A company starts with 8000 workers. The number of workers increases by 5% at the end of the first year, by 10% at the end of the second year and by 20% at the end of the third year. How many workers are there at the beginning of the fourth year?

Introduction / Context:
This percentage growth question is about successive increases. The number of workers grows each year by a given percentage, so the new workforce becomes the base for the next percentage increase. You must apply percentage multipliers in sequence rather than simply adding percentages.

Given Data / Assumptions:
- Initial number of workers = 8000. - Increase after first year = 5% of current number. - Increase after second year = 10% of current number. - Increase after third year = 20% of current number. - All increases are compounded year on year.

Concept / Approach:
A percentage increase of p% means the new quantity is multiplied by (1 + p/100). Because increases are successive, we multiply the original number by each factor in turn: 1.05, 1.10 and 1.20. The final product gives the number of workers at the start of the fourth year.

Step-by-Step Solution:
Step 1: After first year, workers = 8000 * 1.05. Step 2: 8000 * 1.05 = 8400 workers. Step 3: After second year, workers = 8400 * 1.10 = 9240. Step 4: After third year, workers = 9240 * 1.20. Step 5: 9240 * 1.20 = 11088. Step 6: This is the number of workers present at the beginning of the fourth year.

Verification / Alternative check:
Combine the multipliers directly: overall factor = 1.05 * 1.10 * 1.20. This equals 1.386. Multiplying 8000 by 1.386 gives 11088, which matches the detailed stepwise calculation. This confirms the result and shows that we cannot replace the combined growth with a simple 5 + 10 + 20 = 35% increase.

Why Other Options Are Wrong:
- 10188 and 11008 are values that could come from arithmetic mistakes or rounding. - 11808 and 12000 assume larger or linear percentage increases and ignore compounding details.

Common Pitfalls:
Many candidates add percentages and compute 8000 * 1.35, which gives 10800, not found here but still incorrect. Others apply percentages to the wrong base, such as always using 8000 rather than the updated count each year. Always treat each year change as a fresh percentage of the current number of workers.

Final Answer:
The company has 11088 workers at the beginning of the fourth year.