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.
