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

Options

A. 40%
B. 80%
C. 48.8%
D. 51.2%

Answer

To solve the problem, we need to determine how much the expression \( xy^2 \) decreases when both \( x \) and \( y \) are decreased by 20%. Let's go through the solution step by step.

### Step 1: Define the initial values of \( x \) and \( y \)
Let's assume:
- \( x = 10 \)
- \( y = 10 \)

### Step 2: Calculate the initial value of the expression \( xy^2 \)
The initial value of the expression is:
\[ xy^2 = 10 \times (10^2) = 10 \times 100 = 1000 \]

### Step 3: Calculate the new values of \( x \) and \( y \) after a 20% decrease
A decrease of 20% means we multiply the original values by \( 80\% \) (or \( 0.8 \)):
\[ \text{New } x = 10 \times 0.8 = 8 \]
\[ \text{New } y = 10 \times 0.8 = 8 \]

### Step 4: Calculate the new value of the expression with the decreased values
Now we substitute the new values into the expression:
\[ xy^2 = 8 \times (8^2) = 8 \times 64 = 512 \]

### Step 5: Calculate the decrease in the value of the expression
To find the decrease, we subtract the new value from the initial value:
\[ \text{Decrease} = 1000 - 512 = 488 \]

### Step 6: Calculate the percentage decrease
To find the percentage decrease, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{Initial Value}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Decrease} = \left( \frac{488}{1000} \right) \times 100 = 48.8\% \]

### Final Answer
The value of the expression is decreased by **48.8%**.

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