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In a primary school the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students ( both male and female ) is 60.3 kg and the number of male students in the school is 66, what is the number of female students in the school?

A. 162 B. 168 C. 180 D. 112 Answer: Option D
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Solution(By Apex Team)

Let the number of female students be x Let weight of female students = 57x Number of male students = 66 Total weights of male students = 65.9 × 66 Average weight of all the students = 60.3 kg Total weights of all the students = 60.3 (66 + x) According to given information, Then, $\begin{array}{l}\text{⇒ 60.3 (66 + x) = 66 × 65.9 + 57x}\\ \text{⇒ 60.3 × 66 + 60.3x = 66 × 65.9 + 57x}\\ \text{⇒ 60.3x – 57x = 66 (65.9 – 60.3)}\\ \text{⇒ 3.3x = 66 × 5.6}\\ \begin{aligned}\therefore&\mathrm{x}=\frac{66\times5.6}{3.3}\\ \Rightarrow&\mathrm{x}=2\times56\\ \Rightarrow&\mathrm{x}=112\end{aligned}\end{array}$

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