a) 700
b) 720
c) 900
d) 960
Answer: d
Explanation:
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,{\text{A}}:{\text{B}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,5:3 \cr
& {\text{Let }}5x:3x = 8x \cr
& \Rightarrow {\text{New comers}} \cr
& 5y:7y = 12y \cr
& 8x + 12 = 1200 \cr
& \Rightarrow 2x + 3y = 300……(i) \cr
& {\text{Again,}}\frac{{5x + 5y}}{{3x + 7y}} = \frac{7}{5} \cr
& 25x + 25y = 21x + 49y \cr
& \Rightarrow 4x – 24y = 0 \cr
& \Rightarrow 4x = 24y \cr
& \Rightarrow x = 6y………..(ii) \cr
& {\text{From equation }}…….(i) \cr
& 12y + 3y = 300 \cr
& y = 20 \cr
& x = 6 \times 20 = 120 \cr} $$
The number of students initially
8x = 8 × 120 = 960
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