How many people required to complete a job?

Question

I am facing issue solving below problem. Any help?

Total number of tasks are 6780 in a year. And 17 people are efficiently working in a year to complete different tasks to 100%.

Now there will be 20% work increase next year.

How many more people we require to handle that 20% extra load efficiently?

Answer 1

Without loss of generality assume that the workload of the current year corresponds to 100 units (of tasks if you will). Each person can therefore handle $100/17$ units of workload. Next year there will be 120 units, and we know that $x$ people can handle $x\times(100/17)$ units. Thus the solution to how many people we need (in total) for next years 120 units of workload is the solution of: $x\times(100/17)=120$, with respect to $x$.

Answer 2

Work and manpower are in direct proportion (at least this is the ideal case for your problem). So if you have a 20% increase in the work, then you should have a 20%=3.4 people increase in the manpower too in order to complete the work in the same time. This is regardless of the number of tasks.