In an examination, there are a hundred questions. For each correct answer four marks will be awarded and for each wrong answer two marks will deduct while for each un-attempted one mark will deduct. If a student scored 320 marks, then what could be the maximum number of wrongly answered questions attempted by the students.

Solution

Least number of corrected questions = 320/4=80 Number of correctly answered questions must be greater than 80  Maximum number of correctly answer is 86 as If the correctly answered question is above 86 then there are only 13 maximum questions are wrong which does not give the marks 320 So, possible number of correctly answered question is 84, 85, 86 So, taking number of correctly answered question = 84  Marks scored from 84 question = 336 So, only 16 marks is deducted from the wrongly answered and attempted which is not possible Let the number of un-attempted question be x and the un answered questions be y ATQ, 2x + y = 16 x + y =  16 On solving  x = 0 y = 16 So, taking number of correctly answered question = 85  Marks scored from 85 question = 340 So only 20 marks is deducted from the wrongly answered and attempted which is not possible Let the number of un-attempted question be a and the un answered questions be b ATQ, 2a + b = 20 a + b = 15 On solving above equation number of questions unattempt are more than wrongly answered. So, taking number of correctly answered question = 86 Marks scored from 86 question = 344 So only 24 marks is deducted from the wrongly answered and attempted which is not possible Let the number of un-attempted question be c and the unattempt questions be d ATQ, 2c + d = 24 c + d = 14 On solving above equation  c = 10 d = 4 So possible maximum number of wrongly answered question is 10