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      Question

      6 women and 4 children can complete a piece of work in

      12 days. If 3 more women join them, they can finish 3/5 of the work in 6 days. Find the time taken by 18 women to complete the entire work.
      A 16 days Correct Answer Incorrect Answer
      B 28 days Correct Answer Incorrect Answer
      C 10 days Correct Answer Incorrect Answer
      D 17 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      (6W + 4C) × 12 = (6W + 4C + 3W) × [1/(3/5)] × 6

      (72W + 48C) = (9W + 4C) × (5/3) × 6

      (9W + 4C) × 10 = 90W + 40C

      So, 72W + 48C = 90W + 40C

      48C - 40C = 90W - 72W

      8C = 18W

      1W = (8/18)C = (4/9)C

      Now convert all to C:

      (6W + 4C) = (6 × 4/9 + 4)C = (24/9 + 4)C = (24 + 36)/9 = 60/9 = 20/3 C

      Work = (20/3 C) × 12 = 80C

      Now, 18W = 18 × (4/9)C = 8C

      So, time = 80C / 8C = 10 days

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