NIFT PG 2020 Question Paper with solutions

Let the number of students in classes $\mathit{A},\mathit{B}$ and $\mathit{C}$ be $\mathit{a},\mathit{b}$ and $\mathit{c}$ respectively.
(c) Let the number of students in classes $\mathit{A},\mathit{B}$ and $\mathit{C}$ be $\mathit{a},\mathit{b}$ and $\mathit{c}$ respectively.
Total score of class $\mathit{B}=76\mathit{b}$
According to the question,
$\frac{83\mathit{a}+76\mathit{b}}{\mathit{a}+\mathit{b}}=79$  $[\because$ average of $\mathit{A}$ and $\mathit{B}=79]$
$\Rightarrow 4\mathit{a}=3\mathit{b}\Rightarrow \mathit{a}=\frac{3\mathit{b}}{4}$.....(i)
Again, average of $\mathit{B}$ and $\mathit{C}=81$
$\therefore$ Average of $\mathit{A},\mathit{B}$ and $\mathit{C}=\frac{83\mathit{a}+76\mathit{b}+85\mathit{c}}{\mathit{a}+\mathit{b}+\mathit{c}}$
$=\frac{83\times \frac{3\mathit{b}}{4}+76\mathit{b}+85\times \frac{5\mathit{b}}{4}}{\frac{3\mathit{b}}{4}+\mathit{b}+\frac{5\mathit{b}}{4}}$