In an examination 30 of the total students failed in Hindi 45 failed in Enlish and 20 failed in both...........

Quant (SSC) Percentage

In an examination, 30% of the total students failed in Hindi, 45% failed in Enlish and 20% failed in both subjects. Find the percentage of those who passed in both subjects.

35.7%

35%

40%

45%

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Explanation:

Let the number of students be 100.

Number of students who failed in Hindi is 30%

∴ n(H) = 30

Number of students who failed in English is 45%

∴ n(E) = 45

Number of students who failed in both the subjects is 20%

n(H ∩ E) = 20

Applying the set theory rule,

n (H U E) = n(H) + n(E) – n(H ∩ E)

= 30 + 45 – 20 = 55

∴ Percentage of students who failed in Hindi or English or both the subjects = 55%
∴ Number of students who passed in both the subjects = 100 – 55 = 45%