Question:
In a staff room of 25 teachers, 13 drink black coffee, 7 milk coffee, 9 drink both tea and either type of coffee, and everyone drinks either of the beverages. How many teachers drink only tea?
In a staff room of 25 teachers, 13 drink black coffee, 7 milk coffee, 9 drink both tea and either type of coffee, and everyone drinks either of the beverages. How many teachers drink only tea?
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Use Venn diagram-style logic for problems involving overlapping groups. Separate into only A, only B, and both, then use total to find the missing group.
Updated On: Aug 11, 2025
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The Correct Option is B
Solution and Explanation
Step 1: Total teachers = 25
Let: \[ B = \text{Black coffee} = 13, \quad M = \text{Milk coffee} = 7, \quad T = \text{Drink tea and either coffee} = 9 \] We are told that: - Everyone drinks tea or coffee. - 9 drink both tea and any type of coffee. - We must find the number of teachers who drink only tea. Step 2: Total who drink coffee (black or milk)
We must count unique coffee drinkers: \[ \text{Total coffee drinkers} = 13 + 7 = 20 \quad \text{(but may include overlaps)} \] Step 3: Assume no overlap between black and milk coffee
Then 20 drink coffee, and 9 among these also drink tea. So total who drink coffee = 20
Among them, 9 also drink tea
So, only coffee drinkers = \(20 - 9 = 11\) Step 4: Total = Only coffee + both + only tea
\[ 25 = 11 (\text{only coffee}) + 9 (\text{both}) + x (\text{only tea}) \Rightarrow x = 25 - 20 = \boxed{5} \] % Final Answer \[ \boxed{5} \]
Let: \[ B = \text{Black coffee} = 13, \quad M = \text{Milk coffee} = 7, \quad T = \text{Drink tea and either coffee} = 9 \] We are told that: - Everyone drinks tea or coffee. - 9 drink both tea and any type of coffee. - We must find the number of teachers who drink only tea. Step 2: Total who drink coffee (black or milk)
We must count unique coffee drinkers: \[ \text{Total coffee drinkers} = 13 + 7 = 20 \quad \text{(but may include overlaps)} \] Step 3: Assume no overlap between black and milk coffee
Then 20 drink coffee, and 9 among these also drink tea. So total who drink coffee = 20
Among them, 9 also drink tea
So, only coffee drinkers = \(20 - 9 = 11\) Step 4: Total = Only coffee + both + only tea
\[ 25 = 11 (\text{only coffee}) + 9 (\text{both}) + x (\text{only tea}) \Rightarrow x = 25 - 20 = \boxed{5} \] % Final Answer \[ \boxed{5} \]
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