When the price of pressure cooker was increased by 15%, its sale down by 15% . The effect on the money receipt was:

Answer

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

### Step 1: Understand the Initial Situation
Let’s assume the initial price of the pressure cooker is \( P \) and the initial quantity sold is \( Q \). Therefore, the initial revenue (money received) can be calculated as:
\[ \text{Initial Revenue} = P \times Q \]

**Hint:** Start by establishing a baseline for price and quantity sold.

### Step 2: Calculate the New Price After Increase
The price of the pressure cooker is increased by 15%. The new price \( P' \) can be calculated as:
\[ P' = P + 0.15P = 1.15P \]

**Hint:** Remember that a percentage increase means you multiply the original price by \( (1 + \text{percentage}) \).

### Step 3: Calculate the New Quantity Sold After Decrease
The sale of pressure cookers decreases by 15%. The new quantity sold \( Q' \) can be calculated as:
\[ Q' = Q - 0.15Q = 0.85Q \]

**Hint:** A percentage decrease means you multiply the original quantity by \( (1 - \text{percentage}) \).

### Step 4: Calculate the New Revenue
Now, we can calculate the new revenue after the price increase and the quantity decrease:
\[ \text{New Revenue} = P' \times Q' = (1.15P) \times (0.85Q) \]
\[ \text{New Revenue} = 1.15 \times 0.85 \times P \times Q \]
\[ \text{New Revenue} = 0.9775 \times (P \times Q) \]

**Hint:** When calculating new revenue, multiply the new price by the new quantity.

### Step 5: Determine the Effect on Revenue
To find the effect on the money received, we compare the new revenue with the initial revenue:
\[ \text{Effect on Revenue} = \text{New Revenue} - \text{Initial Revenue} \]
\[ \text{Effect on Revenue} = (0.9775 \times (P \times Q)) - (P \times Q) \]
\[ \text{Effect on Revenue} = -0.0225 \times (P \times Q) \]

### Step 6: Calculate the Percentage Loss
To find the percentage loss in revenue, we can express it as:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Initial Revenue}} \right) \times 100 \]
\[ \text{Percentage Loss} = \left( \frac{-0.0225 \times (P \times Q)}{P \times Q} \right) \times 100 \]
\[ \text{Percentage Loss} = -2.25\% \]

### Conclusion
The overall effect on the money received is a loss of **2.25%**.

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