In an examination 54 of the candidates passed in science and 42 failed in mathematics If 32 failed i...........

Quantitative Aptitude (CPO) Percentage

In an examination, 54 % of the candidates passed in science and 42 % failed in mathematics. If 32% failed in both 14 subjects, what

percentage passed in both subjects?

This questions was previously asked in

SSC CPO 12th-March-2019-Shift-1

32%

56%

44%

48%

- To solve this, apply the principle of inclusion-exclusion.

- Let S be the set of students who passed in science, and M be those who passed in mathematics.

- The set of students who passed in both is represented by |S n M|.

- Given, 54% passed in science, so 46% failed in science.

- 42% failed in mathematics, so 58% passed.

- 32% failed in both subjects.

- Using the formula: |S| + |M| - |S n M| = Total percentage who passed at least one subject.

- Substitute the known values: 54% + 58% - |S n M| = 100 - 32.

- Solve: 112 - |S n M| = 68, hence |S n M| = 44%.

The correct option is: Option 3 – 44%

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