A number is decreased by 10 percent and the resulting value is then decreased again by 20 percent. What is the overall percentage decrease from the original number to the final number?

Introduction / Context:
This question involves successive percentage changes. Many learners incorrectly add or subtract percentages directly. The key idea is that each percentage change acts on a new base, not the original number. We must multiply the fractional multipliers to compute the net effect on the original number.

Given Data / Assumptions:
First change: decrease by 10 percent. Second change: decrease by 20 percent applied to the new value. We need the overall percentage decrease from the original number to the final value. Let the original number be N.

Concept / Approach:
A decrease of p percent corresponds to multiplying by (1 - p/100). Therefore, a 10 percent decrease multiplies the number by 0.9 and a 20 percent decrease multiplies by 0.8. Successive changes are combined by multiplying their multipliers: 0.9 * 0.8. The final multiplier shows what fraction of the original remains. The overall percentage decrease is then 100 minus this remaining percentage.

Step-by-Step Solution:
Let original number be N. After a 10 percent decrease, new value is N * (1 - 10/100) = N * 0.9. After a further 20 percent decrease, second new value = (N * 0.9) * (1 - 20/100) = N * 0.9 * 0.8. Compute 0.9 * 0.8 = 0.72. So final value is 0.72N. This means 72 percent of the original number remains. Overall percentage decrease = 100 percent - 72 percent = 28 percent.

Verification / Alternative check:
Use a concrete number to check. Let N = 100. After 10 percent decrease, value is 90. After 20 percent decrease on 90, value is 90 * 0.8 = 72. Overall drop from 100 to 72 is 28 units, which is 28 percent of 100. This numeric example confirms the result.

Why Other Options Are Wrong:
Simply adding the percentages 10 and 20 would give 30 percent, which ignores the fact that the second decrease is on a smaller base. Twenty five percent or 26 percent or 27 percent do not match the computed multiplier 0.72. Only a 28 percent decrease corresponds to the final value being 72 percent of the original.

Common Pitfalls:
The most common mistake is to assume that successive percentage changes can be added or subtracted directly. Another error is to apply the second percentage to the original instead of the intermediate value. Using multipliers for each step and then combining them helps avoid such errors and gives an accurate net effect.

Final Answer:
The overall percentage decrease from the original number to the final number is 28 percent.