If $a$ is directly proportional to $b$ and $b$ is inversely proportional to $c .$ Then what is the proportionality between $a$ and $c$ ?

Direct

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Inverse

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Sometimes direct sometimes inverse

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Can't be determined

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Solution

The correct option is B Inverse
$a \propto b \Rightarrow a = k_{1} b; k_{1}$ is a constant

$b \propto \frac{1}{c} \Rightarrow b = \frac{k_{2}}{c}; k_{2}$ is a constant

$\Rightarrow a = \frac{k_{1} k_{2}}{c} = \frac{k_{3}}{c}; k_{3} = k_{1} k_{2}$ is another constant

$\Rightarrow a \propto \frac{1}{c}$

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If a is directly proportional to b and b is inversely proportional to c. Then what is the proportionality between a and c?

The correct option is B Inversea∝b⇒a=k1b;k1 is a constantb∝1c⇒b=k2c;k2 is a constant⇒a=k1k2c=k3c;k3=k1k2 is another constant⇒a∝1c

If $a$ is directly proportional to $b$ and $b$ is inversely proportional to $c .$ Then what is the proportionality between $a$ and $c$ ?