Discussion
The maximum possible number of students who passed in both Hindi and Marathi in three divisions combined is :
Answer: A
The maximum possible number is 93.
In each division, the number passing both Hindi and Marathi can be at most the smaller of the two counts. The maximum for the three divisions combined is the sum of these:
\[ \begin{aligned} A &: \min(30, 38) = 30 \\ B &: \min(32, 36) = 32 \\ C &: \min(34, 31) = 31 \\ \text{Total} &= 30 + 32 + 31 = 93 \end{aligned} \]
96 is the total of the Hindi column (30 + 32 + 34), but division C has only 31 Marathi passers, so all 34 Hindi passers there cannot have passed Marathi. 105 is the Marathi total and 111 adds larger figures still, both impossible for the same reason.
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