Formula for Time and Work

Time and work topics involve problems that require calculating the time taken by a certain number of workers to complete a task or the number of workers needed to complete a task in a given time frame.

Work done can be defined as the product between the number of persons involved in the work and the number of days taken for the work to be complete.

Formula for Time and Work

Work = (Rate × Time)

Here,

• Rate refers to the rate of work done by a person
• Time refers to the time taken to complete a certain amount of work

If a worker completes a task in x days, their rate of work is 1/x.

Tips for Time and Work

1. If A can do a job in x days, then A's efficiency = 1/x

2. If A's efficiency is a and B's efficiency is b, then (A + B)'s efficiency = a + b

3. Ratio: If 'A' is 'x' times as good a workman as 'B', then

a) Ratio of work done by A and B in equal time = x : 1
b) Ratio of time taken by A and B to complete the work = 1 : x.

This means that 'A' takes (1/x^th) time as that of 'B' to finish the same amount of work.

For example, if A is twice good a workman as B, then it means that

a) A does twice as much work as done by B in equal time i.e. A:B = 2:1
b) A finishes his work in half the time as B.

4. Combined Work:

a) If 'A' and 'B' can finish the work in 'x' and 'y' days respectively, then
A's one day work = 1/x

B's one day work = 1/y

(A + B)'s one-day work = 1/x + 1/y = (x + y)/xy

Together, they finish the work in xy/(x+y) days.

b) If 'A', 'B' and 'C' can complete the work in x, y and z days respectively, then (A + B+ C) 's 1 day work = 1/x + 1/y + 1/z = (xy + yz + xz)/xyz

Together, they complete the work in xyz/xy+ yz+ xz days.

c) If A can do work in 'x' days and if the same amount of work is done by A and B together in 'y' days, then
A's one day work = 1/x

(A + B)'s one-day work = 1/y

B's one day work = 1/y – 1/x = x – y/xy

So, 'B' alone will take xy/x-y days.

d) If A and B together perform some part of work in 'x' days, B and C together perform it in 'y' days and C and A together perform it in 'z' days, then

(A + B)'s one-day work = 1/x

(B + C)'s one-day work = 1/y

(C + A)'s one-day work = 1/z

1/x + 1/y + 1/z = 2(A + B + C)'s 1 one day work

Now, we have at hand (A + B + C)'s one day work =

(A + B + C) will together complete the work in

3) Man -Work -Hour related problems:

where,
M: Number of men
D: Number of days
H: Number of hours
W: Amount of work done

If men are fixed, work is proportional to time.
If work is fixed, time is inversely proportional to men.