Question

Let $f$ be a function such that $f(xy)=\frac{f(x)}{y}$ for all positive real numbers $x,y.$ If $f(20)=15$, then $f(50)=$

• A. $\frac{75}{2}$
• B. 12
• C. 6
• D. 75

Answer 1

Answer: (C)

Given, $f(xy)=\frac{f(x)}{y}$ and $f(20)=15$
$\Rightarrow f(5\times 4)=\frac{f(5)}{4}=15$
$\Rightarrow f(5)=4\times 15=60$
Now, $f(50)=f(5\times 10)=\frac{f(5)}{10}=\frac{60}{10}=6$