out of 80 candidates who appeared for a combined test in English and Hindi, 64 passed at least in one subject. If 45 passed in English and 52 passed in hindi. how many passed in both the subject ?

To find out how many candidates passed in both English and Hindi, we need to use the principle of Inclusion-Exclusion. Let's break down the given information:

- Total candidates = 80
- Passed in at least one subject = 64
- Passed in English (E) = 45
- Passed in Hindi (H) = 52

We need to find the number of candidates who passed in both English and Hindi (E ∩ H).

To solve this problem, we can use the formula:
n(E ∪ H) = n(E) + n(H) - n(E ∩ H), where n represents the number of elements in a set.

Substituting the given values into the formula:
64 = 45 + 52 - n(E ∩ H)

Now, let's solve for n(E ∩ H):

n(E ∩ H) = 45 + 52 - 64
n(E ∩ H) = 97 - 64
n(E ∩ H) = 33

Therefore, 33 candidates passed in both English and Hindi subjects.

If x passed both, then

45+52-x = 64