If the numerator of a fraction is increases by 100% and denominator by 400%, the resultant fraction is `(8)/(15)`. What is the original fraction ?

Options

A. `(7)/(15)`
B. `(3)/(4)`
C. `(5)/(3)`
D. `(4)/(3)`

Answer

To find the original fraction, let's denote the original fraction as \( \frac{x}{y} \).

### Step 1: Understand the changes in the numerator and denominator
- The numerator \( x \) is increased by 100%. This means the new numerator becomes:
\[ x + 100\% \text{ of } x = x + x = 2x \]
- The denominator \( y \) is increased by 400%. This means the new denominator becomes:
\[ y + 400\% \text{ of } y = y + 4y = 5y \]

### Step 2: Set up the equation with the new fraction
According to the problem, the resultant fraction after these changes is \( \frac{8}{15} \). Therefore, we can write:
\[ \frac{2x}{5y} = \frac{8}{15} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 2x \cdot 15 = 8 \cdot 5y \]
This simplifies to:
\[ 30x = 40y \]

### Step 4: Simplify the equation
We can simplify this equation by dividing both sides by 10:
\[ 3x = 4y \]

### Step 5: Express \( x \) in terms of \( y \)
From the equation \( 3x = 4y \), we can express \( x \) in terms of \( y \):
\[ x = \frac{4}{3}y \]

### Step 6: Write the original fraction
Now we can write the original fraction \( \frac{x}{y} \):
\[ \frac{x}{y} = \frac{\frac{4}{3}y}{y} = \frac{4}{3} \]

### Final Answer
The original fraction is:
\[ \frac{4}{3} \]