Question

If $195$ men working $10$ hours a day can finish a job in $20$ days, how many men, working $13$ hours a day, should be employed to finish the job in $15$ days?

Answer 1

Let us analyse the problem. As the number of men increases, number of days required will decrease. Similarly, if the number of working hours increases the number of days decreases. Hence the number of days is inversely proportional to the number of men and number of working hours. Hence the constant of proportionality is $k=195\times 20\times 10$.
Let $x$ be the number of men, working $13$ hours a day, required to finish the job in $15$ days. Then $15$ is inversely proportional to both $x$ and $13$. This gives $k=x\times 13\times 15$. Comparing two expressions for $k$, we obtain
$x=\frac{195\times 20\times 10}{13\times 15}=200$.
Thus the required number of men is $200$.