In a club 45% plays cricket, 20% plays only football. Find the percentage of members who plays only cricket if 10% play both. (Each plays at least one).

Answer

To solve the problem step by step, we will use the information provided and apply the concepts of set theory.

### Step 1: Understand the given information
We have the following percentages:
- Percentage of members who play cricket (P(A)) = 45%
- Percentage of members who play only football (P(B - A)) = 20%
- Percentage of members who play both cricket and football (P(A ∩ B)) = 10%

### Step 2: Find the percentage of members who play only cricket
To find the percentage of members who play only cricket (P(A - B)), we can use the formula:
\[ P(A) = P(A - B) + P(A ∩ B) \]

Where:
- P(A) = Percentage of members who play cricket
- P(A - B) = Percentage of members who play only cricket
- P(A ∩ B) = Percentage of members who play both cricket and football

### Step 3: Rearranging the formula
We can rearrange the formula to find P(A - B):
\[ P(A - B) = P(A) - P(A ∩ B) \]

### Step 4: Substitute the known values
Now, we substitute the known values into the rearranged formula:
\[ P(A - B) = 45\% - 10\% \]

### Step 5: Calculate P(A - B)
Now we perform the calculation:
\[ P(A - B) = 35\% \]

### Conclusion
The percentage of members who play only cricket is **35%**.