Chapter 13, Problem 51A

Interpretation Introduction

Interpretation:

The effect of change of one variable by changing the other variable is to be discussed if they are inversely proportional.

Concept introduction:

Two variables are inversely proportional to each other means-

Increasing the value of one variable by particular factor decreases the value of other variable by same factor and vice-versa.

Answer to Problem 51A

The value of one variable decreases by same factor as the value of other variable increases.

Explanation of Solution

Let there are two variables A and B and they inversely proportional to each other.

Therefore it can be written as:

$\begin{array}{c}A\propto \frac{1}{B}\\ \therefore A=\frac{cons\tan t}{B}\end{array}$

Thus increasing the value of B by a factor decreases the value of A by same factor.

Conclusion

If two variables are inversely proportional to each other, one variable decreases on increasing the other one.