Question 1 - Case Based Questions (MCQ) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Question 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.Question 1 If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?Let Number of questions whose answer he knew = x Number of questions attempted by cheating = y Given that Total Questions attempted = 120 x + y = 120 Also, answer to all questions he attempted by guessing were wrong Marks from all guessed answers = y × (−𝟏)/𝟒 Marks from all attempted answers = x × 1 Now, Total marks = 90 x − 𝑦/4 = 90 4x − y = 90 × 4 4x − y = 360 Thus, we need to solve x + y = 120 …(1) 4x − y = 360 …(2) From (1) x + y = 120 y = 120 − x Putting value in (2) 4x − y = 360 4x − (120 − x) = 360 5x − 120 = 360 5x = 360 + 120 5x = 480 x = 480/5 x = 96 Putting value of x in (1) y = 120 − x y = 120 − 96 y = 24 Number of questions he answered correctly = x = 96 Thus, he answered 96 questions correctly Question 2 How many questions did he guess? Number of questions he guessed = y = 24 ∴ He attempted 24 questions by guessing Question 3 If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got? Given that Total questions = 120 Questions answered correctly = 80 Thus, Questions answered by guessing = 120 − 80 = 40 Now, Total Marks = Question answered correctly × 1 − 1/4 × Questions answered incorrectly = 80 × 1 − 1/4 × 40 = 70 Thus, he got 70 marks Question 4 If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks? Given that Total questions = 120 Let Questions answered correctly = x ∴ Questions answered by guessing = 120 − x Now, Total Marks = Question answered correctly × 1 − 1/4 × Questions answered incorrectly 95 = x × 1 − 1/4 × (120 − x) 95 = x − 1/4 × (120 − x) 95 × 4 = 4x − (120 − x) 380 = 4x − 120 + x 380 + 120 = 5x 500 = 5x 5x = 500 x = 500/5 x = 100 Thus, he answered 100 questions correctly