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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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