CAT Percentages formula sheet, free to download as a 5-page PDF. The topic carries about 6 to 10 marks across Quant and DI, and takes roughly ten minutes to work through, so it earns a slot the night before the exam.

Written for revision, not first learning. For the worked explanations behind each line, the Percentages notes cover the same ground in full.

It Opens With a Classifier, Not a Formula

The first page maps question wording to the rule it actually needs, since that mapping is where most marks in this topic go missing.

  • No figure given anywhere points to assume base 100
  • A change applied on top of an earlier change points to successive change: multiply the factors
  • Price times quantity held fixed points to product constancy
  • "A is x% more or less than B" points to a base flip, since A and B are not measured against the same denominator

The Fraction Table Carries Most of the Sheet

One formulabox lists every clean fraction from a half down to a twenty-fifth. Converting first and multiplying after turns a slow decimal multiplication into one line.

  • 37.5% of 216 becomes 216 times 3/8, which is 81
  • 16.67% is a sixth, 12.5% is an eighth, 8.33% is a twelfth
  • x% of y always equals y% of x, so an awkward direction can be swapped

Change, Reversed Correctly

Going backwards from a changed value, the sheet is explicit that division undoes a multiplier, not subtraction.

  • Increase multiplier is 1 plus x over 100, decrease is 1 minus x over 100
  • After a 20% rise to 600, the original is 600 divided by 1.2, not 600 minus 20% of 600
  • Net of two successive changes is x plus y plus xy over 100, signs included

That net formula is why a 20% rise followed by a 20% fall leaves a 4% loss rather than nothing. The rise sits on the smaller number and the fall on the larger one.

Comparing Two Quantities Without Mixing Up the Base

A is x% more than B does not mean B is x% less than A. The sheet gives both conversions side by side so the direction never has to be re-derived under time pressure.

  • A is 25% more than B means B is 20% less than A, not 25%
  • A rate moving from 5% to 7% is 2 percentage points, but a 40% rise in the rate itself
  • Income equals expenditure plus savings; fixing two pins down the third

Watch Percentage Shortcuts Worked Out

Source: MBA Wallah

How to Revise From It

The final page repeats every line in one table, each checked against a base of 100.

  • Cover the formula column and reproduce it from the quantity name alone
  • Say why the formula holds, not just what it states
  • Re-derive the base-flip fractions rather than memorising two more numbers
  • Time a mixed set: if any question runs past ninety seconds, the base was never fixed

CAT Percentages Formula Sheet FAQs

Ques. Is this formula sheet enough on its own?

Ans. It is built for revision rather than a first read. Each line is compressed to the formula and a one-line reason, so it works best once the topic is already understood. Students meeting percentages for the first time should start with the full notes.

Ques. Why does a 20% rise followed by a 20% fall not cancel out?

Ans. The two changes sit on different bases. The rise applies to the smaller starting number and the fall to the larger one that follows, so the factors multiply out to 0.96, a net loss of 4%.

Ques. Is the fraction table really worth memorising?

Ans. Yes, at least up to a twentieth. It converts most percentage arithmetic into a single division and is the single biggest speed gain available in this topic.

Ques. Can the PDF be downloaded for free?

Ans. Yes. All 5 pages can be read on this page or downloaded at no cost, so it can be printed or kept on a phone for last-minute revision.