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Starting with 8000 workers ,the company ...

Starting with 8000 workers ,the company increases the number of worker by 5% ,10%and 20% at the end of first,second and third year respectively.The number of workers in the fourth year was

A

10188

B

11088

C

11008

D

11808

Text Solution

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The correct Answer is:
To find the number of workers in the fourth year after successive percentage increases, we can follow these steps: 1. **Initial Number of Workers**: Start with the initial number of workers, which is 8000. 2. **First Year Increase**: Calculate the number of workers after the first year, where the increase is 5%. - The formula to calculate the new number of workers after a percentage increase is: \[ \text{New Workers} = \text{Initial Workers} \times \left(1 + \frac{\text{Percentage Increase}}{100}\right) \] - For the first year: \[ \text{Workers after Year 1} = 8000 \times \left(1 + \frac{5}{100}\right) = 8000 \times 1.05 = 8400 \] 3. **Second Year Increase**: Now calculate the number of workers after the second year, where the increase is 10%. - Using the number of workers from the first year: \[ \text{Workers after Year 2} = 8400 \times \left(1 + \frac{10}{100}\right) = 8400 \times 1.10 = 9240 \] 4. **Third Year Increase**: Next, calculate the number of workers after the third year, where the increase is 20%. - Using the number of workers from the second year: \[ \text{Workers after Year 3} = 9240 \times \left(1 + \frac{20}{100}\right) = 9240 \times 1.20 = 11088 \] 5. **Final Count for Fourth Year**: The number of workers at the end of the third year is the number of workers at the start of the fourth year. Thus, the number of workers in the fourth year is: \[ \text{Workers in Year 4} = 11088 \] Therefore, the number of workers in the fourth year is **11088**.
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