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Professional and Subprofessional · Civil Service Exam

Percentages and ratios

Almost every percentage question on the exam is one of three forms: what is P% of N, N is P% of what, and N is what percent of M.

Recognising which of the three you are looking at is most of the work, because the arithmetic is the same equation rearranged. Write it as a sentence with a blank - `___ is 15% of 240` - and the multiplication or division follows without further thought.

The distractors on these items are rarely random. They are usually the answers to the other two forms, which is why a rushed reader who solves the wrong equation still finds their result on the list. Read the sentence twice before you compute.

Ratios divide a total into parts. Add the parts of the ratio to get the number of shares, divide the total by that, then multiply. The commonest error is treating a ratio of parts as though it were a fraction of the whole.

Worked examples

Try these, then read why.

Written for this platform and generated from the same bank the practice sets draw on. Every wrong option is explained, because knowing why a distractor was tempting is most of the learning.

What is 20% of 615?

  1. A492
  2. B615
  3. C1,230
  4. D123 (correct)

Three percentage questions share one relationship: part = whole x rate. 20% means 20/100, so 20% of 615 is 615 x 20/100 = 123. Decide which of the three quantities is missing before you calculate; most errors here are answers to a different one of the three questions.

  • A This is the remaining part rather than the part the question asks for.
  • B This is the number that 123 is 20% of, which answers a different question.
  • C The decimal point has been moved one place; check the size of the result against the original number.

14 is 12.5% of what number?

  1. A14
  2. B98
  3. C1,120
  4. D112 (correct)

Three percentage questions share one relationship: part = whole x rate. If 14 is 12.5% of a number, then the number is 14 x 100/12.5 = 112. Decide which of the three quantities is missing before you calculate; most errors here are answers to a different one of the three questions.

  • A This is 12.5% of 112, which answers a different question.
  • B This is the remaining part rather than the part the question asks for.
  • C The decimal point has been moved one place; check the size of the result against the original number.

For every 12 sacks of rice distributed, a barangay receives 8. At the same ratio, how many does the barangay receive when 588 are distributed?

  1. A196
  2. B392 (correct)
  3. C400
  4. D882

The ratio is 8 to 12, so find how many times 12 fits into 588: it fits 49 times. Scale the other side by the same figure: 8 x 49 = 392. Name which side of the ratio the question asks for before you multiply; the other side is always on offer.

  • A This is what is left after the barangay's share, not the share itself.
  • C This adds the ratio's first figure to the answer instead of scaling by it.
  • D This uses the ratio upside down, which gives more than the whole quantity.

Practise this properly.

Three examples show you the format. Finding out whether percentages and ratios is actually costing you marks takes a measured set, which is what the free diagnostic is for.

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