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9 men can do a piece of work in 21 days. The number of men required to complete the same work in 3 days is:
64
62
67
63
63
Since the time is reduced to 71th of the original days (from 21 days to 3 days), the required number of men must be multiplied by 7: 9×7=63.
Number of men M1=9, Number of days D1=21 days, Target days D2=3 days
M1×D1=M2×D2
Since the time is reduced to 71th of the original days (from 21 days to 3 days), the required number of men must be multiplied by 7: 9×7=63.
Students often accidentally apply direct proportion instead of inverse proportion (e.g., setting up D1M1=D2M2), getting a fractional value instead of multiplying.
Identify the Given Information
Note down the number of men and days provided in the initial condition, and the target days for the second condition.
M1=9,D1=21,D2=3
Apply the Men-Days Formula
Total work done remains constant, so the inverse proportion relationship M1D1=M2D2 applies.
M1×D1=M2×D2
Substitute the Values
Substitute M1=9, D1=21, and D2=3 into the equation to solve for M2.
9×21=M2×3
Solve for M2
Divide the total work units (9×21=189) by 3 to find the required number of men.
M2=39×21=63
D is correct because solving M2=39×21 yields 63 men.
Whenever work done remains constant, men/workers and days are inversely proportional (M∝D1); you can extend this to include hours per day and efficiency using M1D1H1E1=M2D2H2E2.
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