The numerator of a fraction is in creased by 20% and denomina tor is decreased by 20%. The value of the fraction becomes The original fraction is

Options

A. `3/2`
B. `8/15`
C. `7/11`
D. `4/5`

Answer

To solve the problem step by step, we need to understand the effect of increasing the numerator by 20% and decreasing the denominator by 20% on the value of the fraction.

Let's denote the original fraction as \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator.

### Step 1: Increase the Numerator by 20%
When we increase the numerator \( a \) by 20%, the new numerator becomes:
\[ a' = a + 0.2a = 1.2a \]

### Step 2: Decrease the Denominator by 20%
When we decrease the denominator \( b \) by 20%, the new denominator becomes:
\[ b' = b - 0.2b = 0.8b \]

### Step 3: Form the New Fraction
The new fraction after these changes is:
\[ \frac{a'}{b'} = \frac{1.2a}{0.8b} \]

### Step 4: Simplify the New Fraction
To simplify \( \frac{1.2a}{0.8b} \):
\[ \frac{1.2a}{0.8b} = \frac{1.2}{0.8} \cdot \frac{a}{b} \]
Calculating \( \frac{1.2}{0.8} \):
\[ \frac{1.2}{0.8} = \frac{12}{8} = \frac{3}{2} \]
Thus, the new fraction becomes:
\[ \frac{3}{2} \cdot \frac{a}{b} \]

### Step 5: Relate the New Fraction to the Original Fraction
According to the problem, the new fraction is equal to \( \frac{3}{2} \) times the original fraction. Therefore, we can set up the equation:
\[ \frac{3}{2} \cdot \frac{a}{b} = \frac{a'}{b'} \]
This implies that the original fraction \( \frac{a}{b} \) is \( \frac{2}{3} \) of the new fraction.

### Step 6: Conclusion
The original fraction \( \frac{a}{b} \) can be expressed as:
\[ \frac{a}{b} = \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \]

Thus, the original fraction is \( \frac{2}{3} \).