# In a school examination, in which 3000 students appeared, 30% failed in mathematics, 25% failed in English while 20% failed in both the subjects. The

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In a school examination, in which 3000 students appeared, 30% failed in mathematics, 25% failed in English while 20% failed in both the subjects. The number of students who passed in either of the subjects but not in both is

1. 150
2. 200
3. 300
4. 450

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Correct Answer - Option 4 : 450

Given:

Total number of students 3000

30% failed in mathematics, 25% failed in English,

20% failed in both the subjects

Formula Used:

n(AUB) = n(A) + n(B) – n(AnB),

where,

n(A) is number of A,

n(B) is number of B,

n(AnB) is number of A intersection of B,

n(AUB) is number of A union B

Calculation:

Out of 100%, 30% failed in mathematics,

⇒ 100 – 30% = 70% passed in mathematics,

Out of 100%, 25% failed in english,

⇒ 100 – 25% = 75% passed in english,

Out of 100%, 20% failed in both the subjects,

⇒ 100 – 20% = 80% passed in both the subjects

Using the formula,

⇒ n(AUB) = 70 + 75 – 80

⇒ n(AUB) = 65%

65% passed in both subjects,

Number of students passed in both subjects,

⇒ 65% of 3,000

⇒ 65\100 × 3,000

⇒ 65 × 30

⇒ 1,950

Number of students passed in mathematics,

⇒ 70% of 3,000

⇒ 70/100 × 3,000

⇒ 2,100

Number of students passed in English,

⇒ 75% of 3,000

⇒ 75/100 ×  3,000

⇒ 2,250

Number of students only passed in Mathematics,

⇒ 2,100 – 1,950 = 150

Number of students only passed in English,

⇒ 2,250 – 1,950 = 300

Total number of students passed in either of the subjects,

⇒ 150 + 300 = 450

∴ Total number of students is 450.