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44 men can do a piece of work in 48 days. The number of men required to complete the same work in 8 days is:
260
264
266
261
264
Use the inverse proportion formula M1×D1=M2×D2. Since the number of days decreases from 48 to 8 (a factor of 6), the number of men must increase by a factor of 6 (44×6=264).
44 men can complete the work in 48 days. We need to find the number of men required to complete the same work in 8 days.
M1×D1=M2×D2
Use the inverse proportion formula M1×D1=M2×D2. Since the number of days decreases from 48 to 8 (a factor of 6), the number of men must increase by a factor of 6 (44×6=264).
Multiplying men and days incorrectly or setting up a direct proportion (M1/D1=M2/D2) instead of an inverse proportion.
Identify Given Data and Formula
We are given initial men M1=44 and days D1=48. We need to find M2 for D2=8 days using the inverse proportion formula.
M1×D1=M2×D2
Substitute the Values
Substitute the known values into the equation: 44×48=M2×8.
44×48=M2×8
Solve for M2
Isolate M2 by dividing both sides by 8: M2=844×48.
M2=44×848
Calculate Final Result
Simplify the fraction 848=6, then multiply by 44 to get the required number of men.
M2=44×6=264
B is correct because the calculated number of men required to complete the work in 8 days is 264.
This inverse variation concept is also heavily used in pipe-and-cistern and speed-time-distance problems where total work or total distance remains constant.
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