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 \[=3:2\].
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