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 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 $\frac{bd}{a-b}$

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.
The bakery’s rate of work = 180 cakes / 6 days = 30 cakes/day.
Number of cakes baked in 10 days = 30 cakes/day * 10 days = 300 cakes.

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?

Answer: Let the rate of work for the machine be the number of widgets produced per day.
The machine’s rate of work = 240 widgets / 5 days = 48 widgets/day.
Time taken to produce 600 widgets = 600 widgets / 48 widgets/day = 12.5 days.

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.”
Time taken by 6 workers to complete the work in = 18 days
Let there be X workers to complete the same work in 9 days
$X = \frac{6 \times 18}{9}$
$X = 6 \times 2$
X = 12 workers

Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

Also Check Out

Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others