Out of 32 people, 30 people save paper and 14 people save plastic bottles. What is the total number of people who save both paper and plastic bottles? Assume all people save either paper or plastic bottles or both paper and plastic bottles.

Correct option is A

Let:
· Total people = 32
· People who save paper = 30
· People who save plastic bottles = 14
· People who save both = x
Since everyone saves paper or plastic or both, we use the Inclusion–Exclusion Principle:
∣P∪B∣ = ∣P∣ + ∣B∣ − ∣P∩B∣
Here:
32 = 30 + 14 − x
Therefore:
x = 30 + 14 − 32
x = 12
Hence, the number of people who save both paper and plastic bottles is 12.
Information Booster
1. Inclusion–Exclusion Principle for two sets:
∣A∪B∣ = ∣A∣ + ∣B∣ − ∣A∩B∣
2. The phrase "either A or B or both" means A ∪ B contains the entire population.
Additional Knowledge
A quick Venn-diagram check:
· Paper only:
30 – 12 = 18
· Plastic only:
14 – 12 = 2
· Both:
12
Total:
18 + 12 + 2 = 32
So, the result is consistent.