Question

the mean marks obtained by girls in a class is 67 and that of boys is 63. The average marks secured by all the 80students in the class is 64.5. Find the number of the girls and the boys separately in the class.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{there}\mathrm{are}\mathrm{x}\mathrm{boys}\mathrm{and}\left(80-\mathrm{x}\right)\mathrm{girls}\mathrm{so} \\ \frac{67\left(80-\mathrm{x}\right)+63\mathrm{x}}{80}=64.5 \\ 67\left(80-\mathrm{x}\right)+63\mathrm{x}=64.5\times 80=5160 \\ 5360-67\mathrm{x}+63\mathrm{x}=5160 \\ 200=4\mathrm{x} \\ \mathrm{x}=50 \\ \mathrm{So}\mathrm{there}\mathrm{are}50\mathrm{boys}\mathrm{and}30\mathrm{girls}. \end{gathered}$$