Question : Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.
Option 1: $\frac{5}{9}$
Option 2: $\frac{1}{35}$
Option 3: $\frac{45}{7}$
Option 4: $\frac{7}{45}$
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Correct Answer: $\frac{1}{35}$
Solution :
Let the required fraction be $x$.
As per the question,
$\frac{x}{\frac{1}{27}}=\frac{\frac{3}{7}}{\frac{5}{9}}$
⇒ $27x=\frac{27}{35}$
$\therefore x=\frac{1}{35}$
Hence, the correct answer is $\frac{1}{35}$.
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