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In an examination, 60% of the candidates failed in Math and 80% of the candidates failed in physics but 15% of the total candidates passed in both the subjects. If 5500 candidates fail in both the subjects, then find the total number of candidates who appeared in the examination.
1. 10000
2. 6300
3. 5600
4. 7700

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Correct Answer - Option 1 : 10000

Given:

Those who failed in Math = 60%

Those who failed in Physics = 80%

Those who passed in both Math and Physics = 15%

The total number of candidates who failed in both Math and Physics = 5500

Calculation:

Let the total number of candidates who appeared in the examination be 100%.

The total candidates who failed in at least one subject= 100% - Passed in both Math and Physics

⇒ 100% - 15%

⇒ 85%      ----(1)

The total candidates who failed in both examination = Failed in Math + Failed in Physics - Failed in at least one subject

⇒ The total number of candidates who failed in both examinations = 60 + 80 - 85

⇒ The total candidates who failed in both examinations = 55%

According to the question,

⇒ 55% ≡ 5500

⇒ 1% ≡ 100

⇒ 100% ≡ 10000

∴ The total number of candidates who appeared in the examination is 10000.

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