If the price of a commodity is decreased by 20% and, as a result, its consumption is increased by 10%, what will be the overall percentage increase or decrease in the total expenditure on that commodity?

Introduction / Context:
This percentage question tests the effect of successive percentage changes on total expenditure for a commodity. Expenditure on a commodity is the product of its price and the quantity consumed. When one factor decreases and the other increases, many students are unsure whether the overall expenditure increases or decreases and by how much. This problem helps to build intuition about combined percentage changes in daily life situations like shopping, budgeting, and cost analysis.

Given Data / Assumptions:

• The original price of the commodity is taken as some base value, say P.
• The original consumption (quantity bought) is taken as some base value, say Q.
• Price decreases by 20%, so the new price is 80% of P.
• Consumption increases by 10%, so the new quantity is 110% of Q.
• Expenditure is calculated as Price * Quantity.

Concept / Approach:
Expenditure is given by the formula: Expenditure = Price * Quantity. If the price changes by a certain percentage and the quantity changes by another percentage, then the new expenditure is the product of the new price and the new quantity. We compare this new expenditure with the original expenditure and express the difference as a percentage of the original expenditure to find the net percentage increase or decrease. Using assumed convenient numbers like 100 for easy calculation is a common and valid technique in percentage questions.

Step-by-Step Solution:
Step 1: Assume the original price P = 100 units of money and original quantity Q = 100 units. Step 2: Original expenditure = P * Q = 100 * 100 = 10000. Step 3: Price decreases by 20%, so new price = 80% of 100 = 80. Step 4: Quantity increases by 10%, so new quantity = 110% of 100 = 110. Step 5: New expenditure = 80 * 110 = 8800. Step 6: Change in expenditure = New expenditure - Original expenditure = 8800 - 10000 = -1200. Step 7: Percentage change in expenditure = (Change / Original) * 100 = (-1200 / 10000) * 100 = -12%. Step 8: A negative percentage indicates a decrease, so the expenditure has decreased by 12%.

Verification / Alternative check:
We can verify using percentage multiplication factors. A decrease of 20% in price means multiplying by 0.8. An increase of 10% in quantity means multiplying by 1.1. So the overall factor on expenditure is 0.8 * 1.1 = 0.88. This means the new expenditure is 88% of the original, which is 12% less than 100%. Therefore, the net effect is a 12% decrease in total expenditure, confirming our previous calculation.

Why Other Options Are Wrong:
12% increase is wrong because the combined factor 0.8 * 1.1 is less than 1, so expenditure cannot increase. 16% decrease and 16% increase are incorrect because they do not match the derived factor of 0.88. No change in expenditure is also incorrect since there is a clear reduction from 100% to 88% of the original expenditure.

Common Pitfalls:
A frequent mistake is to simply add the percentages, for example treating the change as 10% - 20% = -10% or sometimes 20% - 10% = 10% without calculating the product. Percentage changes on different factors (price and quantity) must be applied multiplicatively, not additively. Another common error is to use inconsistent base values or to forget that the price change acts on price only and the consumption change acts on quantity only.

Final Answer:
The total expenditure on the commodity experiences a 12% decrease compared to the original expenditure.