In a group of 70 persons, 37 like coffee and 52 like tea. Each person like atleast one drink. Find how many persons like both drink ?

Answer

To solve the problem step by step, we can use the principle of inclusion-exclusion.

### Step 1: Define the sets
Let:
- \( C \) = the number of persons who like coffee = 37
- \( T \) = the number of persons who like tea = 52
- \( N \) = the total number of persons = 70
- \( x \) = the number of persons who like both coffee and tea

### Step 2: Use the principle of inclusion-exclusion
According to the principle of inclusion-exclusion, the total number of persons who like at least one of the drinks can be expressed as:
\[ N = C + T - x \]
Substituting the values we have:
\[ 70 = 37 + 52 - x \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 70 = 89 - x \]

### Step 4: Solve for \( x \)
Rearranging the equation to solve for \( x \):
\[ x = 89 - 70 \]
\[ x = 19 \]

### Conclusion
Thus, the number of persons who like both coffee and tea is \( \boxed{19} \).

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