Key facts

  • Percentage means per hundred; a fraction or decimal becomes a percentage by multiplying by 100.
  • Successive percentage change uses the revised base after every step, so a 10 per cent increase followed by a 20 per cent increase gives 32 per cent, n...
  • Reverse-base percentage questions change the denominator; if X is 20 per cent more than Y, then Y is 16.67 per cent less than X.

Key Points at a Glance

  1. 1

    A ratio such as a:b is the same comparison as a/b, and a proportion a:b::c:d is correct only when ad = bc.

  2. 2

    Direct proportion means both quantities move in the same ratio, while inverse proportion means one rises as the other falls in a controlled product relation.

  3. 3

    Percentage means per hundred; a fraction or decimal becomes a percentage by multiplying by 100.

  4. 4

    Successive percentage change uses the revised base after every step, so a 10 per cent increase followed by a 20 per cent increase gives 32 per cent, not 30 per cent.

  5. 5

    Reverse-base percentage questions change the denominator; if X is 20 per cent more than Y, then Y is 16.67 per cent less than X.

  6. 6

    Profit and loss percentages are measured on cost price, while discount percentage is measured on marked price.

  7. 7

    In partnership questions, profit share is proportional to investment multiplied by time, not investment alone.

  8. 8

    Average and mixture questions depend on weighted values; the mean must lie between the two component values in a two-item mixture.

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Ratio and Proportion Basics

Ratio compares two quantities on a relative scale. The form a:b means a divided by b, so it does not by itself state the actual size of either quantity. This is useful in objective questions because many stems give shares, parts, or comparative values without giving full totals. If two ratios are equivalent, they reduce to the same simplest form. For example, 3:5 and 9:15 are equivalent because both simplify to 3:5.

Proportion joins two ratios. The statement a:b::c:d means a/b = c/d. The fastest test is cross-multiplication: a proportion is true when ad = bc. This removes long wording and turns the question into a short arithmetic check. For example, 3:5 and 9:15 satisfy 3 x 15 = 5 x 9. In RSSB objective questions, this method is usually enough to eliminate wrong options quickly.

Exam use: reduce the ratio first, then use cross-multiplication only when the options are not already obvious.

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