in class of 60 pupils 2/3 of them like chocolate as their ice cream flavor 3/4 of the class likes ube flavor.what portion of the class like both? how many pupils prefer both chocolate and ube
Answer (1)
### Given:- Total pupils = 60- (2/3) of the class likes chocolate- (3/4) of the class likes ube### Step 1: Calculate the number of pupils who like each flavor- Pupils who like **chocolate**: (2/3) × 60 = 40- Pupils who like **ube**: (3/4) × 60 = 45### Step 2: Apply the principle of inclusion-exclusionTo find the number of pupils who like **both** chocolate and ube, use the inclusion-exclusion formula: Total who like chocolate or ube = (Chocolate) + (Ube) - (Both)Since the total number of pupils is 60: 60 = 40 + 45 - (Both)Solving for **Both**: (Both) = 40 + 45 - 60 = 25### Step 3: Result- **25 pupils** like both chocolate and ube.- The portion of the class that likes both is: (25/60) = (5/12)### Final Check:- Total pupils = 60- Pupils who like chocolate = 40- Pupils who like ube = 45- Pupils who like both = 25The total number of pupils who like either chocolate or ube is: 40 + 45 - 25 = 60 (which matches the total number of pupils).### Conclusion:- The number of pupils who like both chocolate and ube is 25.- The portion of the class that likes both is (5/12).
