1. Time: Time needed by one or more than one person to complete a job or time for which a person actually worked on the assigned job.
2. Alone time: Time needed by a single person to complete a job.
3. Work: The amount of total work or the part of total work actually done.
Basic Concepts :
1. Total amount of a complete job = 1, always, unless specified.
2. If any person M completes a job alone in t days, then alone time for 'M' = t
3. 1 day's, work by any person = (1/alone time) * Part of total work
4. The reciprocal of 1 day's work gives alone time i.e.
Alone time ∝ 1/ 1 day's work
5. When more than one person working on the same piece of work, then their combined 1 day's work = sum of 1 day's work by each person, i.e
If A, B, c are three persons working on a job, then (A+B+C)'s 1 Day's work = A's 1 Day work + B's 1 Day work + C's 1 Day work.
6. It is the application of concept 4 for more than one person.
The reciprocal of the combined 1 day's work gives the time for completion by the person working together.
i.e time for completion =1/ combined 1 day's work
Concept of Man - Work - Hour Formula:
i. More men can do more work.
ii. More work means more time required to do work.
iii.More men can do the same work in less time
iv.If M1 can do W1 work in D1 days working H1 hr/day for Rs. R1 and If M2 can do W2 work in D2 days working H2 hr/day for Rs. R2
Then,
(M1 D1 H1)/(W1 R1) = (M2 D2 H2)/(W2 R2)
Concept of Negative work:
Suppose A and B are working to build a wall while C is working to break the wall. In such cases the wall is being built by A and B while it is broken by C. Here we consider the work as the building of the wall, We can say that C is doing negative work.
The net combined work per day here is :
A's work + B's work - C's work
Important Formulae:
1. If A can do a piece of work in X days and B can do the same work in Y days, then both of them working together will do the same work in
(XY)/ (X+Y)
2. A, B, C while working alone can complete a work X, Y, Z days receptively then they will together complete the work in
(XYZ)/ (X+Y+Z)
3. Two people A and B working together can complete a piece of work in X days. If A alone can complete the work in (XY)/(X-Y) days
4. If A and B working together, can finish a piece of work in X days, B and C in Y days, C and A in Z days then.
A, B, C working together will finish the job in (2XYZ)/ (XY+YZ+ZX) days
5.If men or b women can do a piece of work in d days then x men and y women together finish the whole work
D = (abd) / (xb + ya)
6. if a men or b women or c children can do a piece of work in d days then x men, y women, and z children together finish the whole work
D= (abcd) / (xbc+ yac + zab)
Alternate Method for calculating Quickly:
L.C.M Method:
If A, B, C complete a piece of work in X, Y, Z Days receptively
Then total work is equal to the L.C.M of X, Y, Z
Then work per day :
For A = L.C.M / X
B = L.C.M /Y
C= L.C.M /Z
Total work per day = work per day of (A+B+C)
Total work is done = L.C.M / Total work per day
Ex. If A, B, C completes a piece of work in 12 days, 15 days, 20 days respectively. In how many days the work is completed if they work together?
Sol. L.C.M of 12,15,20 is 60
Work per day of A= 60/12 = 5
B= 60/15 = 4
C= 60/20 = 3
Total work is done per day (A+B+C) = 12
Total work done by A+B+C in = 60/12 = 5 days
hence they complete work in 5 days if they work together.
Solve it like This:
