Percentage is the base of arithmetic. Profit and loss, discount, interest, ratio, data interpretation and even time and work all use it. If you master percentage, a large part of the quant section becomes quicker. This page gives you the formulas, the shortcuts, worked examples and practice questions.

What percentage means

A percentage is a fraction with 100 as the denominator. 25% means 25 out of 100, which is 25/100 or 1/4. To find what percent one number is of another, divide the part by the whole and multiply by 100.

Core formulas

  • Percentage = (Value / Total) × 100
  • x% of y = (x × y) / 100. Note that x% of y equals y% of x, so 8% of 50 is the same as 50% of 8 = 4.
  • Increase by r%: New value = Original × (100 + r)/100.
  • Decrease by r%: New value = Original × (100 − r)/100.
  • Percentage change = (Change / Original) × 100. The original value is always the base.

Fraction and percentage equivalents

Learning these by heart saves seconds on every question, which adds up over a full paper.

  • 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%
  • 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%
  • 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%

For example, to find 16.67% of 480, you do not need a calculator. 16.67% is 1/6, and 480 / 6 = 80.

Successive percentage change

When a value changes by a% and then by b%, the net change is a + b + (a × b)/100. Use a plus sign for an increase and a minus sign for a decrease.

Example 1. A number is increased by 20% and then decreased by 20%. Net change = 20 − 20 + (20 × −20)/100 = −4%. Check: 100 becomes 120, then 96, so the net change is −4%.

Example 2. A salary of ₹40,000 is increased by 15% and then reduced by 10%. Net change = 15 − 10 − 1.5 = +3.5%. New salary = 40,000 × 1.035 = ₹41,400.

If A is more than B, B is how much less than A?

If A is r% more than B, then B is r/(100 + r) × 100 % less than A. If A is r% less than B, then B is r/(100 − r) × 100 % more than A.

Example 3. A's income is 25% more than B's. B's income is 25/125 × 100 = 20% less than A's.

Example 4. A's income is 20% less than B's. B's income is more than A's by 20/80 × 100 = 25%.

Price and consumption

If the price of an item rises by r%, a person must cut consumption by r/(100 + r) × 100 % to keep expenditure the same. If the price falls by r%, consumption can rise by r/(100 − r) × 100 %.

Example 5. The price of sugar rises by 25%. To keep spending the same, the household must reduce consumption by 25/125 × 100 = 20%.

Elections and pass marks

Example 6. In an election between two candidates, the winner gets 55% of the votes and wins by 3,000 votes. If every vote is valid, the winner's lead is 55% − 45% = 10% of the total votes. So 10% = 3,000 and the total is 30,000 votes.

Example 7. A student needs 40% to pass. He scores 120 marks and fails by 30 marks. The pass mark is 150, and 150 is 40% of the maximum, so the maximum marks = 150 / 0.40 = 375.

Population growth and decrease

If a population P grows at r% per year, after n years it is P × (1 + r/100)n. If it decreases at r% per year, use (1 − r/100). The same idea applies to the value of a machine that depreciates each year.

Common mistakes to avoid

  • Using the wrong base. In "A is 25% more than B", the base is B. In "B is how much percent less than A", the base is A.
  • Adding successive percentages directly. A 10% rise followed by a 10% rise is 21%, not 20%.
  • Forgetting the effect of order. A rise of 20% then a fall of 20% does not bring you back to the start.
  • Rounding too early. Keep fractions like 1/6 until the last step.

Practice questions

  1. What is 12.5% of 640?
  2. 650 is what percent of 2,500?
  3. A price rises by 10% and then by another 10%. What is the net rise?
  4. If 30% of a number is 90, what is the number?
  5. A's income is 20% less than B's. By what percent is B's income more than A's?

Answers: 1) 80, 2) 26%, 3) 21%, 4) 300, 5) 25%.

How to practise

Do 15 to 20 percentage questions a day for a week, and time yourself on every set. Once the fractions are memorised, try the same questions in our mock tests, and see the SSC CGL syllabus to see where percentage fits among other arithmetic topics.

GovAspirant is a private education portal and is not affiliated with any government body. Exam rules change, so always confirm dates, pattern and eligibility in the official notification.