Question

Given that x and y are in inverse proportion, and $y_1,y_2$ are values of y corresponding to the values $x_1,x_2$ of x, respectively. Which of the following is correct?

• A. $x_1{y}_2=x_2{y}_1$
• B. $x_1{y}_1=x_2{y}_2$
• C. $x_1{x}_2=y_1{y}_2$
• D. $\frac{x_1}{y_1}=\frac{x_2}{y_2}$

Answer 1

The correct option is B $x_1{y}_1=x_2{y}_2$

Given $x\propto \frac{1}{y}$
Hence we have
$xy=k$ where k is constant
Therefore, if $x=x_1$ and $y=y_1$, then $x_1{y}_1=k$---------(1)
Again
if $x=x_2$ and $y=y_2$, then $x_2{y}_2=k$---------------(2)
Equating (1) and (2), we have
$x_1{y}_1=x_2{y}_2$