Write a program to calculate in how many days a work will be completed by 3 persons A,B and C together. A,B,C takes x days, y days and z days respectively to do the job alone. The formula to calculate the number of days if they work together is xyz/(xy+yz+zx)days where x,y,z are given as input to the program?
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Time and Work Formula and Solved Problems
Know the important formulae and rules to solve questions based on time & work.
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FORMULAS
The basic formula for solving is: 1/r + 1/s = 1/h
Let us take a case, say a person Hrithik
Let us say that in 1 day Hrithik will do 1/20th of the work and 1 day Dhoni will do 1/30th of the work. Now if they are working together they will be doing 1/20 + 1/30 = 5/60 = 1/12th of the work in 1 day. Now try to analyze, if two persons are doing 1/12th of the work on first day, they will do 1/12th of the work on second day, 1/12th of the work on third day and so on. Now adding all that when they would have worked for 12 days 12/12 = 1 i.e. the whole work would have been over. Thus the concept works in direct as well as in reverse condition.
The conclusion of the concept is if a person does a work in ‘r’ days, then in 1 day- 1/rth of the work is done and if 1/sth of the work is done in 1 day, then the work will be finished in ‘s’ days. Thus working together both can finish 1/h (1/r + 1/s = 1/h) work in 1 day & this complete the task in ’h’ hours.
The same can also be interpreted in another manner i.e. If one person does a piece of work in x days and another person does it in y days. Then together they can finish that work in xy/(x+y) days
In case of three persons taking x, y and z days respectively, They can finish the work together in xyz/(xy + yz + xz) days