Time And Work
Time and work problems hold significant importance in a wide range of competitive exams, including those conducted by banking, SSC, railways, and various government bodies. Proficiency in this topic is key to excelling in these exams. Having a strong grasp of time and work concepts, along with effective formulas and shortcuts, can greatly boost your chances of success. The time and work questions are the foundation of various other concepts including Data interpretation, and Data sufficiency. Read the article below to find the list of formulas tricks and questions that will help you clear your doubts about the subject matter.
Time & Work: Importance
There are many types of questions that are asked on the topic of Time and work though the concept of Time and 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
When you know the 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 thus saving you time for other sections. You can find Time & Work formulas along with important Time & Work Tricks below.
1. Basic Formula:
Work = Rate × Time
Time = Work / Rate
Rate = Work / Time
2. Reciprocal of Rate: Sometimes, it’s easier to work with the reciprocal of the rate, which represents the work done per unit time.
Reciprocal of Rate = 1 / Rate
3. Combined Work:
If A can complete a task in ‘x’ days, then A’s work rate is 1/x.
If B can complete a task in ‘y’ days, then B’s work rate is 1/y.
When A and B work together, their combined work rate is 1/x + 1/y.
4: Time Taken by A and B Together:
If A and B work together, the time taken to complete the task is:
Time = 1 / (1/x + 1/y)
5. Time Taken by More than Two Workers:
When more than two workers are involved, the formula becomes:
Time = 1 / (1/x + 1/y + 1/z + …)
Time And Work: Questions And Tricks
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
- 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
- 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 takes 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
- If A & B working together can finish a piece of work in x days, B & C in y days, and 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 hours 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?
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?
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
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