CLAT Quantitative Techniques Questions: Maths Practice, Formulas and Solutions

Quantitative Techniques is the section many CLAT students fear most, partly because they call it "maths" and imagine advanced formulas. The reality is narrower. CLAT Quant usually tests class-10 mathematical operations through short data sets, tables, charts or word scenarios. You need percentages, ratios, averages, mixtures, profit and loss, interest, time-speed-work, mensuration and basic geometry. You do not need calculus, trigonometric depth or school-board proof writing.

This page gives you a practical question guide for CLAT Quant. It includes solved examples, a formula priority sheet, topic links and a plan for students who are weak in maths. Use it with the Quantitative Techniques hub and topic drills. The goal is not to love maths. The goal is to stop losing accessible marks because the section feels uncomfortable.

What Quantitative Techniques questions test

The section usually asks 10 to 14 questions. That looks small, but the rank impact can be large because many students neglect it. A few accurate Quant attempts can separate you from students who leave the section blank. The questions often come in sets. A small table may show sales, expenses, students, marks, population, distances, prices or survey responses. You then answer two to four questions based on the data. This means reading the data correctly is as important as knowing the formula.

The correct mindset is "data first, operation second". Before calculating, ask what the data represents, what unit is used, what the question asks and what comparison is required. Many wrong options are built from common mistakes: using old value instead of new value for percentage change, adding ratios directly, averaging percentages incorrectly, confusing simple and compound interest, or using perimeter when area is asked.

Topic-wise Quant question bank

Formula sheet: what to know first

Solved Quant questions with answers

How to read data sets

Most CLAT Quant sets are lost before calculation begins. Students read a table too quickly, miss the unit, compare the wrong row or ignore that a value is in thousands. Slow down for the first 20 seconds. Read the title, column labels, row labels, units and footnotes if any. Ask whether the table gives absolute numbers, percentages, ratios or growth rates. Then solve. A calm setup makes calculations faster.

1. 1
   Read title and units

   Is the data in rupees, thousands, percentages, students, marks, kilometres or hours? Unit mistakes are common and avoidable.
2. 2
   Identify the exact row and column

   Before writing numbers, point to the required row and column mentally. Many wrong answers use neighbouring data.
3. 3
   Check the base value

   Percentage change, profit and ratio questions depend on the base. Ask "percentage of what?" before calculating.
4. 4
   Estimate before final arithmetic

   A rough estimate catches absurd answers. If sales rose 10 percent from 1000, the answer cannot be 2000.
5. 5
   Keep working clean

   Write short operations clearly. CLAT Quant is not hard enough to require messy heroics.

If you are weak in maths

A weak maths background does not mean you should abandon Quant. It means your practice must be smaller and more regular. Start with percentages and ratios. These two topics appear everywhere. Then move to averages, profit-loss-interest, time-speed-work and mensuration. Do not begin with mixed full sets if every operation feels shaky. Build one topic at a time, then mix them later.

Set a low-friction daily routine: 20 minutes of Quant, five days a week. In each session, solve five to ten questions, review every error and write the formula or reading mistake. After two weeks, take a timed mini-set. After a month, take a Quant sectional. Fear reduces when the section becomes familiar. You do not need to become a maths topper; you need to become reliable on common operations.

Common Quant mistakes

• ✓Wrong base: calculating percentage change from the new value instead of the old value.
• ✓Ratio shortcut error: adding or comparing ratios without converting to actual shares.
• ✓Average trap: averaging averages without considering group sizes.
• ✓Unit miss: ignoring thousands, lakhs, rupees, hours or kilometres.
• ✓Formula memory without data reading: knowing the formula but using the wrong number.
• ✓Skipping too early: abandoning easy arithmetic because the section looks like maths.

Question PDF versus timed practice

A CLAT maths questions PDF is useful for formula revision and offline practice, but the section is scored under time pressure. If you only solve from PDFs slowly, you may overestimate readiness. Use PDFs for concept cleanup. Use timed drills for performance. Use sectionals to test whether you can handle a small data set without freezing. Use full mocks to test whether you can still do arithmetic after reading-heavy sections have tired you.

