Calculate separately the percentage of employees who are female and working on the project, and the percentage who are male and working on the project, and add them together.

1. Females

45% of the department is female and 90% of females are working on the project, hence the proportion of workers who are female and working on the project is 90% of 45% of the workers.

In terms of fractions this is $$\frac{\var{femaleproject}}{100} \times \frac{\var{females}}{100} = \frac{\var{femaleproject*females}}{10000} = \frac{\var{depfemaleproject}}{100}$$ of the workers, ie 81/2%.

So 81/2% of the departmental staff are working on the project and female.

2. Males

55% of the department is male and 50% of males are working on the project, hence the proportion of workers who are male and working on the project is 50% of 55% of the workers.

In terms of fractions this is $$\frac{\var{maleproject}}{100} \times \frac{\var{males}}{100} = \frac{\var{maleproject*males}}{10000} = \frac{\var{depmaleproject}}{100}$$ of the workers, ie 55/2%.

So 55/2% of the departmental staff are working on the project and male.

So the total percentage of departmental staff working on the project is $\var{depfemaleproject}\% + \var{depmaleproject}\% = \var{project}\%$.