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**Time and Work Formula**

Time and work are important topics for various competitive examinations such as **Banking, SSC, Railways, and others Examinations**. Time and Work is a frequently tested topics in government exams, making it an essential area to master if you want to excel in these tests. Having a strong foundation in this topic can greatly improve your chances of acing the exam with flying colors. It’s important to learn the relevant formulas and shortcuts to quickly and accurately solve time and work questions. You can find a range of time and work questions with answers below to aid in your preparation.

Moreover, understanding time and work questions can also serve as a foundation for other related concepts such as data interpretation and data sufficiency. Thus, investing time and effort in mastering this topic can not only help you perform well in your exams but also benefit your overall understanding of related concepts.

**Time & Work- Importance**

There are many types of questions that are asked on the topic of **Time & Work** though the concept of Time & Work remains the same. It is the most common topic which is asked in every Government Exam. Candidates can expect to see Time & Work questions in data sufficiency and data interpretation also for which it becomes crucial to understand the basic concept of Time & Work. So, in this article, we have covered the Time and Work formulas as well as Time and Work Tricks so that candidates can score more marks in less time.

**Time and Work Formulas**

The most important time and work formula for bank exams are provided in this time and work formula for bank exams post. The candidates should make a use of this time and work formula pdf for bank exams to maximise your marks and accuracy which is available in the time and work formula for bank exams article. These time and work formula for bank exams will help you to make your calculations an easier one while solving the time and work questions in the bank exams.

- Work = Time Taken × Rate of Work
- Rate of Work = 1 / Time Taken
- Time Taken for a work = 1 / Rate of Work
- If a piece of work is completed in x number of days, then the work completed in one day = 1/x
- Total Work = Efficiency × Number of Days
- Efficiency and Time are inversely proportional to each other
- If X: Y is the ratio of the number of men needed to do a work, then the time taken by them to complete the work is Y:X
- If x number of people can do W1 work in D1 days while putting in H1 hours per day, and if x number of people can complete W2 work in D2 days while putting in H2 hours per day, then the relationship between them will be

M1D1H1 / W1 = M1D2H2 / W2

**Time and Work Tricks and Shortcuts For Bank Exams – Based on Wages**

The time and work formula for bank exams based on wages is added here. The aspirants who are sincerely preparing for their bank exams and other competitive exams must be knowledgeable about the time and work formula for bank exams based on wages which is available in this time and work formula for bank exams article. The time and work formula for bank exams based on wages is also mentioned in the time and work formula pdf for bank exams.

- Total Wage = Total number of days × Wage of a person’s daily wage
- Wage is directly proportional to the amount of work performed.
- Wage is directly proportional to the number of hours which each person works in a day
- Wage is inversely related to the amount of time spent by the worker.
- If A and B can complete a task in x and y days, respectively and their salaries will be paid out in a y:x ratio. Therefore, A and B’s salaries will be

Total wages y/(x + y) = Wage of A.

Total wages x/(x + y) = Wage of B

**Time and Work Tricks For Bank Exams**

Time and works tricks for bank exams are added in this time and work formula for bank exams article. The time and work tricks will be very useful for the candidates to solve time and work problems easily in their bank exams and other competitive exams. Aspirants must go through this time and work formula for bank exams article to know more about the time and formula for bank exams. There is also available time and work formula pdf for bank exams, so candidates can exploit this pdf.

- When x can do can work in ‘n’ days, Then The efficiency of x is
**“1/n”.**This is one of the tricks in the time and work formula for bank exams. Download the time and work formula pdf for bank exams to know more formulas related to the time and work topic. - If A and B can complete a task in x days, B and C can complete the same task in y days, and A and C can complete it in z days, then A, B, and C working together can complete that task in,
**2xyz / xy + yz + zx days** - If A can complete the work in ‘x’ days. So in one day, he will do 1/x of the work. B can complete the work in ‘y’ days. So in one day, he will do 1/y of the work. Total work done by both A & B in one day = (1/x) + (1/y). Hence, the total time required to do the work =
**(xy)/(x +y) days.** - When A can attains a work in x days and B can do it more quickly than A, then B will finish the work in
**100 + x / 100 * y days.**

**Time And Work Formulas & Tricks**

When you know Time and Work formula, you can completely link that formula to the solution as soon as you read the question. Knowing Time & Work tricks will also help you solve the questions in a few seconds and thus saving your time for other sections. You can find Time & Work formulas along with important Time & Work Tricks below.

