30 men can do a piece of work in 16 days. How many men would be required to do the same work in 20 days? (Bank P.O., 2008)

### Concept & Inverse Proportion in Work The number of workers and the time required to complete a fixed amount of work are inversely proportional. The product of workers and time is constant. $$ M_1 \times D_1 = M_2 \times D_2 $$ ### Step-by-Step Solution * Given: $M_1 = 30$ men, $D_1 = 16$ days. * Given: $D_2 = 20$ days, $M_2 = ?$ men. * Set up the equation based on total work: $30 \times 16 = M_2 \times 20$. * Solve for $M_2$: $M_2 = \frac{30 \times 16}{20}$. * Simplify the expression: Cancel the zeroes in 30 and 20 to get $\frac{3 \times 16}{2}$. * $M_2 = 3 \times 8 = 24$ men. ### Exam Strategy & Shortcut Look at the ratio of days: $16 : 20 = 4 : 5$. The ratio of men required will be the inverse, $5 : 4$. If 5 parts = 30 men, then 1 part = 6 men. So, 4 parts = $4 \times 6 = 24$ men. ### Common Pitfall Using direct proportion, leading to the incorrect assumption that more days requires more men. Always remember work equations use inverse proportionality. ### Final Answer Therefore, the correct answer is **24**.