If we increased 20% in numerator and 25% in denominator of a fraction, then it is `3/5` then the original fraction is:

Options

A. `8/5`
B. `5/8`
C. `3/8`
D. `8/3`

Explanation

To find the original fraction given that increasing the numerator by 20% and the denominator by 25% results in the fraction \( \frac{3}{5} \), we can follow these steps:

### Step 1: Define the Original Fraction
Let the original fraction be \( \frac{n}{d} \), where \( n \) is the numerator and \( d \) is the denominator.

### Step 2: Apply the Percentage Increases
According to the problem, if we increase the numerator by 20%, the new numerator becomes:
\[ n + 0.2n = 1.2n \]
Similarly, if we increase the denominator by 25%, the new denominator becomes:
\[ d + 0.25d = 1.25d \]

### Step 3: Set Up the Equation
The problem states that the new fraction is equal to \( \frac{3}{5} \):
\[ \frac{1.2n}{1.25d} = \frac{3}{5} \]

### Step 4: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 5 \cdot 1.2n = 3 \cdot 1.25d \]
This simplifies to:
\[ 6n = 3.75d \]

### Step 5: Simplify the Equation
Dividing both sides by 3 gives:
\[ 2n = 1.25d \]
Now, we can express \( n \) in terms of \( d \):
\[ n = \frac{1.25}{2}d = 0.625d \]

### Step 6: Write the Original Fraction
Now we can write the original fraction \( \frac{n}{d} \):
\[ \frac{n}{d} = \frac{0.625d}{d} = 0.625 \]
To express this as a fraction, we can convert 0.625 into a fraction:
\[ 0.625 = \frac{625}{1000} = \frac{5}{8} \]

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