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    James's copy of Numerical reasoning - percentages of subsets

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    Question 1

    In a certain department, 50% of the females and 40% of the males are working on a project. 40% of the department is male.

    What percentage of the department is working on the project?

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      Or, you could:

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        Advice

        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

        60% of the department is female and 50% of females are working on the project, hence the proportion of workers who are female and working on the project is 50% of 60% 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 30%.

        So 30% of the departmental staff are working on the project and female.

        2. Males

         

        40% of the department is male and 40% of males are working on the project, hence the proportion of workers who are male and working on the project is 40% of 40% 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 16%.

        So 16% of the departmental staff are working on the project and male.

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

         
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