Time and Work ( Application of Inverse Proportion (or Product Constancy))

Application of Inverse Proportion (or Product Constancy)

           

As I have already discussed thoroughly the concept of inverse proportion and product constancy in ratio-proportion and it has been widely used in profit loss chapter also.

           

Since the efficiency or rate of work done in one unit of time (mentioned) is inversely proportional to the time i.e., if the rate of work done is greater then the time required will be less and if the rate of work done is less then the time required for the same amount of work will be more.

           

This product constancy method is limited to the constant work, if the amount of work gets changed, then it does not work, then we have to take help form the unitary method.

           

When more than one man/machine work on particular work/Project, the rate of work is calculated as the strength of workers working in particular time. So the amount of work is defined in terms on man-days or man-hours or man-days-hours.

Problems:

If 20 persons can do a piece of work in 7 days then calculate the number of persons required to complete the work in 28 days.

Solution:

Number of persons x days = work

20 x 7 = 140 man-days

X x 28 = 140 man –days

= x = 5

Therefore is second case the number of person is 5

If 25 men can do a piece of work in 36 days working 10 hours a day, then how many men are required to complete the work working 6 hours a day in 20 days?

Solution:

M1 x D1 x H1 = M2 x D2 x H2

25 x 36 x 10 = M2 x 20 x 6

M2 = 75 persons

16 workers working 6 hours a day can build a wall of length 150 meters, breadth 20m and height 12 m in 25 days. In how many days 12 workers, working 8 hours a day can build a wall of length 800m, breadth 15m and height 6 m.

Solution:

Here work is the volume of the wall. So the work force should be increased/decreased in the ratio of volume of the work.

L1B1H1/L2B2H2  = M1D1T1/M2D2T2

Where L,B.H are length, breadth, and height of the wall respectively and M,D,T are men, days and time in hour per day, respectively. 1 indicates the first case, while 2 indicates second case. So the ratio of work force remains constant as the ratio of volume and work.

150 x 20 x 12/800 x 15 x 6 = 16 x 6 x 25/ 12 x 8 x D2

D2 = 50

Hence the required number of days = 50

Please notice that the volume of work become twice ( in the second case) so the work force will be twice to the previous work force.