The tax on an article decreases by 10 percent and its consumption increases by 10 percent. What is the net percentage change in the revenue collected on this article?

Introduction / Context:
This question tests the concept of percentage change in a product of two quantities. Revenue is the product of tax per unit and number of units consumed. When one factor decreases by a certain percentage while the other increases, we need to find the overall effect on the product. This is a classic exam pattern that checks comfort with successive percentage change.

Given Data / Assumptions:

• Tax per unit decreases by 10 percent.
• Consumption (units sold) increases by 10 percent.
• Revenue = tax per unit multiplied by number of units.
• We assume a uniform initial tax and fixed base consumption for comparison.

Concept / Approach:
If a value is reduced by 10 percent, it becomes 90 percent of the original, which is a factor of 0.9. If another value is increased by 10 percent, it becomes 110 percent of the original, which is a factor of 1.1. When two changes affect a product, the new product is the product of the new factors. Therefore, the net change in revenue can be found by multiplying 0.9 and 1.1 and comparing the result to 1, which represents the original revenue.

Step-by-Step Solution:
Step 1: Let the original tax per unit be T and the original consumption be Q units. Then original revenue is R = T * Q.Step 2: Tax decreases by 10 percent, so the new tax per unit is 0.9T.Step 3: Consumption increases by 10 percent, so the new quantity is 1.1Q.Step 4: New revenue R_new = 0.9T * 1.1Q = 0.99TQ.Step 5: Compare with original revenue R = TQ. The ratio R_new / R = 0.99, which means the new revenue is 99 percent of the original.Step 6: If revenue is 99 percent of the original, the decrease is 1 percent.

Verification / Alternative check:
Take a simple numerical example. Assume the original tax is Rs. 10 per unit and 100 units are sold, giving original revenue of Rs. 1000. After the change, tax becomes 10 * 0.9 = Rs. 9 and consumption becomes 100 * 1.1 = 110 units. The new revenue is 9 * 110 = Rs. 990. This is Rs. 10 less than 1000, which is a reduction of 1 percent. This numerical check confirms the algebraic reasoning.

Why Other Options Are Wrong:
A 1 percent increase would require the net factor to be 1.01, not 0.99. A 10 percent decrease would correspond to a net factor of 0.9, which we do not have. No change would require the product of the factors to be exactly 1. The 2 percent increase option corresponds to a factor of 1.02, which again does not match 0.99. Only a 1 percent decrease fits the computed net effect.

Common Pitfalls:
Many learners add the percentage changes directly and claim 10 percent minus 10 percent equals zero net change. This is incorrect because the changes apply to different factors and the overall effect is multiplicative, not additive. Another error is to ignore the direction of change, mixing increase and decrease incorrectly. Always convert each percentage change into a multiplier and then multiply to find the combined effect on a product.

Final Answer:
The revenue decreases slightly and becomes 99 percent of the original, so there is a 1% decrease in revenue. Thus the correct option is 1% decrease.