A numerical ability plan for AFCAT

The official AFCAT notification sets Numerical Ability at matriculation (Class 10) level. That is good news: nothing in it is new to a graduate. The difficulty is time. The whole paper gives you about 72 seconds a question, and the maths questions are the ones most likely to overrun.

For candidates from commerce or arts backgrounds, maths often feels like the weak section. It does not have to be. Arithmetic is a small set of ideas that repeat, and each can be learnt with a few methods and steady practice. This guide gives you the topic list, the order to learn it in, a six-week plan, and the speed methods that save the most time.

What the section covers

The 01/2026 notification lists these topics under Numerical Ability:

Most of it is arithmetic. The newer areas (probability, statistics, mensuration, and heights and distances) need a little Class 10 geometry and trigonometry, but only the basics. Older guides that describe AFCAT maths as "pure arithmetic" leave these out, so don't let them catch you unprepared.

Why percentage comes first

Percentage runs through the whole section. Profit is a percentage of cost price. Interest is a percentage of principal. Discount, population growth, marks and elections are all percentage questions in disguise. Even ratio is closely related: a ratio of 3 : 5 means the first quantity is 3/8, or 37.5%, of the total.

So learn fractions and percentage first, until switching between 3/8, 0.375 and 37.5% is automatic. Half the section becomes easier after that. Our percentage guide covers the methods.

A six-week plan

If you have less time, merge weeks 1 and 2 and weeks 3 and 4. Do not drop week 5: those topics are in the syllabus.

A daily routine (45 minutes)

1. 10 minutes: revise the formulas and methods of one topic, from your own sheet.
2. 25 minutes: solve 15–20 questions on it, with a timer running.
3. 10 minutes: check every wrong answer, find the step that went wrong, and write the correct method in your error log.

Twice a week, replace the topic set with 20 mixed questions from everything you have covered so far. Mixed sets train the skill the exam actually tests: recognising the question type quickly.

Speed methods that actually save time

Learn the fraction–percentage pairs. 12.5% is 1/8, 16⅔% is 1/6, 37.5% is 3/8, 62.5% is 5/8, 83⅓% is 5/6. Why it works: finding 37.5% of 640 by decimals needs a multiplication with a decimal point. As a fraction, it is 640 ÷ 8 × 3 = 240, which you can do in your head.

Use the LCM as the total. In time and work and pipes questions, call the whole job the LCM of the given times. Why it works: every rate becomes a whole number of units, so you add whole numbers instead of fractions.

Use multipliers for changes. An increase of 20% is × 1.2; a fall of 25% is × 0.75. Why it works: successive changes then become one multiplication, and you cannot make the classic mistake of adding percentages.

Check the options first. If the options are far apart, round the numbers and estimate. If only one option is divisible by 9, or only one ends in 5, you may not need the full calculation.

Know the square pattern for area. If every length changes by a factor k, area changes by k². Why it works: area is length × length, so the factor appears twice.

Worked examples

Example 1 (percentage). The price of sugar rises by 25%. By what percentage must a family cut its consumption so that its spending stays the same?

• New price = 1.25 × old. Consumption must become 1 ÷ 1.25 = 0.8 of the old.
• Cut = 20%. Shortcut: r ÷ (100 + r) × 100 = 25 ÷ 125 × 100 = 20%.

Example 2 (time and work). A can finish a job in 12 days and B in 18 days. How long do they take together?

• LCM of 12 and 18 is 36. Call the job 36 units.
• A does 3 units a day and B does 2, so together 5 a day.
• Time = 36 ÷ 5 = 7.2 days, which options usually write as 7⅕ days.

Example 3 (speed). A train 150 m long passes a signal pole in 10 seconds. What is its speed in km/h?

• To pass a pole, the train covers its own length: 150 m in 10 s = 15 m/s.
• Convert: 15 × 18/5 = 54 km/h.

Example 4 (mensuration). The radius of a circle is increased by 10%. By what percentage does its area increase?

• Area depends on r², so the factor is 1.1² = 1.21.
• Area increases by 21%, whatever the original radius.

Example 5 (probability). Two fair dice are thrown. What is the probability that the sum is 8?

• Total outcomes = 6 × 6 = 36.
• Sum 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), which is 5 outcomes.
• Probability = 5/36.

Example 6 (heights and distances). From a point 20 m from the foot of a tower, the angle of elevation of its top is 60°. How tall is the tower?

• tan 60° = height ÷ distance, and tan 60° = √3.
• Height = 20√3 ≈ 20 × 1.732 = 34.64 m.

Practice set

1. Find 37.5% of 640.
2. Find the simple interest on ₹5,000 at 8% a year for 3 years.
3. The average of five numbers is 24. When one number is removed, the average of the rest is 22. What number was removed?
4. A car covers 180 km in 3 hours 45 minutes. What is its average speed?
5. Divide ₹2,100 in the ratio 2 : 5.
6. A bag has 4 red and 6 blue balls. One ball is drawn at random. What is the probability that it is red?
7. Find the median of 12, 5, 9, 15, 7 and 10.
8. Find the compound interest on ₹10,000 at 10% a year for 2 years, compounded annually.

Answers:

1. 240. 37.5% = 3/8, and 640 ÷ 8 × 3 = 240.
2. ₹1,200. 5,000 × 8 × 3 ÷ 100 = 1,200.
3. 32. Total of five = 5 × 24 = 120; total of four = 4 × 22 = 88; removed = 120 − 88 = 32.
4. 48 km/h. 3 h 45 min = 3.75 h, and 180 ÷ 3.75 = 48.
5. ₹600 and ₹1,500. 7 parts = 2,100, so one part = 300.
6. 2/5. 4 favourable out of 10.
7. 9.5. In order: 5, 7, 9, 10, 12, 15. With six values, the median is the average of the middle two: (9 + 10) ÷ 2 = 9.5.
8. ₹2,100. Amount = 10,000 × 1.1 × 1.1 = 12,100, so interest = 2,100.

Common mistakes

• Adding successive percentages. A 10% rise then a 10% fall is a 1% fall, not zero.
• Forgetting to convert units. Minutes to hours, m/s to km/h, and centimetres to metres in area questions.
• Skipping the newer topics. Probability, statistics and heights and distances are short to learn. Leaving them out gives away easy marks.
• Chasing one hard question. If a question passes 90 seconds, mark it and move on. See our guide to speed in numerical ability.

Your checklist

• I have a one-page formula sheet, with a small example beside each formula.
• I know squares to 30, cubes to 15 and the common fraction–percentage pairs.
• I have covered every topic in the official list, including probability, statistics and mensuration.
• I solve 20 mixed questions twice a week under time.
• My error log is up to date, and I read it before every mock.