In an examination, 65% of students passed in Mathematics, 55% passed in Physics, and 40% passed in both. What percentage of students failed in both subjects?

Question

Accepted Answer

Venn diagram concepts (Set Theory) are very important for the DDCET aptitude section.

### Formula:
$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$

### Step-by-Step Solution:
1. Let $M$ be the set of students who passed Mathematics: $n(M) = 65\%$
2. Let $P$ be the set of students who passed Physics: $n(P) = 55\%$
3. Let the percentage who passed in both be $n(M \cap P) = 40\%$
4. Calculate the percentage of students who passed in **at least one** subject ($n(M \cup B)$):
   $$n(M \cup P) = 65 + 55 - 40 = 80\%$$
5. Calculate the percentage of students who **failed in both** subjects:
   $$	ext{Failed in both} = 100\% - 	ext{Passed in at least one}$$
   $$	ext{Failed in both} = 100\% - 80\% = 20\%$$

**Answer:** **20%** of students failed in both subjects.

In an examination, 65% of students passed in Mathematics, 55% passed in Physics, and 40% passed in both. What percentage of students failed in both subjects? - DDCET Q&A

In an examination, 65% of students passed in Mathematics, 55% passed in Physics, and 40% passed in both. What percentage of students failed in both subjects?

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