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In Ngamongo village, a piece of work can be completed by 45 workers in 10 days. They worked for 4 days after which 15 workers were laid off. How many days could it take the remaining workers to comple

Mathematics

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In Ngamongo village, a piece of work can be completed by 45 workers in 10 days. They worked for 4 days after which 15 workers were laid off. How many days could it take the remaining workers to complete the work?

  1. Calculate the total amount of work in worker-days.

    Total work = Number of workers ×\times Total days

    Total work=45 workers×10 days=450 worker-days\text{Total work} = 45 \text{ workers} \times 10 \text{ days} = 450 \text{ worker-days}
  2. Calculate the work done in the first 4 days.

    Work done = Number of workers ×\times Days worked

    Work done=45 workers×4 days=180 worker-days\text{Work done} = 45 \text{ workers} \times 4 \text{ days} = 180 \text{ worker-days}
  3. Calculate the remaining work.

    Remaining work = Total work - Work done

    Remaining work=450 worker-days−180 worker-days=270 worker-days\text{Remaining work} = 450 \text{ worker-days} - 180 \text{ worker-days} = 270 \text{ worker-days}
  4. Calculate the number of remaining workers.

    Workers laid off = 15
    Remaining workers = Original workers - Workers laid off

    Remaining workers=45−15=30 workers\text{Remaining workers} = 45 - 15 = 30 \text{ workers}
  5. Calculate the time taken by the remaining workers to complete the remaining work.

    Time = Remaining work / Remaining workers

    Time=270 worker-days30 workers=9 days\text{Time} = \frac{270 \text{ worker-days}}{30 \text{ workers}} = 9 \text{ days}

    The remaining workers could take 9 days\boxed{9 \text{ days}} to complete the work.


    The table shows marks obtained by a form three class in a certain school.
    Marks (x): 2, 6, 8, 3, 1
    No. of students (f): 9, 6, 8, 3, 1

    Assuming the question asks for the mean mark:

  6. Create a table to calculate fxfx and ∑f\sum f.

    Marks (x)No. of students (f)fxfx
    2918
    6636
    8864
    339
    111
  7. Calculate the sum of frequencies (∑f\sum f).

    ∑f=9+6+8+3+1=27\sum f = 9 + 6 + 8 + 3 + 1 = 27
  8. Calculate the sum of (fxfx) values (∑fx\sum fx).

    ∑fx=18+36+64+9+1=128\sum fx = 18 + 36 + 64 + 9 + 1 = 128
  9. Calculate the mean mark (xˉ\bar{x}).

    The formula for the mean of a frequency distribution is xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}.

    xˉ=12827\bar{x} = \frac{128}{27} xˉ≈4.7407\bar{x} \approx 4.7407

    The mean mark is approximately 4.74\boxed{4.74}.

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