10000 workers were employed to construct a river bridge in four years. At the end of first year, 10% workers were retrenched. At the end of the second year, 5% of the workers at the begining of the second year were retrenched. However to complete the project in time, the number of workers was increased by 10% at the end of the third year. How many workers were working during the fourth year ?

Answer

To solve the problem step-by-step, we will track the number of workers employed at each stage of the project:

### Step 1: Initial Number of Workers
Initially, the number of workers employed is:
\[ \text{Initial Workers} = 10,000 \]

### Step 2: Workers After the First Year
At the end of the first year, 10% of the workers are retrenched. We calculate the number of workers retrenched:
\[ \text{Workers Retrenched} = 10\% \text{ of } 10,000 = \frac{10}{100} \times 10,000 = 1,000 \]
Thus, the number of workers remaining after the first year is:
\[ \text{Remaining Workers after Year 1} = 10,000 - 1,000 = 9,000 \]

### Step 3: Workers After the Second Year
At the end of the second year, 5% of the workers at the beginning of the second year (which is 9,000) are retrenched. We calculate:
\[ \text{Workers Retrenched} = 5\% \text{ of } 9,000 = \frac{5}{100} \times 9,000 = 450 \]
Thus, the number of workers remaining after the second year is:
\[ \text{Remaining Workers after Year 2} = 9,000 - 450 = 8,550 \]

### Step 4: Workers After the Third Year
At the end of the third year, the number of workers is increased by 10%. First, we calculate 10% of the remaining workers:
\[ \text{Increase} = 10\% \text{ of } 8,550 = \frac{10}{100} \times 8,550 = 855 \]
Thus, the number of workers after the increase is:
\[ \text{Workers after Increase} = 8,550 + 855 = 9,405 \]

### Step 5: Final Count of Workers in the Fourth Year
The number of workers working during the fourth year is:
\[ \text{Workers in Fourth Year} = 9,405 \]

### Final Answer
Thus, the number of workers working during the fourth year is **9,405**.

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