Question

In an inverse proportion x an y vary such that xy is always a constant. Explain it briefly.

Answer 1

Inverse proportion means that when one quantity increases, the other decreases. For example, when you increase pressure (P), the volume (V) of air decreases and if you reduce the pressure, the volume of air increases. This change takes in such a way, that the product of the quantities is constant.
Hence xy = constant. You can see that if y is reduced by half, then you must increase x by double so that the product xy is constant. In other words, if new quantity $y_1=\frac{1}{2}$ of y and new quantity $x_1=2x$, then their product $=\left(\frac{y}{2}\right)\left(2x\right)=xy$ which is constant.