In the expression `xy^(2)` , the values of both variables x and y are decreased by 20%. By this the value of the expression will be decreased by

Options

A. 0.4
B. 0.8
C. 0.488
D. 0.512

Answer

To solve the problem step by step, we need to find out how much the expression \( xy^2 \) decreases when both \( x \) and \( y \) are decreased by 20%.

### Step 1: Calculate the new value of \( x \)
The original value of \( x \) is decreased by 20%.
- New value of \( x \) = \( x - 20\% \text{ of } x \)
- This can be expressed as:
\[ \text{New } x = x - 0.2x = 0.8x \]

### Step 2: Calculate the new value of \( y \)
Similarly, the original value of \( y \) is also decreased by 20%.
- New value of \( y \) = \( y - 20\% \text{ of } y \)
- This can be expressed as:
\[ \text{New } y = y - 0.2y = 0.8y \]

### Step 3: Substitute the new values into the expression
Now we substitute the new values of \( x \) and \( y \) into the expression \( xy^2 \):
- New expression = \( (0.8x)(0.8y)^2 \)

### Step 4: Simplify the new expression
Now, we simplify the expression:
- \( (0.8y)^2 = 0.64y^2 \)
- Therefore, the new expression becomes:
\[ \text{New expression} = 0.8x \cdot 0.64y^2 = 0.512xy^2 \]

### Step 5: Calculate the decrease in the value of the expression
To find the decrease, we compare the new expression with the original expression:
- Original expression = \( xy^2 \)
- New expression = \( 0.512xy^2 \)

The decrease in value can be calculated as:
\[ \text{Decrease} = \text{Original expression} - \text{New expression} = xy^2 - 0.512xy^2 = (1 - 0.512)xy^2 = 0.488xy^2 \]

### Step 6: Calculate the percentage decrease
To find the percentage decrease, we use the formula:
\[ \text{Percentage decrease} = \left( \frac{\text{Decrease}}{\text{Original value}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage decrease} = \left( \frac{0.488xy^2}{xy^2} \right) \times 100 = 48.8\% \]

### Final Answer
The value of the expression \( xy^2 \) will be decreased by **48.8%**.

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