Question

If $a$ is directly proportional to $b$ and $b$ is inversely proportional to $c$. Then what is the proportionality between $a$ and $c$ ?
(a) Direct
(b) Inverse
 (c) Sometimes direct sometimes inverse
 (d) Can’t be determined

Answer 1

Hint: In this question take ${k_1},{k_2},{k_3}$ as constant where ${k_3} = {k_1}{k_2}$ and substitute the value of $b$ in $a$ to find the proportionality between $a$ and $c$.

Complete step-by-step solution -
According to the question $a$ is directly proportional to $b$ and $b$ is inversely proportional to $c$.
Hence ,
$a \propto b \Rightarrow a = {k_1}b$ where ${k_1}$is a constant
$b \propto \dfrac{1}{c} \Rightarrow b = \dfrac{{{k_2}}}{c}$ where ${k_2}$is a constant
$ \Rightarrow a = \dfrac{{{k_1}{k_2}}}{c} = \dfrac{{{k_3}}}{c}$ ; where ${k_3} = {k_1}{k_2}$ is another constant
$ \Rightarrow a \propto \dfrac{1}{c}$.

Note: In such types of questions the concept is very necessary i.e. direct proportional is when increase in two numbers is the same like $x:y$ always remains the same and inverse proportional is that when increase in one number results in decrease in another number.