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    Question

    In a group, if 3 people with an average weight of 70 kg

    leave, the average weight of the remaining group drops by 2 kg. However, if 4 people of average weight 68 kg leave, the average decreases by 2.5 kg. How many people were in the group initially?
    A 75 Correct Answer Incorrect Answer
    B 55 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 44 Correct Answer Incorrect Answer

    Solution

    ATQ,


    Let the number of people in group and average weight be 'n' and 'm' kg, respectively.

    So,

    mn - 3 × 70 = (n - 3) × (m - 2)

    ⇒ mn - 210 = mn - 2n - 3m + 6

    ⇒ 2n + 3m = 216 --------- (I)

    And,

    mn - 4 × 68 = (n - 4) × (m - 2.5)

    ⇒ mn - 272 = mn - 2.5n - 4m + 10

    ⇒ 2.5n + 4m = 282 -------- (II)

    Now solving:

    Multiply (I) by 4: 8n + 12m = 864

    Multiply (II) by 3: 7.5n + 12m = 846

    Subtracting:

    0.5n = 18

    ⇒ n = 36

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