# Time and Work

- If A can do a piece of work in X days, then Aâ€™s one dayâ€™s work = part of whole work.
- If Aâ€™s one dayâ€™s work = part of whole work, then A can finish the work in X days.
- If A can do a piece of work in X days and B can do it in Y days then A and B working together will do the same work in days.
- If A, B and C can do a work in X, Y and Z days respectively then all of them working together can finish the work in days.
- If A and B together can do a piece of work in X days and A alone can do it in Y days, then B alone can do the work in days.
- A and B can do a work in â€˜Xâ€™ and â€˜Yâ€™ days respectively. They started the work together but A left â€˜aâ€™ days before completion of the work. Then, time taken to finish the work is
- If â€˜Aâ€™ is â€˜aâ€™ times efficient than B and A can finish a work in X days, then working together, they can finish the work in days.
- If A is â€˜aâ€™ times efficient than B and working together they finish a work in Z days then, time taken by A = days and time taken by B = Z(a + 1) days.
- If A working alone takes â€˜xâ€™ days more than A and B together, and B working along takes â€˜yâ€™ days more than A and B together then the number of days taken by A and B working together is given by days.
- If n men or m women can do a piece of work in X days, then N men and M women together can finish the work in
- If â€˜M
_{1}â€™ persons can do â€˜W_{1}â€™ works in â€˜D_{1}â€™ days and â€˜M_{2}â€™_{ }persons can do â€˜W_{2}â€™ works in â€˜D_{2}â€™ days then M_{1}D_{1}W_{2}= M_{2}D_{2}W_{1}_{1}and T_{2}are the working hours for the two groups then M_{1}D_{1}W_{2}T_{1}= M_{2}D_{2}W_{1}T_{2}_{1}D_{1}W_{2}T_{1}E_{1}= M_{2}D_{2}W_{1}T_{2}E_{2}, where E_{1}and E_{2}are the efficiencies of the two groups. - If A is n times as efficient as B, i.e. A has n times as much capacity to do work as B, A will take of the time taken by B to do the same amount of work.