In a sports survey of 150 students, determine the ratio of students who play Cricket to those who play Badminton.

Play Cricket and Badminton: 30
Play Cricket but not Badminton: 50
Play Badminton but not Cricket: 40
Play neither sport: 30

The correct option is 8:7.

To find the ratio of students who play Cricket to those who play Badminton, we first need to calculate the total number of students playing each sport based on the given survey data.

Let us define the sets of students as follows:
- Number of students who play both Cricket and Badminton = 30
- Number of students who play Cricket but not Badminton = 50
- Number of students who play Badminton but not Cricket = 40

Step 1: Calculate the total number of students who play Cricket
The total number of Cricket players is the sum of students who play Cricket only and those who play both sports.

Total Cricket players = (Play Cricket but not Badminton) + (Play Cricket and Badminton)

$\text{Total Cricket players}=50+30=80$

Step 2: Calculate the total number of students who play Badminton
The total number of Badminton players is the sum of students who play Badminton only and those who play both sports.

Total Badminton players = (Play Badminton but not Cricket) + (Play Cricket and Badminton)

$\text{Total Badminton players}=40+30=70$

Step 3: Determine the required ratio
Now, we find the ratio of students who play Cricket to students who play Badminton.

$\text{Ratio}=\frac{\text{Total Cricket players}}{\text{Total Badminton players}}=\frac{80}{70}=\frac{8}{7}$

Thus, the ratio of students who play Cricket to those who play Badminton is 8:7.