Question

In the equation $a(b+a)=10$, $a$ is _____

• A. Directly proportional to $b$
• B. Inversely proportional to $b$
• C. Not proportional to $b$
• D. (b) and (c) above.

Answer 1

The correct option is C Not proportional to $b$

Two variables are said to be in inverse proportion if the product of the two variables is constant.

Given, $a(b+a)=10$

$\Rightarrow ab+a^2=10$

$\Rightarrow ab=10-a^2$, which is not a constant.

So, '$a$' and '$b$' are not inversely proportional to each other.

Two variables are said to be in direct proportion if their ratio is constant.

Now, $\frac{a}{b}=\frac{10}{b(b+a)}$, which is also not a constant.

$\therefore$ '$a$' and '$b$' are not in direct proportion.

From the above two conditions we can say that '$a$' is not in proportion with '$b$'.