Nested percentage of a percentage: If 16% of 40% of a number equals 8, what is the number?

Introduction / Context:Here, a percentage is taken of another percentage of a number. The key is to translate nested percentages into a single multiplier applied to the unknown. This technique is common in multi-stage discount or tax problems as well.

Given Data / Assumptions:Let the number be N. We are told 16% of 40% of N equals 8.

Concept / Approach:Convert the percentages to decimals and multiply: 16% of 40% of N is (0.16 * 0.40) * N = 0.064N. Then set 0.064N = 8 and solve for N by dividing both sides by 0.064.

Step-by-Step Solution:

Verification / Alternative check:Check forward: 40% of 125 = 50; 16% of 50 = 8. This matches the requirement exactly.

Why Other Options Are Wrong:200 gives 0.064 * 200 = 12.8; 225 gives 14.4; 320 gives 20.48; 100 gives 6.4. Only 125 gives 8.

Common Pitfalls:Adding percentages (16 + 40) instead of multiplying, or converting 16% to 16 rather than 0.16. Always convert percentages to decimal multipliers when applied to numbers.

Final Answer:125