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Inverse Proportionality

A α B such as...

Question

$A α B$ such as $\frac{A}{B} = 5$ and $P α \frac{1}{Q}$
such as $P \times Q = 36$ . Match the values accordingly.

A

P_{1} = 8

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B

A_{1} = 36.2

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C

P_{2} = 20

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D

A_{2} = 23.9

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Solution

As constant of proportionality is given for A and B which are in direct proportion, we know
$\frac{A_{1}}{B_{1}} = \frac{A_{2}}{B_{2}} = \frac{A}{B} = 5$
$\frac{A_{1}}{7.24} = 5$ and $\frac{A_{2}}{4.78} = 5$
hence,
$A_{1} = 5 \times 7.24 = 36.2$ and $A_{2} = 5 \times 4.78 = 23.9$

Similarly,
P and Q are in inverse proportion having constant of proportionality 36.
$P_{1} \times Q_{1} = P_{2} \times Q_{2} = P \times Q = 36$

$P_{1} = \frac{36}{4.5}$ and $P_{2} = \frac{36}{1.8}$
$P_{1} = 8$ and $P_{2} = 20$

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