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In an examination paper of five questions 5% of the candidates answered all of them and 5% answered none. Of the rest 25% candidates answered only one question and 20% answered 4 question. If 396 candidates answered either 2 question or 3 question. The number of candidates that appeared for the examination was
- a)800
- b)1000
- c)850
- d)900
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In an examination paper of five questions 5% of the candidates answere...
Analysis:
To find the total number of candidates that appeared for the examination, we need to consider the percentage of candidates who answered each number of questions given in the problem.
Given Data:
- Candidates who answered all five questions: 5%
- Candidates who answered none of the questions: 5%
- Candidates who answered only one question: 25%
- Candidates who answered four questions: 20%
- Candidates who answered either two or three questions: 396
Solution:
Let's assume the total number of candidates that appeared for the examination is 'x'.
- Candidates who answered all five questions: 0.05x
- Candidates who answered none of the questions: 0.05x
- Candidates who answered only one question: 0.25x
- Candidates who answered four questions: 0.20x
- Candidates who answered either two or three questions: 396
Now, we can write the equation based on the given data:
0.05x + 0.05x + 0.25x + 0.20x + 396 = x
Solving the equation:
0.55x + 396 = x
396 = 0.45x
x = 396 / 0.45
x = 880
Therefore, the total number of candidates that appeared for the examination was 880, which is closest to option 'A' (800).
To find the total number of candidates that appeared for the examination, we need to consider the percentage of candidates who answered each number of questions given in the problem.
Given Data:
- Candidates who answered all five questions: 5%
- Candidates who answered none of the questions: 5%
- Candidates who answered only one question: 25%
- Candidates who answered four questions: 20%
- Candidates who answered either two or three questions: 396
Solution:
Let's assume the total number of candidates that appeared for the examination is 'x'.
- Candidates who answered all five questions: 0.05x
- Candidates who answered none of the questions: 0.05x
- Candidates who answered only one question: 0.25x
- Candidates who answered four questions: 0.20x
- Candidates who answered either two or three questions: 396
Now, we can write the equation based on the given data:
0.05x + 0.05x + 0.25x + 0.20x + 396 = x
Solving the equation:
0.55x + 396 = x
396 = 0.45x
x = 396 / 0.45
x = 880
Therefore, the total number of candidates that appeared for the examination was 880, which is closest to option 'A' (800).
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Community Answer
In an examination paper of five questions 5% of the candidates answere...
Let total number of candidates in Exam = a
Number of candidates answered 5 questions = a x 5% = a x 5/100 = 5a/100 = a/20
Number of candidates answered not any questions = a x 5% = a x 5/100 = 5a/100 = a/20
∴ Remaining students = a - ( a/20 + a/20) = a - ( 2a/20 ) = a - ( a/10 ) = (10a - a)/10 = 9a/10
Number of candidates answered only 1 question = ( 9a/10 ) x 25% = ( 9a/10 ) x 25/100 = 9a/40
Number of candidates answered 4 questions = ( 9a/10 ) x 20% = ( 9a/10 ) x 20/100 = 9a/50
Given number of candidates awarded either 2 questions or 3 questions = 396
⇒ a - ( a/20+ a/20 + 9a/40 + 9a/50 ) = 396
⇒ a - ( a/10 + 9a/40 + 9a/50 ) = 396
⇒ a - ( ( a x 20 + 9a x 5 + 9a x 4 )/200) = 396
⇒ a - ( ( 20a + 45a + 36a )/200) = 396
⇒ a - ( 101a/200) = 396
⇒ ( 200a - 101a)/200 = 396
⇒ ( 99a)/200 = 396
∴ a = 396 x 200/99
∴ a = 4 x 200 = 800
⇒ a = 800
Hence, number of candidates = 800
Number of candidates answered 5 questions = a x 5% = a x 5/100 = 5a/100 = a/20
Number of candidates answered not any questions = a x 5% = a x 5/100 = 5a/100 = a/20
∴ Remaining students = a - ( a/20 + a/20) = a - ( 2a/20 ) = a - ( a/10 ) = (10a - a)/10 = 9a/10
Number of candidates answered only 1 question = ( 9a/10 ) x 25% = ( 9a/10 ) x 25/100 = 9a/40
Number of candidates answered 4 questions = ( 9a/10 ) x 20% = ( 9a/10 ) x 20/100 = 9a/50
Given number of candidates awarded either 2 questions or 3 questions = 396
⇒ a - ( a/20+ a/20 + 9a/40 + 9a/50 ) = 396
⇒ a - ( a/10 + 9a/40 + 9a/50 ) = 396
⇒ a - ( ( a x 20 + 9a x 5 + 9a x 4 )/200) = 396
⇒ a - ( ( 20a + 45a + 36a )/200) = 396
⇒ a - ( 101a/200) = 396
⇒ ( 200a - 101a)/200 = 396
⇒ ( 99a)/200 = 396
∴ a = 396 x 200/99
∴ a = 4 x 200 = 800
⇒ a = 800
Hence, number of candidates = 800
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In an examination paper of five questions 5% of the candidates answered all of them and 5% answered none. Of the rest 25% candidates answered only one question and 20% answered 4 question. If 396 candidates answered either 2 question or 3 question. The number of candidates that appeared for the examination wasa)800b)1000c)850d)900Correct answer is option 'A'. Can you explain this answer?
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