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Q7 (IAS/2008) Miscellaneous & General Knowledge › Important Days, Places & Events › Important Days, Places & Events

In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II: 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students?

Result
Your answer: —  Â·  Correct: A
Explanation

To find the total number of students, we use the principle of set theory.

Step 1: Determine the percentage of students who passed at least one subject.
Since 15% of students failed in both papers, the percentage of students who passed at least one paper is:
100% - 15% = 85%

Step 2: Calculate the percentage of students who passed in both papers.
Let P(I) be those passing Paper I and P(II) be those passing Paper II.
Using the formula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
85% = 70% + 60% - n(Both)
85% = 130% - n(Both)
n(Both) = 130% - 85% = 45%

Step 3: Calculate the total number of students.
We are given that 270 students passed in both papers, which represents 45% of the total.
If T is the total number of students:
45% of T = 270
T = (270 × 100) / 45
T = 600

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