Multiple choice

A team of workers intended to finish a project in 15 days. However, with 15 workers leaving the team every day, the project was eventually completed by the end of the 20th day. How many workers were in the group at the project's outset?

  1. 390

  2. 480

  3. 570

  4. 660

  5. 750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial workers be x. Total work = 15x. Work done = x + (x-15) + (x-30) + ... + (x-15*19). This is an arithmetic progression with 20 terms. Sum = (20/2) * [2x + (20-1)*(-15)] = 10 * [2x - 285] = 20x - 2850. Setting 20x - 2850 = 15x, 5x = 2850, x = 570.

AI explanation

Using the arithmetic progression sum formula for negative leaving workers, the total work done equals the initial number of workers (x) times 20 minus 15 times the sum of the first 19 integers. This simplifies to 20x minus 2850. Equating this to the intended total work of x times 15 gives 20x - 2850 = 15x. Solving this equation yields x = 570. The answer is 570.

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