CLAT 2027 Quantitative Techniques: Topics and 10-Day Plan

Quantitative Techniques is 10 to 14 questions of the 120 in CLAT UG 2027, set in short passages or data sets, and the Consortium’s published syllabus for the previous cycle (CLAT 2025) points candidates to 10th standard mathematics textbooks. That is small enough to learn in ten days. Cover percentages, ratio, averages, profit and loss, interest, time and work, speed, basic geometry and data interpretation, and practise reading numbers from tables quickly.

Why this section is worth ten days

At up to 14 marks it is about one-ninth of the paper. Because the maths is at school level, a few days of focused practice moves most students from fear to a reliable half of the section. Wrong answers cost 0.25, so a careful half beats a rushed whole.

Topics to cover

• Percentages, percentage change, successive changes.
• Ratio, proportion and partnership-type sharing.
• Averages and weighted averages.
• Profit, loss, discount and mark-up.
• Simple and compound interest.
• Time and work, pipes and cisterns.
• Speed, distance and time, including trains.
• Basic algebra and ages.
• Mensuration: area, perimeter, volume of simple shapes.
• Data interpretation: reading tables and graphs, percentage and average from data.
• Number series and simple counting.

The 10-day plan

1. Day 1: Percentages and percentage change.
2. Day 2: Ratio and proportion.
3. Day 3: Averages.
4. Day 4: Profit, loss and discount.
5. Day 5: Simple and compound interest.
6. Day 6: Time and work.
7. Day 7: Speed, distance and time.
8. Day 8: Algebra, ages and mensuration.
9. Day 9: Data interpretation sets, timed.
10. Day 10: A mixed 12-question set in 18 minutes, then review.

Each day: 20 minutes on formulae and examples, 30 minutes on 10 to 15 questions, 10 minutes on an error note. Keep a one-page formula card that you will take into the final revision (see the last 7 days plan).

Ten original practice questions with worked answers

All questions below were written for this guide, and every answer has been checked.

Q1 (profit and discount). A shopkeeper marks an article 25 percent above its cost of Rs 800 and gives a discount of 10 percent on the marked price. What is the profit percentage?

Answer: 12.5 percent. Marked price is 800 times 1.25, which is Rs 1,000. After a 10 percent discount the selling price is Rs 900. Profit is 900 minus 800, which is Rs 100, and 100 divided by 800 is 12.5 percent.

Q2 (ratio). Rs 7,200 is divided among A, B and C in the ratio 2 : 3 : 4. What does C receive?

Answer: Rs 3,200. The parts add to 9, so one part is 7,200 divided by 9, which is Rs 800. C gets 4 times 800, which is Rs 3,200. (A gets 1,600 and B gets 2,400; the three add to 7,200.)

Q3 (averages). The average of five numbers is 24. When one number is removed, the average of the remaining four is 22. What number was removed?

Answer: 32. The total of five is 5 times 24, which is 120. The total of four is 4 times 22, which is 88. The removed number is 120 minus 88, which is 32.

Q4 (time and work). A can finish a job in 12 days and B in 18 days. Working together, in how many days do they finish it?

Answer: 7.2 days. In one day A does 1/12 and B does 1/18. Together that is 3/36 plus 2/36, which is 5/36. So the job takes 36/5, which is 7.2 days.

Q5 (speed). A train 150 metres long runs at 54 km/h. How long does it take to pass a pole?

Answer: 10 seconds. 54 km/h is 54 times 1000 divided by 3600, which is 15 metres per second. Passing a pole means covering its own length, so time is 150 divided by 15, which is 10 seconds.

Q6 (simple interest). What is the simple interest on Rs 5,000 at 8 percent per year for 3 years?

Answer: Rs 1,200. Interest is 5,000 times 8 times 3 divided by 100, which is Rs 1,200.

Q7 (compound interest). What is the compound interest on Rs 5,000 at 10 percent per year, compounded annually, for 2 years?

Answer: Rs 1,050. After one year the amount is 5,500. After two years it is 5,500 times 1.1, which is 6,050. Compound interest is 6,050 minus 5,000, which is Rs 1,050.

Q8 (successive change). A town has a population of 40,000. It rises by 10 percent in one year and then falls by 10 percent in the next. What is the population at the end?

Answer: 39,600. After the rise the population is 44,000. A 10 percent fall of 44,000 is 4,400, so it becomes 39,600. Note it is not back at 40,000, because the second change applies to a larger number (the net change is minus 1 percent).

Q9 (data interpretation). A bookshop sold 120 books in January, 150 in February and 180 in March. (a) By what percentage did sales rise from February to March? (b) What was the average monthly sale?

Answer: (a) 20 percent, (b) 150 books. The rise from February to March is 30, and 30 divided by 150 is 20 percent. The total is 120 plus 150 plus 180, which is 450, and 450 divided by 3 is 150.

Q10 (mensuration). A rectangle measures 12 m by 9 m. Its length is increased by 25 percent and its breadth is decreased by 20 percent. What happens to its area?

Answer: it stays at 108 square metres. The original area is 12 times 9, which is 108. The new length is 15 and the new breadth is 7.2, and 15 times 7.2 is 108. The same result follows from 1.25 times 0.8, which equals 1.

How to practise

• First attempt untimed, to learn the method. From day 6 onward, set a timer at about 90 seconds a question.
• Estimate before calculating. If an answer option is far off your estimate, recheck.
• Learn squares to 25 and cubes to 10, and fraction-to-percentage equivalents (1/8 is 12.5 percent).
• For data sets, read the question first, then find only the numbers you need.

Using the section in the exam

Do not leave this section for the last 3 minutes. Many candidates plan about 18 minutes for it (see time management by section) and answer the easy ones first. If maths is weak, aim for the straightforward half. The wrong-answer penalty is explained in the negative marking guide.

For full-paper practice, Lexfolio’s CLAT 2027 mock pack states that its quantitative techniques sections use caselets with tables; check the product page for details.