A test consists of ‘True’ or ‘False’ questions. One mark is aw

1.	A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while ¼ mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.Type of QuestionMarks given for correctanswerMarks deducted forwrong answerTrue/False10.25 1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?2. How many questions did he guess?3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?
Answer» Let the no of questions whose answer is known to the student x and questions attempted by cheating be y x + y =120 x - 1/4y = 90 solving these two x = 96 and y = 24 1. He answered 96 questions correctly. 2. He attempted 24 questions by guessing 3. Marks = 80- 1/4 of 40 =70 4. x – 1/4 of (120 - x) = 95 5x = 500, x = 100

A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while ¼ mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.Type of QuestionMarks given for correctanswerMarks deducted forwrong answerTrue/False10.25 1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?2. How many questions did he guess?3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?

Answer»

Let the no of questions whose answer is known to the student x and questions attempted by cheating be y

x + y =120

x - 1/4y = 90

solving these two

x = 96 and y = 24

1. He answered 96 questions correctly.

2. He attempted 24 questions by guessing

3. Marks = 80- 1/4 of 40 =70

4. x – 1/4 of (120 - x) = 95

5x = 500, x = 100