**When work is the same.**

* Time∝1/Efficiency*

**If A can do a piece of work in n days.**

** **Then, per day working efficiency of A = 1/n

**If the working efficiency of A & B is → x: y.**

*Then, the time taken by A & B to finish the work is in the ratio → y: x*

e.g. If A does three times faster work than ‘B’, then the ratio of work done by A and B is 3: 1.

Then, the ratio of time taken by A & B = 1 : 3

- If A can do a piece of work in x days and B can do a piece of work in y days, then both of them working together will do the same work in

**XY/(x+y) days**

__Explanation __

⇒ A’s 1 day’s work = 1/x

B’s 1 day’s work = 1/y

(A + B)’s 1 day work = 1/x+1/y =(x + y)/xy

A + B will complete the work in = XY/(x + y)

**Q. A can finish a piece of work by working alone in 6 days and B, while working alone, can finish the same work in 12 days. If both of them work together, then in how many days, the work will be finished? **

**Sol.** x = 6, y = 12

Working together A + B will complete the work in = XY/(x + y)=(6 × 8)/18

= 4 days

**Q.If A, B & C will work alone and can complete a work in x, y, and z days, respectively, then they will together complete the work in**

**XYZ/(xy+yz+zx)**

__Explanation__

⇒ A’s 1 day of work = 1/x

B’s 1-day work = 1/y

C’s 1-day work = 1/z

(A + B + C)’s 1 day work = 1/x+1/y+1/z =(yz+xz+xy)/xyz

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

=xyz/(yz+xz+xy)

**Q. A, B, and C can complete a piece of work in 10, 15, and 18 days, respectively. In how many days would all of them complete the same work working together?**

**Sol.** x = 10 days, y = 15 days & z = 18 days

The work will be completed in

=(10×15×18)/(10×15+15×18+18×10)

=2700/600=4½ days

**Q.Two persons A & B, working together, can complete a piece of work in x days. If A, working alone, can complete the work in y days, then B, working alone, will complete the work in**

**⇒xy/(y-x)**

__Explanation __

⇒ A + B’s 1 day work = 1/x

A’s 1-day work = 1/y

B’s 1 day work = 1/x-1/y

=(y-x)/yx

B will complete the work = yx/(y – x)

**Q. A and B working together take 15 days to complete a piece of work. If A alone can do this work in 20 days, how long would B take to complete the same work?**

**Sol.** x = 15, y = 20

B will complete the work in = (15 × 20)/5

= 60 days

**Q.If A & B working together can finish a piece of work in x days, B & C in y days, C & A in z days. Then, A + B + C working together will finish the job is**

**⇒2xyz/(xy+yz+zx)**

__Explanation__

⇒ A + B’s 1 day work = 1/x

B + C’s 1 day work = 1/y

C + A’s 1 day work = 1/z

[(A + B) + (B + C) + (C + A)]’s 1 day’s work

=1/x+1/y+1/z

=(yz+xz+xy)/XYZ

2 (A + B + C)’s 1 day work = (xy + yz + xz)/XYZ

A + B + C’s 1 day work = (xy + yz + xz)/2xyz

A + B + C working together will complete the work in

=2xyz/(xy+yz+xz)

**Q. A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How long would they take to complete the full work together?**

**Sol. **x = 12 days, y = 15 days, z = 20 days

A+B+C=(2×12×15×20)/(180+300+240)

=7200/720=10 days

**If A can finish a work in x days and B is k times more efficient than A, then the time taken by both A and B, working together to complete the work is**

**x/(1+k)**

__Explanation__

⇒ Ratio of working efficiency, A & B = 1: k

The ratio of Time taken = k: 1

k → x days

1r → x/k days

A → x days

B → x/k days

1-day work of A = 1/x

1-day work of B = k/x days

(A + B)’s 1 day work = 1/x+k/x=(k + 1)/x

(A + B) will complete the work is = x/(k+1)

**Q. Harbans Lal can do a piece of work in 24 days. If Bansi Lal works twice as fast as Harbans Lal, how long would it take to finish the work working together?**

**Sol.** x = 24, k = 2

Working together they will complete the work in = 24/(1 + 2)

=24/3=8 days

**If A & B working together can finish a work in x days & B is k times more efficient than A, then the time taken by,**

**Working Alone will take ⇒ (k + 1) x**

**B working Alone will take ⇒ ((k+1)/k)x**

__Explanation__

⇒ Efficiency Ratio → 1: k

Time Ratio → k: 1

A’s 1-day work = 1/k

B’s 1-day work = 1

(A + B)’s 1 day work = 1/x

1/k+1=1/x

(k+1)/k=1/x

k = (k + 1) x

An alone working together will take ⇒ (k + 1) x days

1 ratio = ((k + 1) x)/k

B Alone working Alone will take

⇒((k + 1) x)/k

**Q. A and B together can do a piece of work in 3 days. If A does thrice as much work as B in a given time, find how long A alone would take to do the work.**

