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 Question

Marks given for correct
answer

Marks given for correct answer

True/False

1

0.25

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Question 1

If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?

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Question 2

How many questions did he guess?

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Question 3

If answer to all questions he attempted by guessing were wrong and
answered 80 correctly, then how many marks he got?

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Question 4

If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?

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  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables (Term 1)
  2. Serial order wise

Transcript

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

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.