Question

In college B, each student participated in any one or both the sports, Hockey and Football. 36% of the students participated in both the sports. The number of students who participated in only Football is 120% more than those who participated in only Hockey. The total number of students who participated in only one of the sports is 960. Find the ratio of number of students who participated in hockey to those in only football?

• A. 2:21
• B. 14:11
• C. 29:49
• D. 41:31

Hint:

For problems involving overlapping sets (like sports), using algebraic expressions for each section (Only A, Only B, Both) is a very effective approach to building and solving the equations.

Answer 1

The Correct Option is B

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.
- \(B = 0.36 T\)
- \(F = H + 1.20 H = 2.2H\)
- \(H + F = 960\)
Step 2: Solve for H and F.
Substitute \(F = 2.2H\) into the third equation:
\(H + 2.2H = 960 \Rightarrow 3.2H = 960 \Rightarrow H = 300\).
Then, \(F = 960 - 300 = 660\).

Step 3: Calculate total students (T) and students in both (B).
\(T = H + F + B = 960 + 0.36T \Rightarrow 0.64T = 960 \Rightarrow T = 1500\).
\(B = 0.36 \times 1500 = 540\).

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) = \(840 : 660 = 84 : 66 = 14 : 11\).