KJSEA 2025 Maths Q24 — Proportion (Work Rate) with Man-Hours
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The Question
“Five men working six hours a day take 12 days to pack a quantity of flour. Determine how many more days three men working eight hours a day will take to pack the same amount of flour.”
Find the total work in man-hours
The size of the job never changes, so measure it in man-hours. Multiply the number of men by the hours worked each day and by the number of days. This total tells you exactly how much labour the whole job requires, no matter who does it or how they split it up.
Work out the daily rate for the new crew
The same job of 360 man-hours must now be done by three men working eight hours a day. Multiply the men by their daily hours to see how much labour they supply in one day.
Find how many days the new crew needs
Divide the fixed total work by the labour the new crew supplies each day. This gives the number of days they must work to finish the same job.
Answer the actual question — how many MORE days
The question does not ask for the total number of days, it asks how many extra days are needed compared with the original schedule. Subtract the original 12 days from the new 15 days.
Final Result
The three men working eight hours a day will take 3 more days than the original crew.
Why this method works
The job contains a fixed amount of labour, and man-hours capture that amount by combining people, hours and days into one number. Because the total man-hours is constant, fewer men or fewer hours each day must be balanced by more days. Here the second crew supplies only 24 man-hours a day instead of the original 30, so they need 15 days rather than 12. Reading the question carefully matters: it asks for the difference in days, so the final step subtracts to give 3 extra days.
Verify by re-multiplying: 3 men times 8 hours times 15 days equals 360 man-hours, matching the original total.