Time & Work

Time and work:
i) If A completes a work in X days , B in Y days and C in Z days, then
A and B will complete the work in = XY/ X+Y days
A, B and C will complete the work in= XYZ/ XY+YZ+ZX days

ii) If A+B complete the work in X days, B+C in Y days and A+C in Z days then,
A,B,C will complete the work in = 2xyz/ xy+yz+zx days.
A will complete the work in = 2xyz/xy+yz-zx days

iii) A takes N times to complete B and C’s work.
Then A will complete the work in = (n+1) * time taken by A,B and C to complete the work

iv) A’s work/ B’s work = B’s time/ A’s time

v) If A completes a work in X days , B in Y days and C in Z days , then

A and B start a work together , but A leaves the work N days after , then the work will be completed in = (x+n)y/x+y days

If A, B and C start a work together but A leaves the work after N days, then the work will be completed in: = (x+n)yz/xy+yz+zx

If A,B and C start a work together but A stops working N days before the completion of work and B leaves M days before , then the work will be completed by C in = xyz/xy+yz+zx [1+ n/x + m/y]

vi) A completes a work in X days , B in Y days and C in Z days. If all of three start work together but,

A leaves the work after N days then, it would be completed in = yz/y+z [ 1- n/x) days

A leaves the work after N days, B leaves the work in M days , then, it would be completed in:
Z [ 1- n/x – m/x ] days