Question

If ‘a’ is inversely proportional to ‘b’ and ‘b’ is inversely proportional to ‘c’, then what is the proportionality between ‘a’ and ‘c’.
a) Direct
b) Inverse
c) No Proportionality
d) Cannot be determined

Answer 1

HINT: Before solving this question, we must know about Proportionality.
PROPORTIONALITY: When quantities have the same relative size, the two quantities are then said to be proportional to each other. In other words they have the same ratio.

Complete step-by-step answer:

Let us now solve this question.

The statement ‘a’ is inversely proportional to ‘b’ can also be written as:-

\[\dfrac{1}{a}\ \alpha \ b\]

Now, \[\dfrac{1}{a}\ \alpha \ b\] can also be written as follow:-

\[a\ \alpha \ \dfrac{1}{b}\]

‘b’ is inversely proportional to ‘c’

\[\dfrac{1}{b}\ \alpha \ c\]

After the above explanation, we can say that:-

\[a\ \alpha \ \dfrac{1}{b}\ \alpha \ c\]

Therefore,

\[a\ \alpha \ c\]

So, ‘a’ is directly proportional to ‘c’, i.e. ‘c’ is directly proportional to ‘a’.

Therefore, the correct option is (a) Direct.

NOTE: Let us now know about Direct Proportionality and Inverse Proportionality.
DIRECT PROPORTIONALITY AND INVERSE PROPORTIONALITY: In direct proportionality, as one number increases, so does the other. This is also called direct variation. In inverse proportionality, it's exactly the opposite. As one number increases, the other decreases. This is also called inverse variation.