A good Quant resource should show steps, not just answers. It should explain why the base is old value, why ratio parts matter, why a weighted average is needed, or why a geometry formula applies. If a solution jumps from question to answer without showing the operation, it may not help students who are weak in maths.

A 21-day Quant repair plan

1. 1
   Days 1-4: Percentages

   Use Percentages drills. Practise percentage of a value and percentage change until the base is automatic.
2. 2
   Days 5-8: Ratio and proportion

   Use Ratio & Proportion drills. Convert parts into actual values and compare ratios carefully.
3. 3
   Days 9-12: Averages and mixtures

   Use Averages & Mixtures drills. Focus on total-sum thinking and weighted averages.
4. 4
   Days 13-16: Profit, interest and rates

   Use Profit, Interest & TSW drills. Keep cost price, selling price, principal, rate and time clear.
5. 5
   Days 17-19: Mensuration

   Use Mensuration & Geometry drills. Revise area and perimeter formulas with data reading.
6. 6
   Days 20-21: Timed mixed sets

   Attempt a Quant sectional or mixed mock questions. Review by error type, not only score.

How to decide when to skip Quant questions

Skipping is not failure. It is exam management. The trick is to skip for the right reason. If a set is data-heavy, unclear or calculation-intensive, mark it and move if time is tight. But do not skip every Quant question because of fear. First identify whether the operation is familiar. If it is percentage, ratio, average or profit-loss with clean numbers, attempt it. If it needs long calculation and you have easier marks elsewhere, skip responsibly and return later.

How Quant fits into a full mock

Quant often appears late in a student's preferred order because it feels risky. That can work if you still leave enough mental energy. But if you always reach Quant with five minutes left, you are not giving the section a chance. Try different section orders in mocks. Some students do better by attempting Quant after one reading section, when the brain is still fresh. Others prefer finishing reading-heavy sections first. The right order is the one that gives you stable marks, not the one that sounds popular.

In review, compare attempted Quant questions with skipped Quant questions. Were the skipped ones actually hard, or just intimidating? Were wrong answers caused by weak formulas or rushed arithmetic? Did you leave easy percentage questions because you assumed the whole section would be difficult? These questions will recover marks faster than another generic formula list.

How to make a Quant error sheet

A Quant error sheet should be short and operational. Do not copy every formula from a textbook. Write only the errors that cost you marks. One line might say: "Percentage decrease uses old value as base." Another might say: "Average of two groups needs total sum and total count, not average of averages." Another might say: "In ratio questions, first find total parts." Read this sheet before every Quant practice session. It reminds you how you actually lose marks.

Add one solved mini-example below each rule. If the rule is about percentage change, use a two-line example with numbers. If it is about ratio, write a split-total example. The point is retrieval. In the exam, you will not remember a long chapter; you will remember a familiar mistake and the correction attached to it.

Mental maths that is worth practising

You do not need flashy mental maths tricks, but some fluency helps. Know common fractions as percentages: 1/2 is 50 percent, 1/3 is about 33.33 percent, 1/4 is 25 percent, 1/5 is 20 percent, 1/8 is 12.5 percent and 1/10 is 10 percent. Know quick percentage operations such as 10 percent, 20 percent, 25 percent and 50 percent of common numbers. Practise multiplying and dividing by small integers cleanly. These small skills reduce friction in data sets.

Mental maths should support accuracy, not replace written work. If a calculation is multi-step, write enough to avoid losing the thread. CLAT does not reward showing work, but your brain benefits from clean intermediate steps. Fast and sloppy is worse than slightly slower and correct.

Also practise option checking. If your calculated answer is close to an option but not exact, do not force it. Recheck the base, unit and arithmetic. If the options are far apart, estimation may save time. If the options are close, exact work matters. This judgement develops only when you review both right and wrong Quant attempts.

When reviewing, rewrite one slow solution in fewer steps. The second version should be cleaner, not just shorter. This teaches efficient setup: choose the right base, cancel simple factors, estimate when safe and avoid unnecessary decimal work. Better setup is often the difference between attempting two Quant questions and attempting eight.

Keep a small rough-work discipline in every timed set. One line for data, one line for operation, one line for answer check. This prevents mental arithmetic from becoming invisible guesswork.