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A class consists of 3 sections $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ with 35,35 and 30 students respectively. The arithmetic means of the marks secured by students of sections $\mathrm{A}$ and $\mathrm{B}$, who appeared fol a test of 100 marks are 74 and 70 respectively. The arithmetic mean of the marks secured by students of section $\mathrm{C}$, who appeared for a test in the same subject which carried marks is 51 . What is the averagc perocntage of marks socuros by all the 100 student of the three sections? $\quad$
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The correct answer is:
$70 . \mathrm{E}$
Total no. of students in section A $=74 \times 35=2590$
Total no. of students in section $\mathrm{B}$ $=70 \times 35=2450$
Now, total no. of students in section $\mathrm{C}$
$=\frac{51}{75} \times 100 \times 30=2040$
Thus, total students in all $=2590+2450+2040$ $\begin{aligned} &=7080 \\ \text { Thus, Required percentage } &=7080 \div 100 \\ &=70.8 \end{aligned}$
Total no. of students in section $\mathrm{B}$ $=70 \times 35=2450$
Now, total no. of students in section $\mathrm{C}$
$=\frac{51}{75} \times 100 \times 30=2040$
Thus, total students in all $=2590+2450+2040$ $\begin{aligned} &=7080 \\ \text { Thus, Required percentage } &=7080 \div 100 \\ &=70.8 \end{aligned}$
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