Editorially revised on 9 October 2026.
Build a method you can check
Quantitative aptitude practice becomes more useful when you can explain the quantity, unit and relationship before reaching for a shortcut. This guide gives original worked problems on percentages, ratios, averages, profit, work rates, speed, divisibility and data interpretation. They are practice questions created for this article, not previous-year exam questions or a prediction of a particular paper's topic weights.
Start with the current examination notice and syllabus. A recruitment test and a campus aptitude assessment may allow different tools, impose different time limits and use different marking rules. Do not assume that a calculator, a rough sheet or skipping and returning to a question is permitted. For exam-specific preparation, use the actual instructions alongside the exam preparation hub.
The central habit is to preserve the base of a percentage, the order of a ratio and the units of a rate. Memorised facts can help calculation, but a particular range of multiplication tables or squares is not a universal admission requirement. Develop fluency where your own errors and syllabus show a need.
NCERT's Comparing Quantities exemplar unit supports the elementary distinctions between compatible units, ratios, percentages and cost-based profit. It does not establish current recruitment weighting. The problems and solutions below are original, independently calculated illustrations.
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Original problem: a practice book costs ₹800. Its price increases by 10%, and the new price then receives a 10% discount. What is the final price?
The increase is 800 × 10/100 = ₹80, giving ₹880. The discount is applied to ₹880, not ₹800: 880 × 10/100 = ₹88. The final price is ₹792. Compared with the original ₹800, it is ₹8 lower, which is a 1% decrease. Equal percentage increases and decreases do not cancel when their bases differ.
Check: multiply 800 × 1.10 × 0.90 = 792. Both methods agree. This is an arithmetic illustration, not a claim about an actual product's price or available discount.
Another useful distinction is approximation. One sixth equals 0.1666… and therefore 16⅔%. The finite percentage 16.66% equals 0.1666 exactly, which is slightly smaller than one sixth. You may approximate when the question allows it, but do not replace an exact fraction with a rounded decimal and present the result as exact.
Ratios: keep the total and order visible
Original problem: a fictional study group divides 45 worksheets between Group A and Group B in the ratio 2:3. How many does each group receive?
The ratio contains 2 + 3 = 5 equal parts. Each part represents 45/5 = 9 worksheets. A receives 2 × 9 = 18; B receives 3 × 9 = 27. Check the total, 18 + 27 = 45, and the simplified ratio, 18:27 = 2:3.
A common error is treating 2:3 as two thirds of the total for A. Two thirds would describe A relative to B in this ratio, while A's share of the combined total is two fifths. Translate the wording before choosing the denominator. If the question gives only a ratio without a total or another independent condition, the actual quantities may remain undetermined.
Averages: return to the total
Original problem: four practice-session scores have an average of 18. A fifth score is 23. What is the new average?
The first four scores sum to 4 × 18 = 72. The new total is 72 + 23 = 95, across five scores. The new average is 95/5 = 19. It lies between 18 and 23, which is a useful plausibility check. You cannot find it by averaging 18 and 23 directly, because 18 represents four scores while 23 represents one.
When groups have different sizes, account for those sizes. A group of two people averaging 10 and a group of three averaging 20 have a combined total of 20 + 60 = 80 across five people, giving 16. The unweighted average of the two group means, 15, would be wrong for this question.
Profit and discount: distinguish the reference amount
Original problem: an item has a fictional cost price of ₹600 and sells for ₹750. Find the profit and profit percentage on cost.
Profit is 750 − 600 = ₹150. Profit percentage on cost is 150/600 × 100 = 25%. If someone instead calculates 150/750 × 100 = 20%, they have found the profit as a percentage of selling price. That is a different denominator and answers a different question.
Do not automatically treat a marked price as a cost price. If a question provides a marked price and discount but no cost or equivalent relationship, profit may not be determined. Label the quantities before inserting them into a formula. These examples exclude actual taxes, business costs and pricing decisions; they teach the stated arithmetic relationship only.
Work rates: add rates under the stated assumptions
Original problem: A completes one identical task in six hours and B in three hours. Assume constant independent rates, simultaneous work without interference and no setup time. How long do they need together?
A's rate is 1/6 task per hour. B's is 1/3 task per hour. Together the rate is 1/6 + 1/3 = 1/2 task per hour. Time for one task is 1 ÷ 1/2 = two hours. Check the contributions: A completes 2/6 = one third and B completes 2/3 = two thirds, totalling one task.
Adding six and three hours would not model simultaneous work. Also, real teams do not necessarily satisfy these simplified assumptions. Use the model specified by the question; do not turn a textbook rate result into a promise about actual team productivity.
Speed: convert units before multiplying
Original problem: a vehicle moves at a constant 54 kilometres per hour for 40 seconds. Find the distance in metres.
Convert 54 km/h using 1 kilometre = 1,000 metres and 1 hour = 3,600 seconds. The speed is 54 × 1,000/3,600 = 15 metres per second. Distance is 15 × 40 = 600 metres. Leaving the speed in kilometres per hour while multiplying by seconds mixes units and produces an incorrect result.
A constant-speed assumption matters. If a problem supplies changing speeds, stops or segments, calculate the relevant distances and elapsed times instead. For a round trip covering equal distances at 30 and 60 km/h, average speed is not 45 km/h. Using a 60-km leg each way gives two hours out and one hour back: 120/3 = 40 km/h overall.
Last digits: use a shortcut within its limits
Original problem: find the units digit of 7 to the power 23. The units digits of successive positive powers repeat 7, 9, 3, 1. Dividing 23 by four leaves remainder three, so the required digit is the third entry, 3.
This determines one digit, not the whole number. A units-digit check can eliminate choices with impossible endings, but it does not necessarily distinguish choices sharing that ending. State what the shortcut establishes and finish any remaining calculation the question requires.
Data interpretation: separate counts and percentages
Original problem: a fictional practice register lists 24 completed attempts on Monday and 36 on Tuesday. These are attempts, not distinct learners. What percentage of the combined attempts occurred on Tuesday?
Combined attempts are 24 + 36 = 60. Tuesday's share is 36/60 × 100 = 60%. The increase from Monday to Tuesday is a different calculation: (36 − 24)/24 × 100 = 50%. Both results are correct for their respective questions. Neither establishes how many unique people took a test.
Keep a short error log
| Error observed | Next check |
|---|---|
| Wrong percentage base | Name the reference amount before calculating |
| Ratio total confused | Write the combined number of equal parts |
| Groups averaged equally | Recover each group's total and size |
| Units mixed | Convert to compatible units first |
| Shortcut overextended | State the limited result it proves |
Try a new problem after correcting the method. A timed session can reveal where you hesitate, but speed without accurate review can repeat errors. Track attempted, correct and omitted questions separately, using the actual assessment's scoring rules. A practice log is feedback, not a guaranteed selection score.
Short practice check
Try these before reading the answers: 20% of 350; division of 42 in the ratio 1:2; average of 8, 12 and 16; distance covered at 10 m/s for 25 seconds. Answers are 70; 14 and 28; 12; and 250 metres. Check each answer by reconstructing the total or unit relationship.
For further practice, select a relevant mock test and review the actual question explanations. Do not assume the examples here appeared in that test or match its difficulty. The useful improvement is a calculation you can reproduce and check, followed by practice under the real exam's rules.