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. 31 to 35
    Mr Gaurav decided to go to a amusement park along with his family. The cost of a entry ticket is Rs. 25.00 for children and Rs.50.00 for adults. On that particular day, attendance at the circus is 2,000 and the total gate revenus is Rs. 70,000.
    Based on the given information, give the answer of the following questions:
    If we let the number of children and adults who bought ticket on that day as x and y respectively, form the pair of Linear equations describing the above situation are given as:

    A) \[\text{x}+\text{ y}=\text{2}000\]and \[x+2y=2800\]

    B) \[\text{x}+\text{2y}=\text{2}000\]and \[\text{x}+\text{y}=\text{28}00\]

    C) \[\text{2x}+\text{y}=\text{2}000\]and \[\text{x}+\text{y}=\text{28}00\]

    D) \[\text{x}+y=\text{2}000\]and \[\text{2x}+\text{y}=\text{28}00\]

    Correct Answer: A

    Solution :

    We have, x = the number of children and y = the number of adults who visited the amusement park on that particular day.
    The total attendance = 2,000.
    Therefore,    \[x+y=2000\]                   ... (1)
    As the ticket for a child is Rs.25 and for an adult is Rs.50, the total revenue is:
    Dividing both sides by 25, we get
    \[x+2y=2800\]                     ...(2)
    Hence, the system of linear equations describing the given situation is \[x+y=2000\]and \[x+2y=2800\].
    So, option [a] is correct.

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