Question

If $a:b=c:d$, then $(ma+nc):(mb+nd)$ is equal to ____________.

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

Answer 1

Answer: (C)

$a:b$

Let $\frac{a}{b}=\frac{c}{d}=x$ (say) ..........(i)

$\Rightarrow a=bx,c=dx$ .....(ii)

Now, $\frac{ma+nc}{mb+nd}=\frac{mbx+ndx}{mb+nd}$ [using (ii)]

$\Rightarrow \frac{ma+nc}{mb+nd}=\frac{(mb+nd)x}{mb+nd}=x$

$\Rightarrow \frac{ma+nc}{mb+nd}=\frac{a}{b}$ [using (i)].