Question

A housewife made a chocolate cake and a vanilla cake that were exactly of the same size. The chocolate cake was cut into 6 equal pieces and vanilla cake was cut into 12 equal pieces. She gave 2 pieces of chocolate cake to her driver and 2 pieces of vanilla cake to her maid. She gave the rest of the cake to her children. What fraction of each cake was given to her children ?

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{chocolate}\mathrm{cake}=6 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{vanilla}\mathrm{cake}=12 \\ \mathrm{Number}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{chocolate}\mathrm{cake}\mathrm{given}\mathrm{to}\mathrm{driver}=2 \\ \mathrm{Number}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{vanilla}\mathrm{cake}\mathrm{given}\mathrm{to}\mathrm{maid}=2 \\ \mathrm{Fraction}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{chocolate}\mathrm{cake}\mathrm{given}\mathrm{to}\mathrm{driver}=\frac{2}{6}=\frac{1}{3} \\ \mathrm{Fraction}\mathrm{of}\mathrm{pieces}\mathrm{of}\mathrm{vanilla}\mathrm{cake}\mathrm{given}\mathrm{to}\mathrm{maid}=\frac{2}{12}=\frac{1}{6} \\ \mathrm{Fraction}\mathrm{of}\mathrm{chocolate}\mathrm{cake}\mathrm{left}=1-\frac{1}{3}=\frac{2}{3} \\ \mathrm{Fraction}\mathrm{of}\mathrm{vanilla}\mathrm{cake}\mathrm{left}=1-\frac{1}{6}=\frac{5}{6} \\ \mathrm{So},\mathrm{two}-\mathrm{third}\mathrm{of}\mathrm{the}\mathrm{chocolate}\mathrm{cake}\mathrm{was}\mathrm{given}\mathrm{to}\mathrm{children} \\ \mathrm{and}\mathrm{Five}-\mathrm{sixth}\mathrm{of}\mathrm{the}\mathrm{vanilla}\mathrm{cake}\mathrm{was}\mathrm{given}\mathrm{to}\mathrm{children}. \end{gathered}$$