In a group of 40 persons ,10 drinks tea but not coffee and 26 drinks tea. How many drink coffee but not tea ?

Answer

To solve the problem step by step, we can use the concept of sets and a Venn diagram. Here’s how we can approach the question:

### Step 1: Define the Sets
Let:
- Set C = Persons who drink coffee
- Set T = Persons who drink tea

### Step 2: Identify Given Information
From the problem, we know:
- Total number of persons = 40
- Persons who drink tea but not coffee = 10
- Total persons who drink tea = 26

### Step 3: Find Persons Who Drink Both Tea and Coffee
Since 26 persons drink tea in total and 10 of them drink only tea (not coffee), we can find the number of persons who drink both tea and coffee.

Using the formula:
\[ \text{Persons who drink both tea and coffee} = \text{Total tea drinkers} - \text{Tea only drinkers} \]
\[ = 26 - 10 = 16 \]

### Step 4: Set Up the Equation for Coffee Drinkers
Let \( x \) be the number of persons who drink coffee but not tea.

Now, we can set up the equation based on the total number of persons:
\[ x + \text{(Persons who drink both)} + \text{(Tea only drinkers)} = \text{Total persons} \]
\[ x + 16 + 10 = 40 \]

### Step 5: Solve for \( x \)
Now, simplify the equation:
\[ x + 26 = 40 \]
Subtract 26 from both sides:
\[ x = 40 - 26 \]
\[ x = 14 \]

### Conclusion
Thus, the number of persons who drink coffee but not tea is \( 14 \).

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