In an examination 75% of the total students passed in English and 65% passed in Mathematics, while 15% failed in English as well as Mathematics. If a total of 495 candidates who passed in both exams. Find the total number of students who appeared in the exam.a)850b)900c)1000d)1050Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given information:
- 75% of students passed in English.
- 65% of students passed in Mathematics.
- 15% of students failed in both English and Mathematics.
- Total number of students who passed in both exams = 495.

To find:
- Total number of students who appeared in the exam.

Solution:
Let the total number of students be x.

From the given information, we can derive the following equations:

- Number of students who passed in English = 0.75x
- Number of students who passed in Mathematics = 0.65x
- Number of students who failed in both English and Mathematics = 0.15x
- Number of students who passed in both English and Mathematics = 495

Using these equations, we can find the total number of students as follows:

- Number of students who passed in at least one subject = (Number of students who passed in English) + (Number of students who passed in Mathematics) - (Number of students who passed in both English and Mathematics)
= (0.75x) + (0.65x) - 495
= 1.4x - 495

- Number of students who failed in at least one subject = Total number of students - Number of students who passed in at least one subject
= x - (1.4x - 495)
= 495 - 0.4x

- Number of students who failed in both English and Mathematics = 0.15x

Since the number of students who failed in at least one subject is equal to the number of students who failed in both English and Mathematics, we can equate the above two equations:

0.15x = 495 - 0.4x
0.55x = 495
x = 900

Therefore, the total number of students who appeared in the exam is 900.

Answer: Option B (900).

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