If the numerator of a fraction is decreased by 20% and its denominator is increased by 10%, then fraction will be `16/55`
The fraction is

Options

A. `2/5`
B. `5/2`
C. `3/5`
D. `5/3`

Answer

To solve the problem, we need to find the original fraction given the conditions about its numerator and denominator. Let's denote the original fraction as \( \frac{x}{y} \), where \( x \) is the numerator and \( y \) is the denominator.

### Step 1: Define the changes to the numerator and denominator
According to the problem:
- The numerator is decreased by 20%. This means the new numerator becomes:
\[ \text{New Numerator} = x - 0.2x = 0.8x \]

- The denominator is increased by 10%. This means the new denominator becomes:
\[ \text{New Denominator} = y + 0.1y = 1.1y \]

### Step 2: Set up the equation for the new fraction
After the changes, the new fraction is given as:
\[ \frac{0.8x}{1.1y} = \frac{16}{55} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 0.8x \cdot 55 = 16 \cdot 1.1y \]
This simplifies to:
\[ 44x = 17.6y \]

### Step 4: Rearranging the equation
We can rearrange this equation to express \( x \) in terms of \( y \):
\[ x = \frac{17.6}{44}y \]
Simplifying \( \frac{17.6}{44} \):
\[ x = \frac{17.6 \div 4}{44 \div 4}y = \frac{4.4}{11}y \]

### Step 5: Finding the original fraction
Now we can express the original fraction:
\[ \frac{x}{y} = \frac{\frac{4.4}{11}y}{y} = \frac{4.4}{11} \]

### Step 6: Simplifying the fraction
To simplify \( \frac{4.4}{11} \):
\[ \frac{4.4}{11} = \frac{44}{110} = \frac{2}{5} \]

Thus, the original fraction is:
\[ \frac{2}{5} \]

### Final Answer
The original fraction is \( \frac{2}{5} \).

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