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    Question

    Average weight of a group of ‘x’ people increased by

    2 kg, when a person weighing 70 kg joined the group, while the average weight increased by 3 kg when two persons weighing 68 kg each joined the group. Find the value of ‘x’.
    A 4 Correct Answer Incorrect Answer
    B 5 Correct Answer Incorrect Answer
    C 6 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer

    Solution

    Number of people in the group = ‘x’
    Let, average weight of each person in the group be ‘y’ kg
    Total weight of all the persons in the group = x × y = ‘xy’ kg
    ATQ,
    (xy + 70) = (x + 1) × (y + 2)
    Or, xy + 70 = xy + y + 2x + 2
    Or, y + 2x = 68 ------------(I)
    Also,
    (xy + 68 × 2) = (x + 2) × (y + 3)
    Or, xy + 136 = xy + 2y + 3x + 6
    Or, 2y + 3x = 130 ------------(II)
    Putting value of ‘y’ from equation (I) in equation (II), we get
    y = 68 – 2x
    So, 2(68 – 2x) + 3x = 130
    Or, 136 – 4x + 3x = 130
    Or, –x = –6
    So, x = 6
    So, value of ‘x’ = 6

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