If the numerator of a fraction is increased by `40%` and the denominator is doubled the new fraction obtained is 7/16 . What was the original fraction ?

Options

A. 5/8
B. 3/8
C. 7/8
D. Cannot be determined

Answer

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

### Step 1: Define the original fraction
Let the original fraction be:
\[ \frac{x}{y} \]

### Step 2: Increase the numerator by 40%
When the numerator \( x \) is increased by 40%, the new numerator becomes:
\[ x + 0.4x = 1.4x \]

### Step 3: Double the denominator
The new denominator, when doubled, becomes:
\[ 2y \]

### Step 4: Form the new fraction
The new fraction after these changes is:
\[ \frac{1.4x}{2y} \]

### Step 5: Set the new fraction equal to \( \frac{7}{16} \)
According to the problem, this new fraction is equal to \( \frac{7}{16} \):
\[ \frac{1.4x}{2y} = \frac{7}{16} \]

### Step 6: Cross-multiply to eliminate the fractions
Cross-multiplying gives:
\[ 1.4x \cdot 16 = 7 \cdot 2y \]
This simplifies to:
\[ 22.4x = 14y \]

### Step 7: Simplify the equation
Dividing both sides by 2:
\[ 11.2x = 7y \]

### Step 8: Express \( \frac{x}{y} \)
Rearranging the equation gives:
\[ \frac{x}{y} = \frac{7}{11.2} \]

### Step 9: Simplify \( \frac{7}{11.2} \)
To simplify \( \frac{7}{11.2} \), we can multiply the numerator and denominator by 10:
\[ \frac{7 \times 10}{11.2 \times 10} = \frac{70}{112} \]
Now, simplifying \( \frac{70}{112} \) by dividing both by 14:
\[ \frac{70 \div 14}{112 \div 14} = \frac{5}{8} \]

### Conclusion
Thus, the original fraction is:
\[ \frac{5}{8} \]