Common numerical ability mistakes in AFCAT, and how to stop making them

Look back at the maths questions you got wrong in your last mock. Very few will be questions you had no idea how to solve. Most will be questions you knew how to do and still got wrong: a percentage taken on the wrong base, a speed in km/h mixed with metres, a question that asked for something slightly different from what you found.

In AFCAT these errors cost more than a blank. Each wrong answer takes away 1 mark, and the 3 you would have earned are lost as well. So a careless error is a 4-mark swing compared with a correct answer. The good news is that careless errors repeat, and repeated errors can be fixed.

1. Taking a percentage on the wrong base

The trap. "A is 25% more than B, so B is 25% less than A."

Why it is wrong. A percentage is always "of" something. The 25% is of B. When you compare the other way, the base changes to A.

Worked. Let B = 100, so A = 125. B is 25 less than A, and 25 out of 125 is 20%. The general rule: if A is r% more than B, then B is r/(100 + r) × 100 % less than A.

2. Profit on selling price, and discount on cost price

The trap. Treating profit as a percentage of the selling price.

The fix. Profit and loss percentages are on the cost price unless the question says otherwise. Discount is on the marked price.

Worked. An article sells for ₹660 at a 10% profit. Find the cost price. The wrong route is 10% of 660 = 66, giving ₹594. The right route: SP = 1.1 × CP, so CP = 660 ÷ 1.1 = ₹600. Check: 10% of 600 is 60, and 600 + 60 = 660.

3. Averaging speeds directly

The trap. A car goes somewhere at 40 km/h and returns at 60 km/h, so the average is 50 km/h.

Why it is wrong. Average speed is total distance ÷ total time. The car spends longer at the slower speed, so the average is pulled below 50.

Worked. Take the distance as 120 km each way, since 120 is the LCM of 40 and 60. The trip out takes 3 hours and the return takes 2. Total 240 km in 5 hours = 48 km/h. For equal distances the formula is 2ab/(a + b) = 2 × 40 × 60 ÷ 100 = 48.

4. Mixed units

The trap. Using a speed in km/h with a length in metres, or a rate per year with a time in months.

Worked. A train 150 m long runs at 72 km/h. How long does it take to pass a pole? Convert first: 72 × 5/18 = 20 m/s. Time = 150 ÷ 20 = 7.5 seconds. Dividing 150 by 72 gives nonsense.

5. Order of operations

The trap. 48 ÷ 6 × 2 = 48 ÷ 12 = 4.

The fix. Division and multiplication have equal priority and are done left to right. So 48 ÷ 6 = 8, then 8 × 2 = 16. The same applies to addition and subtraction: 20 − 5 + 3 = 18, not 12.

6. Adding successive percentage changes

The trap. A price rises 20% and then falls 20%, so it is back where it started.

Worked. 100 → 120 → 120 − 24 = 96. The net change is −4%, because the fall is 20% of a bigger number. The formula for successive changes a and b is a + b + ab/100: 20 − 20 + (20 × −20)/100 = −4.

7. Using simple interest for compound interest

The trap. Working out CI as P × R × T ÷ 100.

Worked. ₹8,000 at 5% a year compound for 2 years. Year 1 interest = 400. Year 2 interest = 5% of 8,400 = 420. Total CI = ₹820, not ₹800. The extra ₹20 is interest on the first year's interest.

8. Confusing a ratio with a fraction of the total

The trap. A : B = 3 : 5 and the total is 64, so A = 3/5 × 64.

The fix. A ratio of 3 : 5 means 8 parts in all. A = 3/8 × 64 = 24 and B = 40. "A is 3/5 of B" is a different statement from "A is 3/5 of the total".

9. Answering a different question

The trap. You find the time B works alone, but the question asked for the total time. You find the cost price, but it asked for the marked price.

The fix. Before choosing an option, reread the last line of the question. Underline or note words like "remaining", "total", "less than", "not", "approximately" and "difference".

10. Rounding too early, and staying too long

Rounding at every step lets errors pile up. Round once, at the end, and only if the options are far apart. Our guide to approximation explains when it is safe.

The last mistake is about time. Spending three minutes on one question costs you two or three easier ones later. If a question is not moving after about 90 seconds, mark it and come back.

The mistakes at a glance

Why this matters under negative marking

With four options, +3 and −1, a blind guess has an expected value of zero: (1 × 3 − 3 × 1) ÷ 4 = 0. So guessing is not what hurts most candidates. Confident wrong answers are. If you are sure of an answer and you are wrong, a careless error cost you. Fixing these errors is the cheapest way to raise your score, because you already know the maths. Our guide to negative marking covers when a guess is worth taking.

Practice: spot the error

Each statement contains a common mistake. Find the correct answer.

1. "Price rose by 25%. To get back to the original price, it must fall by 25%."
2. "A cyclist rides out at 30 km/h and back at 60 km/h. Average speed = 45 km/h."
3. "SP = ₹660 at 10% profit, so CP = ₹594."
4. "36 km/h = 36 × 18/5 = 129.6 m/s."
5. "CI on ₹10,000 at 10% for 2 years = ₹2,000."
6. "60 ÷ 5 × 3 − 4 = 0."
7. "A salary is cut by 10% and then raised by 10%, so there is no change."
8. "A : B = 2 : 3 and B : C = 4 : 5, so A : B : C = 2 : 3 : 5."

Answers:

1. 20%. 100 → 125. Falling 25 on 125 is 20%.
2. 40 km/h. 2 × 30 × 60 ÷ 90 = 40.
3. ₹600. 660 ÷ 1.1.
4. 10 m/s. Multiply by 5/18, not 18/5.
5. ₹2,100. 10,000 × 1.21 = 12,100, so the interest is 2,100.
6. 32. 60 ÷ 5 = 12, 12 × 3 = 36, 36 − 4 = 32.
7. A 1% fall. 100 → 90 → 99.
8. 8 : 12 : 15. Make B the same in both: 2 : 3 = 8 : 12 and 4 : 5 = 12 : 15.

What to do next: keep an error log

• After every practice set or mock, write each wrong answer in a notebook: the question, your answer, the correct method, and the type of mistake from the table above.
• Every Sunday, count the mistakes by type. Most candidates find that three or four types account for most of their errors.
• For your top two types, add a fixed check to your routine, such as "reread the last line" or "convert units first".
• Revise the formulas behind these traps with the numerical revision sheet.