Time and Work Formula

If A can do a piece of work in n days, then A’s 1-day work is= 1/n

If A’s 1 day’s work is 1/n, then A can finish the work in n days.

If A is thrice as good a workman as B, then-

The ratio of work done by A and B = 3:1

The ratio of time taken by A and B to finish work = 1:3

If M1 men can do a W1 piece of work, working T1 hours daily in D1 days and M2 men can complete W2 work, working T2 hours in D2 days then-

M1 D1 T1 W2 = M2 D2 T2 W1

If A completes a piece of work alone in x days and B completes the same work in y days. Then they together will finish the work in–

(x × y/x+y) days

If ‘A’ and ‘B’ completes a piece of work together in x days and B alone completes the same work in y days. Then ‘A’ alone will finish the work in-

(x – y/y – x) days

If three men A, B, and C alone finish a piece of work in x, y, and z days. Then they together finish the work in-

( xyz/xy + yz + zx ) days

EXAMPLE-

1. P can do a work in 10 days and Q in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is?

Solution-

P’s 1 day’s work = 1/10

Q’s 1 day’s work = 1/20

(P + Q)’s 1 day’s work = $\frac { 1 }{ 10 } +\frac { 1 }{ 20 }$ = 3/20

(P + Q)’s 5 day’s work = $5\times \frac { 3 }{ 20 } =\frac { 3 }{ 4 }$

So, now the Remaining work is = 1 – (3/4) = 1/4 (Answer)