If the price of a commodity is decreased by 10% and its consumption is increased by 20%, then what will be the increase or decrease in the expenditure of the commodity?

Options

A. 8% decrease
B. 8% Increase
C. 10% Increase
D. 10% decrease

Answer

To solve the problem step by step, we will analyze the changes in price and consumption and then calculate the resultant change in expenditure.

### Step 1: Understand the changes in price and consumption
- The price of the commodity is decreased by 10%. This means if the original price is \( P \), the new price will be:
\[ \text{New Price} = P - 0.10P = 0.90P \]

- The consumption of the commodity is increased by 20%. This means if the original quantity consumed is \( Q \), the new quantity will be:
\[ \text{New Quantity} = Q + 0.20Q = 1.20Q \]

### Step 2: Calculate the original expenditure
The original expenditure \( E \) is given by:
\[ E = \text{Price} \times \text{Quantity} = P \times Q \]

### Step 3: Calculate the new expenditure
The new expenditure \( E' \) after the changes in price and consumption will be:
\[ E' = \text{New Price} \times \text{New Quantity} = (0.90P) \times (1.20Q) \]
Calculating this gives:
\[ E' = 0.90P \times 1.20Q = 1.08PQ \]

### Step 4: Determine the change in expenditure
To find the change in expenditure, we can compare the new expenditure \( E' \) with the original expenditure \( E \):
\[ \text{Change in Expenditure} = E' - E = 1.08PQ - PQ = (1.08 - 1)PQ = 0.08PQ \]

### Step 5: Calculate the percentage change in expenditure
To find the percentage change in expenditure, we use the formula:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Expenditure}}{\text{Original Expenditure}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left(\frac{0.08PQ}{PQ}\right) \times 100 = 8\% \]

### Conclusion
Since the percentage change is positive, this indicates an increase in expenditure. Therefore, the expenditure on the commodity has increased by **8%**.

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