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.

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: $50 \times 12 = M_2 \times 50$, which instantly gives $M_2 = 12$.

Students often mistakenly set up a direct proportion (e.g., $50/12 = M_2/50$) instead of an inverse proportion, since fewer men take more days and more men take fewer days.

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.