question_answer

The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of number of boys in the number of girls who appeared in the examination.

Answer:

Let the number of boys \[={{n}_{1}}\]

and number of girls \[={{n}_{2}}\]

Average boys' score \[=71=\overline{{{X}_{1}}}\] (Let)

Average girls? score \[=73=\overline{{{X}_{2}}}\] (Let)

Combined mean \[=\frac{{{n}_{1}}{{\overline{X}}_{1}}+{{n}_{2}}{{\overline{X}}_{2}}}{{{n}_{1}}+{{n}_{2}}}\]

\[71.8=\frac{{{n}_{1}}(71)+{{n}_{2}}(73)}{{{n}_{1}}+{{n}_{2}}}\]

\[71{{n}_{1}}+73{{n}_{2}}=71.8{{n}_{1}}+71.8{{n}_{2}}\]

\[71{{n}_{1}}-71.8{{n}_{1}}=71.8{{n}_{2}}-73{{n}_{2}}\]

\[-0.8{{n}_{1}}=-1.2{{n}_{2}}\]

\[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{1.2}{0.8}\Rightarrow \frac{{{n}_{1}}}{{{n}_{2}}}=\frac{3}{2}\]

\[\Rightarrow {{n}_{1}}:{{n}_{2}}=3:2\]

\[\therefore \] No. of boys: No. of girls \[=3:2\].