a + b + c + d + e + f + g = 1200
a = 360, b = 240, and c = 300
e = 20/100 * 300 = 60
The number of students who play both cricket and volleyball but not football is 50% more than the number of students who play both football and cricket but not volleyball.
=> f = 150/100 * e = 150/100 * 60 = 90
The number of students who play all three sports together is one third of the number of students who play both cricket and volleyball but not football.
g = 1/3 * 90 = 30
Number of people who play both football and volleyball but not cricket is twice of the students who play both football and cricket but not volleyball.
d = 2 * e = 2 * 60 = 120
Required average = (300 + 240)/2 = 270
Study Notes
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