A shopkeeper increases the price of a product by 25 percent and, as a result, a customer buys only 70 percent of the earlier quantity. What is the net percentage change in the customer expenditure on that product?

Introduction / Context:
This question examines combined percentage changes in price and quantity and their effect on total expenditure. Expenditure is the product of price per unit and quantity purchased. When the price goes up and the quantity purchased goes down, we must determine the overall impact using multiplicative reasoning rather than simply adding or subtracting percentages.

Given Data / Assumptions:

• The price per unit of a product increases by 25 percent.
• The customer now buys only 70 percent of the original quantity.
• Expenditure equals price per unit multiplied by quantity purchased.
• We compare the new expenditure with the original expenditure.

Concept / Approach:
If a quantity is increased by 25 percent, its new value is 1.25 times the original. If another quantity is reduced to 70 percent, its new value is 0.70 times the original. The new expenditure will be 1.25 multiplied by 0.70 times the old expenditure. The factor 1.25 * 0.70 gives the overall multiplicative effect on expenditure. Comparing this to 1 tells us whether expenditure has increased or decreased and by what percentage.

Step-by-Step Solution:
Step 1: Let the original price per unit be P and the original quantity be Q. Then original expenditure E = P * Q.Step 2: After the 25 percent price increase, the new price is 1.25P.Step 3: After the reduction in quantity, the new quantity is 0.70Q.Step 4: New expenditure E_new = 1.25P * 0.70Q = 0.875PQ.Step 5: Since original expenditure was PQ, the ratio E_new / E = 0.875.Step 6: A factor of 0.875 means the new expenditure is 87.5 percent of the original, so the reduction is 100 percent minus 87.5 percent = 12.5 percent decrease.

Verification / Alternative check:
Use simple numbers to verify. Assume the original price is Rs. 100 per unit and the original quantity is 10 units, giving original expenditure of Rs. 1000. After the price increase, the price becomes Rs. 125. After the quantity reduction, the customer buys 70 percent of 10, which is 7 units. The new expenditure is 125 * 7 = Rs. 875. This is 125 less than 1000. The difference of 125 out of 1000 is 12.5 percent, confirming our calculation.

Why Other Options Are Wrong:
A 5 percent or 10 percent decrease would correspond to new expenditure equal to 95 percent or 90 percent of the original, not 87.5 percent. No change in expenditure would require a net factor of exactly 1, which is not the case. A 12.5 percent increase would correspond to a factor of 1.125, opposite to our result. Only a 12.5 percent decrease is consistent with the factor 0.875 derived from the combined changes.

Common Pitfalls:
Many students simply subtract 25 percent and 30 percent (from 100 percent to 70 percent) and assume a 5 percent or similar net change, which is incorrect because the changes affect different factors (price and quantity) and must be handled multiplicatively. Another common mistake is to apply the percentage change to the wrong base or forget to interpret 70 percent as 0.70 in decimal form.

Final Answer:
The customer expenditure decreases and becomes 87.5 percent of the original, which is a 12.5% decrease, so the correct option is 12.5% decrease.