Question

If 18 men can finish a piece of work in 42 days, how many more men should be added to finish the work in 36 days.

Answer 1

9 more men to complete in 30 days. ( Total 27 men required).

This is just a simple srithmatical example using INVERSE RATIO and PROPORTION METHOD.

Since the total workload is same, and ASSUMING that all men are working at same efficiency, the total men required to complete the task would be derived by computing total men work hours.

Thus, 18 men × 45 days= 810 men hours workload.

Hence to finish in 30 days (45–15), you need ,810 manhours/ 30 days, equaling 27 men, which is 9 more men.

Answer 2

We can solve this problem using the idea of "man-days", which is the total amount of work that can be done by a man in one day.

Let the total work to be done be represented by "W". We can find the man-days required to complete the work using the formula:

man-days = (total work) / (time to complete work)

For the given situation, we have:

man-days = W / (18 * 42)

man-days = W / 756

Now, let's consider the second part of the problem. We want to know how many more men should be added to finish the work in 36 days. Let's call the number of additional men needed "x". We can set up a new equation using the same formula for man-days:

man-days = (total work) / (time to complete work)

For the new situation, we have:

man-days = W / (18 + x) * 36

We want to find the value of "x" that makes this equation true.

We can start by setting the two expressions for man-days equal to each other:

W / 756 = W / ((18 + x) * 36)

Next, we can cross-multiply and simplify:

W * (18 + x) * 36 = 756 * W

648 * (18 + x) = 756

Now we can solve for "x":

648 * 18 + 648x = 756

11,664 + 648x = 756

648x = 92

x = 92/648

x ≈ 0.14

So we need approximately 0.14 more men to finish the work in 36 days. Since we can't have a fraction of a person, we can round up to the nearest whole number and conclude that we need 1 additional man to finish the work in 36 days.