# Math Help - Direct & Inverse Proportions

1. ## Direct & Inverse Proportions

120 men can finish a work in 200 days. After 5-days, 30 men left the work. Now in how many days the work will be completed?

2. Originally Posted by gajesh
120 men can finish a work in 200 days. After 5-days, 30 men left the work. Now in how many days the work will be completed?
In one day one man does $1/(120 \times 200)=1/24000$-th of the work.

CB

3. As CaptainBlack has pointed out, each man does $\displaystyle\frac{1}{24000}$-th of the work each day.

For 5 days, we have 120 men doing work. $\displaystyle120*5=600$

$\displaystyle\frac{600}{24000}=\frac{1}{40}$-th of the work has been done in those five days.

Now we have 90 men working. Let's assign a variable x to the number of days required to finish the work.

$\displaystyle90*\frac{1}{24000}=\frac{9}{2400}$ of the work is done each day with 90 men.

now we have:

$\displaystyle\frac{9}{2400}*x=\frac{39}{40}$ because 1/40 of the work was done in the first five days.

x=260 days.

Now we add the initial 5 days and we come to a total of 265 days.

4. Originally Posted by gajesh
120 men can finish a work in 200 days. After 5-days, 30 men left the work. Now in how many days the work will be completed?
Alternatively,

there is an inverse proportion between the number of men required
and the time taken for completion.

Similar to the concept of "man-hours", here we have "man-days".

$men(days)=constant$

$120(200)=$ "man-days" required for completion.

$120(5)+x(90)=120(200)\Rightarrow\ x(90)=120(200-5)$

$\displaystyle\Rightarrow\ x=\frac{120(195)}{90}$

"x" is the remaining days needed for completion.