If 25% of a group of 200 people like sports, 15% like music, and 5% like both, w
Practice Questions
Q1
If 25% of a group of 200 people like sports, 15% like music, and 5% like both, what percentage of people like only sports?
20%
15%
10%
5%
Questions & Step-by-Step Solutions
If 25% of a group of 200 people like sports, 15% like music, and 5% like both, what percentage of people like only sports?
Step 1: Determine the total number of people in the group, which is 200.
Step 2: Calculate the number of people who like sports. Since 25% of 200 like sports, multiply 200 by 0.25 to get 50 people.
Step 3: Calculate the number of people who like music. Since 15% of 200 like music, multiply 200 by 0.15 to get 30 people.
Step 4: Calculate the number of people who like both sports and music. Since 5% of 200 like both, multiply 200 by 0.05 to get 10 people.
Step 5: To find the number of people who like only sports, subtract the number of people who like both from the number of people who like sports. So, 50 (like sports) - 10 (like both) = 40 people who like only sports.
Step 6: To find the percentage of people who like only sports, divide the number of people who like only sports (40) by the total number of people (200) and multiply by 100. So, (40 / 200) * 100 = 20%.
Percentage Calculation – Understanding how to calculate percentages from a total and how to apply them to subsets of a group.
Set Theory – Applying the principles of set theory to determine the number of people in overlapping categories (like both sports and music).
