Percentages
Percentages underpin half of the quantitative section — profit and loss, interest, data interpretation and ratio questions are all percentage questions wearing a different hat. Getting fluent here lifts your score across topics, not just this one.
Updated 19 September 2026 · Appears in almost every campus aptitude paper, often 3-5 questions.
How to think about percentages
What a percentage actually is
A percentage is a fraction with 100 fixed as the denominator. "35%" is exactly 35/100. Every percentage question becomes easier the moment you rewrite it as a fraction — 25% is 1/4, 12.5% is 1/8, 16.66% is 1/6. Memorising those fraction equivalents up to 1/12 is the single highest-return thing you can do for speed.
Why successive changes are not additive
A 20% rise followed by a 20% fall does not return you to where you started. The second change applies to the new, larger base. This trips up more candidates than any other percentage idea, and test setters know it — expect at least one question built on exactly this trap.
The "more than / less than" asymmetry
If A is 25% more than B, B is not 25% less than A. The reference point changed. A is 125 when B is 100, so B is 25/125 = 20% less than A. Read carefully which quantity the question is comparing against.
Formulas and shortcuts
- Basic percentage
x% of y = (x / 100) × y - Percentage change
Change % = ((New − Old) / Old) × 100Always divide by the ORIGINAL value, not the new one.
- Successive change
Net % = a + b + (ab / 100)Use a negative sign for a decrease. Works for two changes in a row.
- A is x% more than B → B is less than A by
(100x) / (100 + x) % - A is x% less than B → B is more than A by
(100x) / (100 − x) % - Price rise, expenditure fixed
Reduce consumption by (100x) / (100 + x) %Same formula as above — the "price up, consumption down" question is the asymmetry question in disguise.
Solved examples
Q1. The price of rice rises by 25%. By what percentage must a family cut consumption so that its spending on rice does not change?
- Expenditure = Price × Consumption. For expenditure to stay fixed, consumption must fall in the same proportion that price rose.
- Use the reduction formula: (100 × 25) / (100 + 25)
- = 2500 / 125
Answer: 20% reduction
Sanity check with numbers: price 100 → 125, consumption 100 → 80. Spend before = 10,000. After = 125 × 80 = 10,000. Unchanged.
Q2. A number is increased by 20% and the result is then decreased by 20%. What is the net change?
- Do not add +20 and −20 to get zero — the decrease applies to the larger number.
- Net % = a + b + (ab / 100), with a = +20 and b = −20
- = 20 − 20 + ((20 × −20) / 100)
- = 0 − 4
Answer: A net decrease of 4%
Check: 100 → 120 → 120 × 0.8 = 96. That is 4 less than 100.
Q3. A student scores 35% and fails by 40 marks. Another scores 45% and gets 20 marks more than the pass mark. Find the total marks in the exam.
- Let the total be T. The pass mark can be written two ways from the two students.
- From student 1: pass mark = 0.35T + 40
- From student 2: pass mark = 0.45T − 20
- Set them equal: 0.35T + 40 = 0.45T − 20
- 60 = 0.10T
- T = 600
Answer: Total marks = 600 (and the pass mark is 250)
Check: 35% of 600 = 210, which is 40 short of 250. 45% of 600 = 270, which is 20 above 250.
Practice questions with answers
1. What is 40% of 250?
Answer: B. 100 — (40 / 100) × 250 = 100. Faster: 40% = 2/5, and 2/5 of 250 = 100.
2. If 15% of a number is 45, what is the number?
Answer: C. 300 — 0.15x = 45 → x = 45 / 0.15 = 300.
3. A salary rises from ₹25,000 to ₹30,000. What is the percentage increase?
Answer: B. 20% — Increase = 5,000. Divide by the ORIGINAL: 5000 / 25000 = 0.20 = 20%.
4. Successive discounts of 20% and 10% are equivalent to a single discount of:
Answer: B. 28% — Net = a + b + ab/100 with a = −20, b = −10 → −20 − 10 + (200/100) = −28. A single 28% discount.
5. If the price of a commodity falls by 20%, by how much can consumption rise so spending stays the same?
Answer: C. 25% — (100 × 20) / (100 − 20) = 2000 / 80 = 25%.
6. In a class, 60% of students passed and 240 failed. How many students are there in total?
Answer: C. 600 — Failures are 40% of the total. 0.40T = 240 → T = 600.
7. Two numbers are respectively 20% and 50% more than a third number. The first as a percentage of the second is:
Answer: B. 80% — Let the third be 100. First = 120, second = 150. (120 / 150) × 100 = 80%.
8. A's income is 25% more than B's. By what percent is B's income less than A's?
Answer: B. 20% — (100 × 25) / (100 + 25) = 2500 / 125 = 20%. Not 25% — the comparison base changed.
Where marks get lost
- Dividing by the new value instead of the original when computing percentage change.
- Adding successive percentages (+20% then −20% is not 0%, it is −4%).
- Assuming "A is x% more than B" implies "B is x% less than A".
- Losing time on arithmetic you could do with a fraction — learn 1/8 = 12.5%, 1/6 = 16.66%, 1/3 = 33.33%.
Reading is not practising.
Run a timed set on percentages and see which step you actually lose time on. Free, no card needed.
Start a timed set