A team of workers with identical efficiency can finish a project in 4 days. However, every second day starting from day 2, three workers leave the team, and every second day starting from day 3, two workers join the team. If the project now takes 7 days to complete, determine how many workers were initially part of the team.

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Accepted Answer

Let's denote the initial number of workers as n. Since these n workers can complete the job in 4 days, the total work is equivalent to 4n worker-days.

One worker's daily contribution would be 1/(4n) of the total job.

The number of workers present on each day changes as follows:
- Day 1: n workers (initial team)
- Day 2: (n-3) workers (3 workers leave)
- Day 3: (n-1) workers (2 workers join)
- Day 4: (n-4) workers (3 workers leave)
- Day 5: (n-2) workers (2 workers join)
- Day 6: (n-5) workers (3 workers leave)
- Day 7: (n-3) workers (2 workers join)

The total work completed over 7 days must equal the entire job:

[n + (n-3) + (n-1) + (n-4) + (n-2) + (n-5) + (n-3)] × (1/4n) = 1

Simplifying the expression inside the brackets:
(7n - 18) × (1/4n) = 1

Multiplying both sides by 4n:
7n - 18 = 4n

Solving for n:
3n = 18
n = 6

Therefore, the team initially consisted of **6 workers**.

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