Class 8 · Chapter 13

Direct and Inverse Proportions

Direct proportion ( $y=kx$ ) and inverse proportion ( $xy=k$ ); word problems.

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Detailed theory

y \propto x

means

y = kx

for constant

k

. As

x

increases,

y

increases at the same rate. E.g. cost of a fixed-price commodity.

Key concepts & formulas

Direct:

\dfrac{x_1}{y_1} = \dfrac{x_2}{y_2}

(both increase together).

Inverse:

x_1 y_1 = x_2 y_2

(one increases as the other decreases).

Cost of items and quantity: direct.

Number of workers and time to finish: inverse.

Speed and time (for fixed distance): inverse.