Formulas For Work And Time

Work and Time Formulas

Go through the entire page to know easy Formulas For Work And Time that will help you to solve problems quickly.

Work: When the certain amount of job is assigned  to an individual known as Work

Time: Time is defined as the required duration to complete the task.

Formulas For Work And Time

Introduction to Work and Time

Definition

  • Work: In terms of mathematics work is defined as the amount of job assigned or the amount of job actually done.
  • Time: Time is defined as the number of days or hours required to complete the task

Formula's for Work and Time

Work from Days:

If A can do a piece of work in n days, then A’s one day work = \frac{1}{n}

Days from work:

If A’s one day work = \frac{1}{n}, then A can finish the work in n days

Work Done by A and B

A and B can do a piece of work in ‘a’ days and ‘b’ days respectively.

When working together they will take \frac{ab}{a+b} days to finish the work

In one day, they will finish ( \frac{a+b}{ab})^{th}  part of work.

Ratio:

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

Ratio of work done by A and B = 3: 1.

Ratio of times taken by A and B to finish a work = 1: 3

Efficiency:

Efficiency is inversely proportional to the

Time taken when the amount of work done is constant.

Efficiency α = \frac{1}{Time  Taken}

Basic Rules for Work and Time

Rule 1: If A completes a piece of work in x days. And B can completes same piece of work in y days .

Then,

One day work of A = \frac{1}{x} One day work of B = \frac{1}{y}

Work done by A + B = \frac{1}{x} + \frac{1}{y} = \frac{x+y}{xy}

Total time = \frac{xy}{x + y}

Rule 2: If A completes a piece of work in x days. B completes same piece of work in y days .C completes same piece of work in z days

Then,

One day work of A = \frac{1}{x}

One day work of B = \frac{1}{y}

One day work of C = \frac{1}{z}

Work done by A + B + C = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{yz+xz+xy}{xyz}

Total time = \frac{xyz}{xy + yz + zx}.

Rule 3If M1 men can complete a work W1 in D1 days and M2 men can complete a work W2 in D2 days then, \frac{M_{1}D_{1}}{W_{1}} = \frac{M_{2}D_{2}}{W_{2}}  .

If Time required by Both M1 and M2 is T1 and T2 respectively, then relation is \frac{M_{1}D_{1}T_{1}}{W_{1}} = \frac{M_{2}D_{2}T_{2}}{W_{2}}

Rule 4:  If A alone can complete a certain work in ‘x’ days and A and B together can do the same amount of work in ‘y’ days,

Work done by b =\frac{1}{y} – \frac{1}{x} = \frac{x-y}{xy}

Then B alone can do the same work in \frac{xy}{(x-y)} days

Rule 5: If A and B can do work in ‘x’ days.

If B and C can do work in ‘y’ days.

If C and A can do work in ‘z’ days.

Work done by A,B and C = \left ( \frac{1}{2}\right )\left ( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right )

Total time taken when A, B, and C work together \frac{2xyz}{ ( xy+yz+zx )}

Rule 6: Work of one day = \frac{Total  work}{Total  number  of  working  days}

Total work = one day work × Total number of working days

Remaining work =  1 – work done

Work done by A = A’s one day work × Total number of working days of A

Rule 7:If A can finish \frac{m}{n} part of the work in D days.

Then total time taken to finish the work by A = \frac{D}{\frac{m}{n}} = \frac{n}{m} × D days

Rule 8:

If A can do a work in ‘x’ days

B can do the same work in ‘y’ days

When they started working together, B left the work ‘m’ days before completion then total time taken to complete the work = (y+m)x/(x+y)

Rule 9: A and B finish work in a days.

They work together for ‘b days and then A or B left the work.

B or A finished the rest of the work in ‘d’ days.

Total time taken by A or B alone to complete the work = \frac{ad}{a – b} or \frac{bd}{a-b}

Work and Time Formulas & Three Universal Rules

  • If M1 persons can do W1 work in D1 days and M2 persons can do W2 works in D2 days then the formula \frac{M_{1}D_{1}}{W_{1}} =   \frac{M_{2}D_{2}}{W_{2}} .It can be written as M1D1W2 = M2D2W1.
  • If the persons work T1 and T2 hours per day respectively  \frac{M_{1}D_{1}T_{1}}{W_{1}} \frac{M_{2}D_{2}T_{2}}{W_{2}}
  • It can be written as, M1D1 T1 W2 = M2D2 T2W1
  • If the persons has efficiency of E1 and E2 respectively then \frac{M_{1}D_{1}T_{1}E_{1}}{W_{1}} = \frac{M_{2}D_{2}T_{2}E_{2}}{W_{2}} Therefore, M1D1T1E1W2 = M2D2T2E2W1.

In all the above formula,

M = Number of workers

D = Number of days
T = Time required
W = Units of work
E = Efficiency of workers

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