\nThe given information is:
\n– Cricket: Batch I + Batch II + 8 = 14 => Batch I + Batch II = 6
\n– Football: Batch I + Batch II + 10 = 16 => Batch I + Batch II = 6
\n– Hockey: 6 + Batch II + 6 = 17 => Batch II = 17 – 12 = 5<\/p>\nUsing Batch II = 5 in the first two equations:
\n– Batch I + 5 = 6 => Batch I = 1
\n– Batch I + 5 = 6 => Batch I = 1 (Consistent)<\/p>\n
The number of students in each batch is the sum of players across sports:
\n– Batch I Total: Cricket (1) + Football (1) + Hockey (6) = 8
\n– Batch II Total: Cricket (5) + Football (5) + Hockey (5) = 15
\n– Batch III Total: Cricket (8) + Football (10) + Hockey (6) = 24
\n– Grand Total: 8 + 15 + 24 = 47 (Also 14 + 16 + 17 = 47)<\/p>\n
Now, evaluate the options:
\nA) Batch II is empty (Batch II has 15 students) – False
\nB) Batch I and Batch II do not have equal number of students (Batch I = 8, Batch II = 15. 8 != 15) – True
\nC) Batch I and Batch III can have equal number of students (Batch I = 8, Batch III = 24. They are not equal) – False
\nD) Batch II and Batch III can have equal number of students (Batch II = 15, Batch III = 24. They are not equal) – False
\n<\/section>\n