If the numerator of certain fraction is increased by 100% and the denominator is increased by 200% the new fraction thus formed is `(4)/(21)` . What is the original fraction ?

Options

A. `(2)/(7)`
B. `(3)/(7)`
C. `(2)/(5)`
D. `(4)/(7)`

Explanation

To solve the problem step by step, let's denote the original fraction as \( \frac{x}{y} \).

### Step 1: Understand the changes to the fraction
- The numerator \( x \) is increased by 100%.
- The denominator \( y \) is increased by 200%.

### Step 2: Calculate the new numerator and denominator
- When the numerator \( x \) is increased by 100%, it becomes:
\[ x + 100\% \text{ of } x = x + x = 2x \]
- When the denominator \( y \) is increased by 200%, it becomes:
\[ y + 200\% \text{ of } y = y + 2y = 3y \]

### Step 3: Write the new fraction
After the changes, the new fraction formed is:
\[ \frac{2x}{3y} \]

### Step 4: Set up the equation
According to the problem, this new fraction equals \( \frac{4}{21} \):
\[ \frac{2x}{3y} = \frac{4}{21} \]

### Step 5: Cross-multiply to solve for \( \frac{x}{y} \)
Cross-multiplying gives:
\[ 2x \cdot 21 = 4 \cdot 3y \]
This simplifies to:
\[ 42x = 12y \]

### Step 6: Simplify the equation
Dividing both sides by 6:
\[ 7x = 2y \]

### Step 7: Express \( \frac{x}{y} \)
Rearranging gives:
\[ \frac{x}{y} = \frac{2}{7} \]

### Step 8: Conclusion
Thus, the original fraction is:
\[ \frac{x}{y} = \frac{2}{7} \]