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# Formulas For Time and Work

## Time and Work Formulas

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

## Formula's For Time and Work

**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} 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}

## Rules for Time and Work

**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 3****: **If M_{1} men can complete a work W_{1} in D_{1} days and M_{2} men can complete a work W_{2} in D_{2} days then**, ** \frac{M_{1}D_{1}}{W_{1}} = \frac{M_{2}D_{2}}{W_{2}} _{ . }

If Time required by Both M_{1} and M_{2} is T_{1} and T_{2} 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}

## Questions based on above formulas:

**Question 1: ***A construction crew of 8 workers can build a house in 24 days. How many days will it take for 12 workers to build the same house?*

**Answer: **Let the amount of work required to build the house be represented as “1 house.”

8 workers can build the house in = 24 days

Day taken by 12 workers to build the house = \frac{8 \times 24}{12}

= {8 \times 2}

= 16 days

**Question 2: A bakery can bake 180 cakes in 6 days. How many cakes can it bake in 10 days?**

**Answer:**Let the rate of work for the bakery be the number of cakes baked per day.

**Question 3:**

*If 15 painters can paint a house in 9 days, how many days will it take for 9 painters to paint the same house?*

**Answer: **Let the amount of work required to paint the house be represented as “1 house.”

Time taken by 15 painters to paint a house = 9 days

Time taken by 9 painters to paint the same house =

\frac{15 \times 9}{9}

= {15 \times 1}

= 15 days

**Question 4: **

*A machine can produce 240 widgets in 5 days. How long will it take for the machine to produce 600 widgets?*** **

**Question 5 :**

*If a team of 6 workers can complete a project in 18 days, how many workers are needed to complete the project in 9 days?***Answer:**Let the amount of work required for the project be represented as “1 project.”

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