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10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank Case Based (MCQs) - Pair of Linear Equations in Two Variables

  • question_answer
    Case Study : Q. 36 to 40
    A test consists of True' or 'False' questions. One mark is awarded for every correct answer while \[\frac{1}{4}\] 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 answer 120 questions and got 90 marks.
    Type of Question     Marks given for correct answer        Marks deducted for wrong answer
    True/False 1 0.25
    Based on the above information, give the answer of the following questions:
    If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?

    A) 24

    B) 96

    C) 70

    D) 100

    Correct Answer: B

    Solution :

    Let the number of questions he answered correctly be x and number of questions he answered by giving be y.
    Then,          \[x+y=120\]                    ...(1)
    and   \[x+1+y\times \left( -\frac{1}{4} \right)=90\,\,\,\,\,\,\,\Rightarrow \,\,\,x-\frac{y}{4}=90\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x-y=360\]                    ...(2)
    On solving eqs. (1) and (2), we get
    \[x=96\]    and   \[y=24\]
    Hence, he answered 96 questions correctly.
    So option [b] is correct.


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