Question : If $\frac{(a+b)}{c}=\frac{6}{5}$ and $\frac{(b+c)}{a}=\frac{9}{2}$, then what is the value of $\frac{(a+c)}{b}\; ?$
Option 1: $\frac{9}{5}$
Option 2: $\frac{11}{7}$
Option 3: $\frac{7}{11}$
Option 4: $\frac{7}{4}$
Correct Answer: $\frac{7}{4}$
Solution :
Given: $\frac{(a+ b)}{c} = \frac{6}{5}$
⇒ $5a + 5b = 6c$ ........(i)
Also, $\frac{(b+c)}{a} = \frac{9}{2}$
⇒ $2b + 2c = 9a$ .........(ii)
Adding both the equations (i) and (ii),
⇒ $-4a + 7b = 4c$
⇒ $4(a + c) = 7b$
⇒ $\frac{(a + c)}{b} = \frac{7}{4}$
Hence, the correct answer is $\frac{7}{4}$.
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