There were 120 multiple choice questions.a candidate was given 1mark for each correct answercand penalised ¼ mark for every wrong answer.the candidate answered all the questions and scored 80marks.find the number of correct answers given by the candidate.
If there were x correct answers, then there were (120-x) incorrect answers. So,
x - (120-x)/4 = 80
To find the number of correct answers given by the candidate, we need to set up an equation based on the given information.
Let's assume that the candidate answered "x" questions correctly. Since there are 120 multiple-choice questions in total, the candidate would have answered (120 - x) questions incorrectly.
According to the scoring system, the candidate receives 1 mark for every correct answer and is penalized 1/4 mark for every wrong answer.
So, the candidate's total score can be calculated as follows:
Score = (marks for correct answers) - (penalty for wrong answers)
80 = x - (1/4)(120 - x)
Now, let's solve this equation to find the value of x, which represents the number of correct answers given by the candidate.
80 = x - (1/4)(120 - x)
Let's simplify the equation and solve for x:
80 = x - 30 + (1/4)x
Combining like terms:
80 = (5/4)x - 30
Add 30 to both sides:
110 = (5/4)x
Now, multiply both sides by (4/5) to isolate x:
x = (110 * 4) / 5
x = 88
Therefore, the candidate answered 88 questions correctly.