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The workload required to develop a system is estimated at 80 person-months if it is carried out by one person. When four staff members with the same productivity work together to develop the system, each member’s productivity is expected to decrease by 20%. How many working days does it take for the four members to develop this system? Here, this development work can be equally divided into four parts, and the four members can perform each individual part in parallel. In addition, each member can work 22 working days per month.

80 person-months is : $\cfrac{1}{80}$

So for the 4 of them we have : $0.8*t*\cfrac{4}{80} => t = \cfrac{80}{3.2} = 25$

And the result is : $ 25 * 22 = 550 $ days

But the correct result is 528, what am I doing wrong here? Please show me, thanks alot!

f855a864
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If each worker's productivity is cut by 20%, that means the total amount of work is $80 + .2*80 = 96$. Thus, there are a total of $96*22/4 = 528$ working days.

Euler....IS_ALIVE
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    That’s apparently the intended solution, but it’s not the way I would interpret the $20$% reduction in productivity or expect anyone else to interpret it. I agree with the OP’s interpretation: if one person working alone does $\frac1{80}$ of the job in one month, someone working at $80$% of that productivity does $0.8\cdot\frac1{80}=\frac1{100}$ of the job in one month. That is, in each month he does $20$% less work. On your interpretation it takes him $\frac{96}{80}=\frac65$ as long to do the job, so he works only $5/6$ as productively and therefore loses $16\frac23$% of his productivity. – Brian M. Scott Oct 22 '14 at 08:07
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    @BrianM.Scott Agreed. Time to send a letter to the author. – Euler....IS_ALIVE Oct 22 '14 at 08:10
  • Thanks alot! I misread the question! Again :(! – f855a864 Oct 22 '14 at 08:13