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1. The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was

A. 162

B. 108

C. 96

D. 54

Solution:

Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x + 3x + 4x = 9x

\begin{aligned} According to the question, \\ \frac{2 x + 12}{3 x + 12} = \frac{8}{11} \\ o r, 24 x + 96 = 22 x + 132 \\ o r, 2 x = 132 - 96 \\ o r, x = \frac{36}{2} = 18 \\ Hence, \\ Original number of students, \\ 9 x = 9 \times 18 \\ = 162 \end{aligned}

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