The price of an item was increased by 10%. This reduced the monthly total sales by 20%.The overall effect on the value of monthly sales is a

Options

A. 10% Increase
B. 10% decrease
C. 12% Increase
D. 12% decrease

Answer

To solve the problem step by step, we will analyze the effects of the price increase and the decrease in sales on the overall value of monthly sales.

### Step 1: Define the Initial Price and Sales
Let’s assume the initial price of the item is \( P \) and the initial quantity sold is \( Q \).

### Step 2: Calculate the New Price After the Increase
The price of the item is increased by 10%. Therefore, the new price \( P' \) can be calculated as:
\[ P' = P + 0.10P = 1.10P \]

### Step 3: Calculate the New Quantity Sold After the Decrease
The monthly total sales decrease by 20%. Therefore, the new quantity sold \( Q' \) can be calculated as:
\[ Q' = Q - 0.20Q = 0.80Q \]

### Step 4: Calculate the Initial Revenue
The initial revenue \( R \) can be calculated as:
\[ R = P \times Q \]

### Step 5: Calculate the New Revenue After Price Increase and Quantity Decrease
The new revenue \( R' \) after the price increase and the decrease in quantity sold can be calculated as:
\[ R' = P' \times Q' = (1.10P) \times (0.80Q) = 0.88PQ \]

### Step 6: Calculate the Overall Effect on Revenue
To find the overall effect on the value of monthly sales, we compare the new revenue \( R' \) to the initial revenue \( R \):
\[ \text{Overall Effect} = R' - R = 0.88PQ - PQ = -0.12PQ \]
This indicates a decrease in revenue.

### Step 7: Calculate the Percentage Decrease in Revenue
To find the percentage decrease in revenue, we can use the formula:
\[ \text{Percentage Decrease} = \left(\frac{\text{Decrease in Revenue}}{\text{Initial Revenue}}\right) \times 100 = \left(\frac{-0.12PQ}{PQ}\right) \times 100 = -12\% \]

### Final Answer
The overall effect on the value of monthly sales is a decrease of **12%**.

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