Question

If $a:b=c:d$ , then $\frac{ma+nc}{mb+nd}$ is equal to ______.

• A. $m:n$
• B. $na:mb$
• C. $a:b$
• D. $md:nc$

Answer 1

The correct option is C $a:b$

$\Rightarrow$ $\frac{ma+nc}{mb+nd}$

$\Rightarrow$ Let $\frac{a}{b}=\frac{c}{d}=k$.

$\Rightarrow$ Then, $a=bk$ and $c=dk$

$\therefore$ $\frac{ma+nc}{mb+nd}$

$\Rightarrow$ $\frac{mbk+ndk}{mb+nd}$

$\Rightarrow$ $\left(\frac{mb+nd}{mb+nd}\right)$

$\Rightarrow$ $k$

$\Rightarrow$ $\frac{a}{b}=a:b$