Key facts

  • Ratio compares two quantities in the same unit; 3:5 means 3 parts out of a total of 8 parts when the whole is split in that relation.
  • Proportion states equality of two ratios; a:b::c:d is true when a x d equals b x c after cross-multiplication.
  • Direct proportion means both quantities move in the same ratio, while inverse proportion means one rises as the other falls in a linked way.
  • Profit and loss percentage are always calculated on cost price, not on marked price or selling price.
  • Discount is calculated on marked price; selling price equals marked price minus discount.

Key Points at a Glance

  1. 1

    Ratio compares two quantities in the same unit; 3:5 means 3 parts out of a total of 8 parts when the whole is split in that relation.

  2. 2

    Proportion states equality of two ratios; a:b::c:d is true when a x d equals b x c after cross-multiplication.

  3. 3

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

  4. 4

    Profit and loss percentage are always calculated on cost price, not on marked price or selling price.

  5. 5

    Discount is calculated on marked price; selling price equals marked price minus discount.

  6. 6

    Successive discounts do not simply add; a 20 percent discount followed by a 10 percent discount gives a 28 percent net discount.

  7. 7

    Partnership profit is divided according to investment x time, so capital alone is not enough when partners invest for different durations.

  8. 8

    Practice questions in this chapter should be solved by fixing the base first: total parts, cost price, marked price, or investment-time value.

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Ratio and proportion

Ratio is a compact way to compare quantities. If two students share Rs 800 in the ratio 3:5, the total number of parts is 8. One part is Rs 100, so the shares are Rs 300 and Rs 500. The ratio does not by itself give the absolute value; it gives the relation. That is why the same ratio 3:5 can describe Rs 300 and Rs 500, 30 boys and 50 girls, or 12 kg and 20 kg after simplification.

Proportion goes one step further. It says that two ratios are equal. In a:b::c:d, the test is a x d = b x c. For example, 4:7 and 20:35 are proportional because both reduce to 4:7 and because 4 x 35 equals 7 x 20. At CET Senior Secondary level, this cross-multiplication test is usually faster than long verbal reasoning. Keep units common before comparing; 2 kg : 500 g is not 2:500 until 2 kg is converted to 2000 g.

Remember: simplify ratios only after all quantities are in the same unit.

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