Question

If $a,b$ and $c$ are positive integers, then $\frac{a+c}{b+c}$ is

• A. always smaller than $\frac{a}{b}$
• B. always greater than $\frac{a}{b}$
• C. greater than $\frac{a}{b}$ only if $a>b$
• D. greater than $\frac{a}{b}$ only if $a<b$

Answer 1

The correct option is D greater than $\frac{a}{b}$ only if $a<b$

Let,$\frac{a+c}{b+c}>\frac{a}{b}$

$\Rightarrow$ $ab+bc>ab+ac$

$\Rightarrow$ $bc>ca$
$\Rightarrow$ $b>a$
$\Rightarrow \frac{a+c}{b+c}>\frac{a}{b}$, if $b>a$
Hence, option 'D' is correct.