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Get Hiring UpdatesFormulas For Time and Work
Time and Work Formula (Formulas for Time and Work)
Time and Work Formula
Formula's For Time and Work(Time and Work Formula)
Work from Days(Work Formula):
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 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.
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
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FAQs - Time and Work Aptitude Formula
The fundamental formulas used in Time and Work questions are:
- Work Done = Time Taken × Rate of Work
- Rate of Work = 1 / Time Taken
- Time Taken = 1 / Rate of Work
These help in determining how much work is completed over a period or how long it will take to finish a task based on efficiency or rate.
When two people, A and B, can complete a work in ‘a’ and ‘b’ days respectively, the time taken when they work together is:
- Time taken together = (ab)/(a+b)
Their combined one-day work is:
(1/a) + (1/b) = (a+b)/(ab)
This formula extends to more workers as well.
Efficiency and time are inversely proportional. If a worker is more efficient, they take less time to complete the same work. The formula is:
Efficiency= Amount of Work / Time Taken
- If the efficiency ratio of A to B is X:Y, then the time taken ratio is Y:X
For pipes and cisterns:
Net Rate = Inflow Rate − Outflow Rate
If Pipe A fills a tank in x hours and Pipe B empties it in y hours, the net work done in one hour is:
- 1/x − 1/y
The total time to fill or empty the tank is the reciprocal of the net rate
For alternate working days (e.g., A and B work on alternate days), calculate the total work done in one cycle (one day by A, one by B), then divide the total work by the work done per cycle. For fractional work:
Work Done = Efficiency × Time
- To find the fraction of work completed after X days, multiply the daily efficiency by the number of days worked.
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