Question

$X$ and $Y$ are positive number and $X$ is inversely proportional to $Y$. By what percent would the value of $Y$ decrease, if the value of $X$ is increased by $50\%$

• A. $25\%$
• B. $33\frac{1}{3}\%$
• C. $50\%$
• D. $66\frac{2}{3}\%$
• E. $75\%$

Answer 1

The correct option is B $33\frac{1}{3}\%$

For inversely proportional numbers their product is always the same

i.e. $X\times Y=k$

Now, changing$X$ and$Y$ to $X^{\prime }$ and $Y^{\prime }$

$X^{\prime }\times Y^{\prime }=k$

and $X^{\prime }=\frac{3X}{2}$

Thus $\frac{3X}{2}\times Y^{\prime }=X\times Y$

i.e. $Y^{\prime }=\frac{2}{3}Y$

i.e. $Y$ decreases by $33.3$