Question

If $(a-b)$:$(a+b)=1:11$, find the ratio
$(5a+4b+15)$:$(5a-4b+3)$

Answer 1

Find the ratio $(5a+4b+15)$:$(5a-4b+3)$

Given :$(a-b)$ : $(a+b)=1:11$
$\Rightarrow \frac{a-b}{a+b}=\frac{1}{11}$
$\Rightarrow 11(a-b)=(a+b)1$ [Cross-multiplication]
$\Rightarrow 11a-11b=a+b$
$\Rightarrow 11a-a=11b+b$
$\Rightarrow 10a=12b$
$\Rightarrow \frac{a}{b}=\frac{12}{10}$
$=\frac{6}{5}$
Let $a=6k$ and $b=5k$
Now, $(5a+4b+15):(5a-4b+3)=\frac{5a+4b+15}{5a-4b+3}$
$=\frac{5\times 6k+4\times 5k+15}{5\times 6k-4\times 5k+3}$
$=\frac{30k+20k+15}{30k-20k+3}$
$=\frac{50k+15}{10k+3}$
$=\frac{5(10k+3)}{10k+3}$
$=\frac{5}{1}$

Hence, the ratio of $(5a+4b+15):(5a-4b+3)$ is$5:1$