Question

Smita made a large chocolate cake. She gave $\frac{1}{2}$ of the cake to her daughter, $\frac{1}{3}$ to her son, 3 pieces to her son's friend and $2$ pieces to her daughter's friend. Find the total number of pieces she divided the cake into and her son's and daughter's shares.

Answer 1

Gave to her daughter $=\frac{1}{2}$

Gave to her son $=\frac{1}{3}$

so left $=1-\frac{1}{3}-\frac{1}{2}$

$=\frac{6-2-3}{6}$

$=\frac{1}{6}$

She divided the left cake in $5$ pieces so our pieces contain $=\frac{1}{30}$

so she divided cake into $\frac{1}{\frac{1}{30}}$ pieces i.e $30$ pieces.

Her daughter have $\frac{1}{2\times 1}\times 30=15$ pieces

Her son have $\frac{1}{3\times 1}\times 30=10$ pieces