In a survey of a group of 180  students, 50 students say to like cricket game only, 30 students say to like basketball game only and 50 students say do not like both games.

Let, the set of students who like cricket be C and the set of students who like basketball be B.

Then, n(U) = 180, n_o(C) = 50, n_o(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 

n_o(C) + n_o(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) = n_o(C)  + n(C∩B) = 50 + 50 = 100

And, n(B) = n_o(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