Question

If the numerator of a fraction is increased by 10% and its denominator is diminished by 10%, then the fraction becomes 11/45. Find the original fraction.

• A. 2/3
• B. 1/5
• C. 4/5
• D. 2/5

Answer 1

Answer:

B. 1/5

Let the original fraction be $( \frac{x}{y} )$.

After changes:

• Numerator increased by 10% → (1.1x)

• Denominator decreased by 10% → (0.9y)

So new fraction:
$\frac{1.1x}{0.9y} = \frac{11}{45}$

Simplify:
$\frac{11x}{9y} = \frac{11}{45}$

Cancel 11:
$\frac{x}{9y} = \frac{1}{45}$

Cross multiply:
$45x = 9y$
$\Rightarrow 5x = y$

So,
$\frac{x}{y} = \frac{x}{5x} = \frac{1}{5}$

Final Answer: $<b>( \frac{1}{5} )</b>$