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

A. $$\frac{5}{9}$$

B. $$\frac{2}{7}$$

C. $$\frac{{10}}{9}$$

D. $$\frac{{10}}{7}$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{{2a + b}}{{a + 4b}} = 3{\text{ }}\left( {{\text{Given}}} \right) \cr & \Rightarrow 2a + b = 3\left( {a + 4b} \right) \cr & \Rightarrow 2a + b = 3a + 12b \cr & \Rightarrow - a = 11b \cr & \Rightarrow a = - 11b \cr & \therefore \frac{{a + b}}{{a + 2b}} \cr & \Rightarrow \frac{{ - 11b + b}}{{ - 11b + 2b}} \cr & \Rightarrow \frac{{ - 10b}}{{ - 9b}} \cr & \Rightarrow \frac{{10}}{9} \cr} $$

This Question Belongs to Arithmetic Ability >> Algebra

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