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In an examination 60% students in Mathematics and 65% students in Science were passed. While 30% students in both the subjects were failed. If total 9
Question

In an examination 60% students in Mathematics and 65% students in Science were passed. While 30% students in both the subjects were failed. If total 900 students appeared in the examination, then the total number of passed students is

A.

330

B.

435

C.

465

D.

495

Correct option is D

Given:
Passed in Mathematics = 60%
Passed in Science = 65%
Failed in both subjects = 30%
Total students = 900
Formula Used:
n(AB)=n(A)+n(B)n(AB)n(A \cup B) = n(A) + n(B) - n(A \cap B)​​
Percentage of students passed in at least one subject = 100 - Percentage of students failed in both.
Solution:
First, find the percentage of students who passed in at least one subject.
Percentage passed in at least one = 100 - 30 = 70%
Let the percentage of students who passed in both subjects be x.
70 = 60 + 65 - x
70 = 125 - x
x = 55%
The percentage of students who passed in both subjects is 55%.
Total number of passed students =  55100\frac{55}{100}​ × 900
Total number of passed students = 55 × 9 = 495
Final Answer
So the correct answer is (d)

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