Let, the set of students who like cricket be C and the set of students who like basketball be B.
Then, n(U) = 180, no(C) = 50, no(B) = 30 and \(n\left(\overline{C\cup B}\right)\) = 50
To find: n(C):n(B) = ?
Let, n(C∩B) = x.
Now, representing above information in Venn-diagram we get,
From above Venn-diagram
no(C) + no(B) + n(C∩B) + \(n\left(\overline{C\cup B}\right)\) = n(U)
Or, 50 + 30 + x + 50 = 180
Or, 130 + x = 180
Or, x = 180 - 130
Or, x = 50
∴ n(C∩B) = x = 50
Here, n(C) = no(C) + n(C∩B) = 50 + 50 = 100
And, n(B) = no(B) + n(C∩B) = 30 + 50 = 80
So, n(C):n(B) = 100:80 = \(\frac54\) = 5:4
Hence, the ratio of the students who like cricket game and basketball game is 5:4