**Sol**. x = 3, k = 3

Time taken by A, working Alone to complete the work = ((3 + 1)/3) × 3 = 4 days

**If A working Alone takes a day more than A & B, & B working Alone takes b-days more than A & B. Then,**

**The number of days, taken by A & B working together to finish a job is = √ab**

__Explanation :__

⇒ Let A + B takes x days

A → x + a days

B → x + bdays

1/(x+a)+1/(x+b)=1/x

(2x+a+b)/(x²+xa+xb+ab)=1/x

2x² + xa + BX = x² + xa + xb + ab

x² = ab

x = √ab days

**Q. An alone would take 8 hrs more to complete the job than if both A and B worked together. If B worked alone, he took 41/2 hrs more to complete the job than A and B worked together. What time would they take if both A and B worked together?**

**Sol. **a = 8, b = 9/2

A + B will take = √(8×9/2)

=√36

= 6 days

**Q. 4 men and 5 boys can do a piece of work in 20 days while 5 men and 4 boys can do the same work in 16 days. In how many days can 4 men and 3 boys do the same work?**

a. 10 days

b. 15 days

c. 20 days

d. 25 days

**Correct answer:**(c)

**Sol: **Assume 1 man’s 1 day work = x & 1 boy’s 1 day work = y

From the given data, we can generate the equations as : 4x + 5y = 1/20 —(1) & 5x + 4y = 1/16 —(2)

By solving the simultaneous equations (1) & (2),

x = 1/ 80 & y = 0

Therefore, (4 men + 3 boys ) 1 day work = 4 x 1 + 3 x 0 = 1

80 20

Thus, 4 men and 3 boys can finish the work in 20 days.

**Q. Sonal and Preeti started working on a project and they can complete the project in 30 days. Sonal worked for 16 days and Preeti completed the remaining work in 44 days. How many days would Preeti have taken to complete the entire project all by herself? **

- 20 days
- 25 days
- 55 days
- 46 days
- 60 days

**Correct answer: 60 days**

**Sol: **Let the work done by Sonal in 1 day be x

Let the work done by Preeti in 1 day be y

Then, x+y = 1/30 ——— (1)

⇒ 16x + 44y = 1 ——— (2)

Solving equations (1) and (2),

x = 1/60

y = 1/60

Thus, Preeti can complete the entire work in 60 days

**Q. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together, working 8 hours a day, in how many days can they complete the work?**

**Correct Answer: 60/11**

**Sol: **P can complete the work in (12 x 8) hrs = 96 hrs

Q can complete the work in (8 x 10) hrs=80 hrs

Therefore, P’s 1 hour work=1/96 and Q’s 1-hour work= 1/80

(P+Q)’s 1 hour’s work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs

Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11

**Q. (x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?**

**Correct Answer:** **12 days****Sol: **34×(x−2)x=(x+7)(x−10)34×(x-2)x=(x+7)(x-10)

⇒x2−6x−280=0⇒x2-6x-280 =0

=> x= 20 and x=-14

so, the acceptable value is x=20

Therefore, Total work =(x-2)x = 18 x 20 =360 unit

Now 360 = 30 x k

=> k=12 days

**Q. A is thrice efficient as B and C is twice as efficient as B. what is the ratio of several days taken by A, B, and C, when they work individually?**

**Correct Answer:** **2:6:3**

**Sol:**

A: B: C

The ratio of efficiency is 3: 1: 2

The ratio of No.of days 1/3: 1/1: 1/2

or 2: 6 : 3

Hence A is correct.

**Time and Work Formula For Bank Exams FAQs**

**Q. If A can do a piece of work in 10 days, then what is A’s one day work?**

**Q. If A can do a piece of work in 10 days, then what is A’s one day work?****A. **If A can do a piece of work in 10 days, then A’s one day work will be 1/10

**Q. How to calculate the time taken for the work?**

**A. **Time Taken for a work = 1 / Rate of Work

**Q. What are the tricks to solve time and work questions based on the time and work formula for bank exams? **

**A. **The tricks to solve the time and work questions based on the time and work formula for bank exams are mentioned above in the article. Candidates can go through this time and work formula for bank exams article to know more tricks to solve time and work questions.