calculation. Scan the answer choices first. If you can rule out two options immediately on units or order-of-magnitude grounds, your working time on the remaining two is half the full calculation. This is especially fast for profit% and simple interest questions where two of four options are typically in the wrong range.

Memorise all formula variants, not just the primary form. For profit and loss, you need all three forms (profit%, CP, SP). For simple interest, you need to isolate P, R, and T separately. For time and work, you need the inverse. Placement papers switch which variable is unknown, and having the derived form ready saves 20 to 30 seconds per question.

Practice under timed conditions from the first session. Untimed practice builds formula recall; it doesn’t build the pressure-tested speed placement tests demand. Use a timer from day one. For books that pair timed practice with concept explanations, the aptitude books guide for placement preparation has options across budget and difficulty levels.

The systematic approach in placement tests and beyond

The four-step structure this article uses (given, asked, formula, substitute) is how systematic problem-solving works across domains. For the 26-question TCS NQT Numerical section, that structure converts abstract formulas into reliable answers under a 40-minute timer. The same input-output reasoning applies to building with AI: give a language model structured inputs with clear constraints, and the output becomes far more predictable. TinkerLLM is the ₹299 starting point for that next layer, once the aptitude gate is behind you.