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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
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- 800
- 1000
- 850
- 900
Correct Option: A
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
