Some formulae related with work and time ..

I )      If ‘m₁’ persons do a work in d₁ days and ‘m₂’ persons do the same work in d₂ days, then m₁d₁=m₂d₂

II)      ‘m₁’ persons can do ‘w₁’ work in ‘d₁’ days and ‘m₂’ persons do ‘w₂’ work in ‘d₂’ days, then (w₁ / m₁d₁)= (w₂ / m₂d₂)

III)     If ‘m₁’ persons can do ‘w₁’ work in ‘d₁’ days working ‘t₁’ hours a day and ‘m₂’ persons can do ‘w₂’ work in ‘d₂’ days, working ‘t₂’ hours a day. Then,

(w₁ / m₁ d₁ t₁) = (w₂ / m₂ d₂ t₂).

IV)    A can do a work in ‘x’ day. B can do the same work in ‘y’ days. Then A and B together can complete the work in xy / (x+y) days.

V)      If A working alone takes ‘x’ days more  and B working alone takes ‘y’ days more than A and B together, then the number of days taken by A and B working together is given by √xy days.