In an examination a batch of 60 students made an average score of 55 marks and another batch of 40 students made 45. what is the overall average score?

Answers (1)

$average\;of\;score\;obtained\;by\;60\;students=55\\*\Rightarrow 55=\frac{x_1+x_2+........+x_{60}}{60}\\* average\;of\;score\;obtained\;by\;40\;students=45\\*\Rightarrow 45=\frac{y_1+y_2+........+y_{40}}{40}\\* x_1+x_2+........+x_{60}=55\times 60\\* y_1+y_2+........+y_{40}=45\times 40\\* overall\;average\;of\;all\;students=\frac{x_1+x_2+........+x_{60}+y_1+y_2+........+y_{40}}{100}\\* overall\;average\;of\;all\;students=\frac{(40\times 45)+(55\times 60)}{100}\\*overall\;average\;of\;all\;students=\frac{1800+3300}{100}=51\\* Hence,\;the\;overall\;average\;score\;of\;100\;students\;is\;51.$

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