Question
If $$\frac{{2a + b}}{{a + 4b}} = 3{\text{,}}$$ Â then find the value of $$\frac{{a + b}}{{a + 2b}} = ?$$
Answer: Option C
$$\eqalign{
& \frac{{2a + b}}{{a + 4b}} = 3{\text{ }}\left( {{\text{Given}}} \right) \cr
& \Rightarrow 2a + b = 3\left( {a + 4b} \right) \cr
& \Rightarrow 2a + b = 3a + 12b \cr
& \Rightarrow - a = 11b \cr
& \Rightarrow a = - 11b \cr
& \therefore \frac{{a + b}}{{a + 2b}} \cr
& \Rightarrow \frac{{ - 11b + b}}{{ - 11b + 2b}} \cr
& \Rightarrow \frac{{ - 10b}}{{ - 9b}} \cr
& \Rightarrow \frac{{10}}{9} \cr} $$
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$$\eqalign{
& \frac{{2a + b}}{{a + 4b}} = 3{\text{ }}\left( {{\text{Given}}} \right) \cr
& \Rightarrow 2a + b = 3\left( {a + 4b} \right) \cr
& \Rightarrow 2a + b = 3a + 12b \cr
& \Rightarrow - a = 11b \cr
& \Rightarrow a = - 11b \cr
& \therefore \frac{{a + b}}{{a + 2b}} \cr
& \Rightarrow \frac{{ - 11b + b}}{{ - 11b + 2b}} \cr
& \Rightarrow \frac{{ - 10b}}{{ - 9b}} \cr
& \Rightarrow \frac{{10}}{9} \cr} $$
Was this answer helpful ?
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