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In a club, there are 58 members. Among them, 25 members drink tea, 23 members drink coffee and only 7 members drink both tea and coffee. What is the ratio of the number of members who drink tea or coffee but not both, to the number of members who drink neither tea nor coffee?
Explanation
To find the required ratio, we apply set theory principles based on the given data:
- Total members = 58
- Members drinking tea (T) = 25
- Members drinking coffee (C) = 23
- Members drinking both (T ∩ C) = 7
Step 1: Calculate members who drink tea or coffee but not both
Only Tea = 25 - 7 = 18
Only Coffee = 23 - 7 = 16
Sum (but not both) = 18 + 16 = 34
Step 2: Calculate members who drink neither
Total drinking at least one beverage = (Only Tea) + (Only Coffee) + (Both) = 18 + 16 + 7 = 41
Neither = Total members - Total drinking at least one = 58 - 41 = 17
Step 3: Determine the ratio
Ratio = (Tea or coffee but not both) : (Neither) = 34 : 17 = 2 : 1.
SIMILAR QUESTIONS
In a party, each person takes at least one beverage. There are three beverages in the party - tea, coffee and milk. Each beverage is consumed by 30 persons. Five persons, who take tea, also take milk. Ten persons, who take milk, also take coffee. However, no person takes tea and coffee both. How many persons are there in the party ?