A) 30
B) 40
C) 50
D) 60
Correct Answer: B
Solution :
The formula for combined mean is \[\bar{x}=\frac{{{n}_{1}}{{{\bar{x}}}_{1}}+{{n}_{2}}{{{\bar{x}}}_{2}}}{{{n}_{1}}+{{n}_{2}}}\] Given, \[\bar{x}=30\], \[{{\bar{x}}_{1}}=32\], \[\overline{{{x}_{2}}}=27\] Let \[{{n}_{1}}+{{n}_{2}}=100\] and \[{{n}_{1}}\] denotes men,\[{{n}_{2}}\] denotes women for this \[{{n}_{2}}=100-{{n}_{1}}\] \[30=\frac{32{{n}_{1}}+(100-{{n}_{1}})27}{100}\]Þ \[30=\frac{32{{n}_{1}}+2700-27{{n}_{1}}}{100}\] Þ \[3000-2700=32{{n}_{1}}-27{{n}_{1}}\]Þ\[300=5{{n}_{1}}\]Þ\[{{n}_{1}}=60\] So, \[{{n}_{2}}=40\] Hence, the percentage of women in the group is 40.
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