Question

If $\frac{(2a+b)}{(a+4b)}=3$, then find the value of $\frac{a+b}{a+2b}$

• A. $$\frac{2}{7}$$
• B. \fra{9}{7}
• C. $$\frac{5}{3}$$
• D. \fra{10}{9}

Answer 1

Answer:

\fra{10}{9}

Solution:

Given $\frac{2a+b}{a+4b}=3$

$2a+b=3\times{(a+4b)}$

$2a+b=3a+12b$

$a=-11b$

Substituting this in $\frac{a+b}{a+2b}$

$=\frac{-11b+b}{-11b+2b}$

$=\frac{-10b}{-9b}$

$=\frac{10}{9}$

Hence Option(D) is the correct answer.