Set Theory

Step 1: Set up variables and equations from the given data. Let H = students in only Hockey, F = students in only Football, B = students in both. Total = T.
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Step 2: Solve for H and F.
Substitute into the third equation:
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Then, .

Step 3: Calculate total students (T) and students in both (B).
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Step 4: Calculate the values needed for the ratio.
Total students in Hockey = (Only Hockey) + (Both) = H + B = 300 + 540 = 840.
Students in only Football = F = 660.

Step 5: Find the ratio.
Ratio = (Total Hockey) : (Only Football) = .