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

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    Case Study : Q. 11 to 15
    Akhila went to a fair in her village. She wanted to enjoy rides on the giant wheel and play hoopla (a game in which you throw a ring on the items kept in a stall and if the ring covers any object completely you get it). The number of times she played hoopla is half the number of times she rides the giant wheel. If each ride costs Rs.3 and a game of hoopla costs Rs. 4 and she spent Rs. 20 in the fair.
    Based on the given information, give the answer of the following questions.
    The representation of given statement algebraically is:

    A) \[\text{x}-\text{2y}=0\]and \[\text{3x}+\text{4y}=\text{2}0\]

    B) \[\text{x}+\text{2y}=0\]and \[\text{3x}-\text{4y}=\text{2}0\]

    C) \[\text{x}-\text{2y}=0\]and \[\text{4x}+\text{3y}=\text{2}0\]

    D) \[None\,\, of\,\, the\,\,above\]

    Correct Answer: A

    Solution :

    Let x and y be the number of rides on the giant wheel and number of hoopla respectively played by Akhila.         
    Then, according to the given condition,                   
    \[y=\frac{x}{2}\]and \[3x+4y=20\]                
    \[\therefore \]The given situation can be algebraically represented by the following pair of the linear equations.
    \[x-2y=0\]                         ...(1)
    and       \[3x+4y=20\]                      ...(2)
    So, option [a] is correct.

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