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6400 workers were employed to construct a river bridge in four years. At the end of the first year, $25 %$ workers were retrenched. At the end of the second year, $25 %$ of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by $25 %$ at the end of the third year. How many workers were working during the fourth year?

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7500

4590

4500

4700

answer is A.

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Detailed Solution

Given,
Initial number of workers, P=6400,
Decrease rate of workers in first year,

R 1 = 25 %

,
Decrease rate of workers in second year,

R 2 = 25 %

,
Increase rate of workers in third year,

R 3 = 25 %

.
If P is the population of a city at the beginning of specific year and

are its growth rates during first year, second year, respectively, then,
Population after two years

= P 1 + R 1 100 × 1 + R 2 100

The formula can be extended for more than two years.
And, if R% is the decrease rate, then Population after n years

= P 1 − R 100 n

Let the number of workers working during the fourth year be W,

W = P 1 − R 1 100 × 1 − R 2 100 × 1 + R 3 100 ⇒ W = 6400 1 − 25100 × 1 − 25100 × 1 + 25100 ⇒ W = 6400 × 34 × 34 × 54 ⇒ W = 4500

Hence, the number of workers working during the fourth year is 4500.
Therefore, option (1) is correct.

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