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50 men can do a piece of work in 12 days. The number of men required to complete the same work in 50 days is:
12
11
19
15 2024/12/20-TEAMMC Q
12
Since the total man-days required for the work remains constant, if the number of days increases from 12 to 50, the number of men must decrease proportionally. Alternatively, equate the total man-days: 50×12=M2×50, which instantly gives M2=12.
50 men can do a work in 12 days. Let M2 be the number of men required to complete the same work in D2 = 50 days.
M1×D1=M2×D2
Since the total man-days required for the work remains constant, if the number of days increases from 12 to 50, the number of men must decrease proportionally. Alternatively, equate the total man-days: 50×12=M2×50, which instantly gives M2=12.
Students often mistakenly set up a direct proportion (e.g., 50/12=M2/50) instead of an inverse proportion, since fewer men take more days and more men take fewer days.
Understand the Inverse Proportion Concept
Since the amount of work is constant, the product of the number of men and the number of days remains constant (Man-Days = Constant).
M1×D1=M2×D2
Identify Given Values
From the question, we are given M1=50, D1=12, and the target days D2=50. We need to find M2.
50×12=M2×50
Calculate the Required Number of Men
Dividing both sides by 50, we get the required number of men: M2=5050×12=12.
M2=12
A is correct because the calculated number of men required to complete the work in 50 days is 12.
This inverse variation principle is also widely applied in pipe-cistern problems and speed-time-distance scenarios where total work or total distance remains constant.
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