In a club having 100 members, 20 play carrom, 24 play table -tennis and 16 play cricket and the remaining members do not play any game. No member plays more than one game. Find the ratio of the number of members who play.
a. Carrom to the number of those who play table tennis.
b. Cricket to the number of those who play carrom.
c. Cricket to the number of those who do not play any game.
d. Table tennis to the number of those who do not play any game.
e. Some game to the number of those who do not play any game.

Answer

To solve the problem step by step, we will analyze the given data and calculate the required ratios.

### Given Data:
- Total members in the club = 100
- Members who play Carrom = 20
- Members who play Table Tennis = 24
- Members who play Cricket = 16

### Step 1: Calculate the number of members who do not play any game.
To find the number of members who do not play any game, we first calculate the total number of members who play games.

Total members who play games = Members who play Carrom + Members who play Table Tennis + Members who play Cricket

Total members who play games = 20 + 24 + 16 = 60

Now, we can find the number of members who do not play any game:

Members who do not play any game = Total members - Total members who play games

Members who do not play any game = 100 - 60 = 40

### Step 2: Find the ratio of members who play Carrom to those who play Table Tennis.
The ratio of members who play Carrom to those who play Table Tennis is given by:

Ratio (Carrom: Table Tennis) = Members who play Carrom : Members who play Table Tennis

Ratio (Carrom: Table Tennis) = 20 : 24

To simplify, we divide both numbers by 4:

Ratio (Carrom: Table Tennis) = 5 : 6

### Step 3: Find the ratio of members who play Cricket to those who play Carrom.
The ratio of members who play Cricket to those who play Carrom is:

Ratio (Cricket: Carrom) = Members who play Cricket : Members who play Carrom

Ratio (Cricket: Carrom) = 16 : 20

To simplify, we divide both numbers by 4:

Ratio (Cricket: Carrom) = 4 : 5

### Step 4: Find the ratio of members who play Cricket to those who do not play any game.
The ratio of members who play Cricket to those who do not play any game is:

Ratio (Cricket: No Game) = Members who play Cricket : Members who do not play any game

Ratio (Cricket: No Game) = 16 : 40

To simplify, we divide both numbers by 8:

Ratio (Cricket: No Game) = 2 : 5

### Step 5: Find the ratio of members who play Table Tennis to those who do not play any game.
The ratio of members who play Table Tennis to those who do not play any game is:

Ratio (Table Tennis: No Game) = Members who play Table Tennis : Members who do not play any game

Ratio (Table Tennis: No Game) = 24 : 40

To simplify, we divide both numbers by 8:

Ratio (Table Tennis: No Game) = 3 : 5

### Step 6: Find the ratio of members who play any game to those who do not play any game.
The total number of members who play any game is 60 (from Step 1). The number of members who do not play any game is 40.

Ratio (Some Game: No Game) = Members who play any game : Members who do not play any game

Ratio (Some Game: No Game) = 60 : 40

To simplify, we divide both numbers by 20:

Ratio (Some Game: No Game) = 3 : 2

### Summary of Ratios:
a. Carrom to Table Tennis = 5 : 6
b. Cricket to Carrom = 4 : 5
c. Cricket to No Game = 2 : 5
d. Table Tennis to No Game = 3 : 5
e. Some Game to No Game = 3 : 2