If the price of a commodity is decreased by 40% and its consumption is increased by `20%`, then what will be the increase or decrease in the expenditure of the commodity?

Options

A. `28%` decrease
B. `28%` increase
C. `20%` increase
D. `20%` decrease

Answer

To solve the problem of determining the change in expenditure when the price of a commodity is decreased by 40% and its consumption is increased by 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the original price of the commodity be \( P \).
- The price is decreased by 40%, so the new price \( P' \) can be calculated as:
\[ P' = P - 0.4P = 0.6P \]

2. **Calculate the Change in Consumption**:
- Let the original quantity consumed be \( Q \).
- The consumption is increased by 20%, so the new quantity \( Q' \) can be calculated as:
\[ Q' = Q + 0.2Q = 1.2Q \]

3. **Calculate the Original Expenditure**:
- The original expenditure \( E \) is given by:
\[ E = P \times Q \]

4. **Calculate the New Expenditure**:
- The new expenditure \( E' \) after the price decrease and consumption increase is:
\[ E' = P' \times Q' = (0.6P) \times (1.2Q) = 0.72PQ \]

5. **Determine the Change in Expenditure**:
- The change in expenditure can be calculated as:
\[ \text{Change in Expenditure} = E' - E = 0.72PQ - PQ = -0.28PQ \]
- This indicates a decrease in expenditure.

6. **Calculate the Percentage Change**:
- To find the percentage change in expenditure:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Expenditure}}{E}\right) \times 100 = \left(\frac{-0.28PQ}{PQ}\right) \times 100 = -28\% \]

### Conclusion:
The expenditure on the commodity decreases by 28%.