In the following two examples, two methods have been outlined. Product constancy is the recommended and the quickest method, if you are sound in the logic to be applied. Otherwise, we suggest you use the standard worker-day approach.
Example 3
12 men can build a wall in 20 days. 5 days after they started working, 3 of them had to leave. If no other worker leaves or joins this group, what is the expected delay (in days) in construction?
Solution
12 men worked for 5 days and then 3 men left. Let's define overall work as 12×20=240 man-days.
Work completed in 5 days =12×5=60 man-days
Work Remaining =240−60=180 man-days
As remaining work is completed by 9 workers in x days, 9×x=180
⇒ x=20
Total time taken =20+5=25 days
This is 5days more than the initial time taken of 20 days.
Alternatively (Product Constancy)
After 12 men worked for 5 days, 15 days of work is left. However, 3 of the 12 men left.
As number of workers decreased by41, the time taken would have increased by4−11.
Work Delay =31×15=5days
Answer: 5 days
Example 4
8 women take 15 hours to complete a piece of work. 9 hours after the 8 women started working, some of them had to leave. If it took a total of 17 hours to complete the work, how many women left at the end of 9 hours?
Solution
Total work =8×15=120 women-hours (w−h)
Work completed in 9 hours =8×9=72w−h
Remaining work (120−72=48w−h) is completed in 8 more hours.
Number of women left =848=6 women
Number of women who left =8−6=2women
Alternatively (Product Constancy)
After 8 women worked for 9 hours, instead of taking 6 more hours, it took 8 more hours to finish the work.
As time increased by 31, women would have decreased by 3+11=41.
Number of women who left =41×8=2women
Alternatively
8 women work for the first 9 hours in both scenarios. So, this can be ignored.
8 women work for the remaining 6 hours in a normal scenario. When a few women left, the remaining x women took 8 hours to complete the work.
As the work done is the same in both the scenarios, 8×6=x×8
⇒ x=6
∴ Number of women who left =8−6=2women
Answer: 2 women
2.1.2 Wrong assessment of time taken to complete
As stated in 2.1.1, apply the product constancy method, only if you're sound in this logic.
Example 5
Kunal takes a contract to construct a warehouse in 60 days and deploys 40 of his men for this job. At the end of 20 days, if only 25% of the construction is complete, how many more men does he need to deploy on this project, in order to complete the construction on schedule?
Solution
Work done by 40 men in 20 days =20×40=800 man-days
If this is 25% of the total work, then total work =800×4=3200 man-days
Work remaining after 20 days =3200−800=2400 man-days
Time left to complete the work on schedule =60−20=40 days
Number of men required to complete the work on schedule =402400=60 men
Extra men required =60−40=20 men
Alternatively (Product Constancy)
25% of the work is completed by 40 men in 20 days. So, with 40 men, the remaining 75% of the work will be completed in 60more days.
However, the remaining work is to be completed in 40 more days.
So, if time taken decreases by 31, then men required will increase by 3−11=21
Extra men required =21×40=20 men
Answer: 20 men
2.1.3 Several variables influencing work
In these questions, work can be expressed as area, volume, etc. The same can be expressed as worker-hours or worker-days as well. These two works will be directly proportional to each other. We can then use variation to solve these questions.
Example 6
80 workers can tile a rectangular floor of dimensions 80m×72m in 40 hours. How many hours will it take 50 workers to tile a floor of dimensions 90m×60m?
Solution
It takes 80×40 worker-hours to tile an area of 80×72m2.
Let t hours be the time taken by 50 workers. It takes 50×t worker-hours to tile an area of 90×60m2.
Here, there is a direct relationship between area, which is the work to be completed, and worker-hours.
50×t80×40=90×6080×72
⇒ 58×t40=98×56
⇒ t=60hours
Answer: 60 hours
For additional variables in a 3-dimensional figure and hours per day worked, the approach remains the same.
Example 7
50 workers take 8 days to build 6 walls that are each 40m, 50m and 60m in length, breadth and height respectively, working 6 hours on each day. If 60 workers work 9 hours a day for 6 days, then how many wall of dimensions 54m×30m×40m can they build?
Solution
This question has more variables than those in example 6. However, the approach remains the same. Let n be the number of walls built in the second case.
60×6×950×8×6=n×54×30×406×40×50×60
⇒ n=15 walls
Answer: 15 walls
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