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In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.
Correct answer is '116450'. Can you explain this answer?
Verified Answer
In an examination, 65% of the candidates passed in Mathematics, 55% pa...
Let the percentage total number of candidates who passed in both the subjects be x.
Let the sets M and H represent students who passed in Mathematics and History respectively.
Let the sets M and H represent students who passed in Mathematics and History respectively.
65 - x + x + 55 - x = 100 - 22
x = 42%
Now, 42% i.e. 48909 students passed in both the subjects.
Now, 42% i.e. 48909 students passed in both the subjects.
Answer: 116450
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Most Upvoted Answer
In an examination, 65% of the candidates passed in Mathematics, 55% pa...
Given:
- 65% candidates passed in Mathematics
- 55% candidates passed in History
- 22% candidates failed in both subjects
- 48909 candidates passed in both subjects
To find:
- Total number of candidates
Solution:
Let the total number of candidates be x.
Number of candidates who passed in Mathematics = 65% of x = 0.65x
Number of candidates who passed in History = 55% of x = 0.55x
Number of candidates who failed in both subjects = 22% of x = 0.22x
Number of candidates who passed in at least one subject = Total number of candidates - Number of candidates who failed in both subjects
= x - 0.22x
= 0.78x
Number of candidates who passed in both subjects = 48909
Using the formula for the union of two sets,
Total number of candidates who passed in at least one subject = Number of candidates who passed in Mathematics + Number of candidates who passed in History - Number of candidates who passed in both subjects
0.78x = 0.65x + 0.55x - 48909
0.78x - 1.2x = -48909
-0.42x = -48909
x = 116450
Therefore, the total number of candidates is 116450.
- 65% candidates passed in Mathematics
- 55% candidates passed in History
- 22% candidates failed in both subjects
- 48909 candidates passed in both subjects
To find:
- Total number of candidates
Solution:
Let the total number of candidates be x.
Number of candidates who passed in Mathematics = 65% of x = 0.65x
Number of candidates who passed in History = 55% of x = 0.55x
Number of candidates who failed in both subjects = 22% of x = 0.22x
Number of candidates who passed in at least one subject = Total number of candidates - Number of candidates who failed in both subjects
= x - 0.22x
= 0.78x
Number of candidates who passed in both subjects = 48909
Using the formula for the union of two sets,
Total number of candidates who passed in at least one subject = Number of candidates who passed in Mathematics + Number of candidates who passed in History - Number of candidates who passed in both subjects
0.78x = 0.65x + 0.55x - 48909
0.78x - 1.2x = -48909
-0.42x = -48909
x = 116450
Therefore, the total number of candidates is 116450.
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In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer?.
In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer?.
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In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer?, a detailed solution for In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? has been provided alongside types of In an examination, 65% of the candidates passed in Mathematics, 55% passed in History, 22% failed in both the subjects and 48909 passed in both the subjects. Find the total number of candidates.Correct answer is '116450'. Can you explain this answer? theory, EduRev gives you an
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