Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{10}$
Option 3: $\frac{2}{5}$
Option 4: $\frac{1}{10}$
Correct Answer: $\frac{1}{5}$
Solution :
Given: $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$
⇒ $A+\frac{1}{1+\frac{1}{\frac{7}{3}}}=\frac{9}{10}$
⇒ $A+\frac{1}{1+\frac{3}{7}}=\frac{9}{10}$
⇒ $A+\frac{1}{\frac{10}{7}}=\frac{9}{10}$
⇒ $A+\frac{7}{10}=\frac{9}{10}$
⇒ $A=\frac{9}{10}-\frac{7}{10}=\frac{2}{10}=\frac{1}{5}$
Hence, the correct answer is $\frac{1}{5}$.
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