Time and Work is one of the most basic concepts in Quantitative Aptitude, which is tested extensively in government exams. Undoubtedly, having a strong background in this topic can give candidates an upper hand and help them to score well in competitive exams. A candidate needs to be aware of the basic concept and the types of questions that may be asked in the exams, mainly Banking and SSC exams.
The following article consists of question patterns and formulas that will be useful to the candidates while preparing for the examination. Try and practice the questions given below for a better understanding of the topic.
Question Patterns on Time and Work
- To find the efficiency of an individual or a group
- To find the time taken by a person or a group to do a piece of work or a job.
- A certain work done by an individual in a certain period
- A certain work done by a group of individuals in a certain period
- To find wages.
Time and Work Formulas
“Time and Work” topic deals with the time taken by an individual or a group to complete a job or a piece of work and its efficiency. The formulas can completely help you to find a solution as soon as you read the question. Thus, it makes the solution and the related calculations simpler.
Some of Important Formulas and Concepts on Time and Work are:
- Work Done by a person = Time Taken × Rate of Work
- Rate of Work of a person = 1 / Time Taken by him
- Time Taken by him = 1 / Rate of Work
- If a piece of work or a job is done in n number of days, then the work done in one day = 1/n
- Total Work Done = Number of Days × Efficiency
- Efficiency of work done and Time are inversely proportional to each other.
- M : W is the ratio of the number of men and women which are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be W : M.
- If W1 work is done by M1 people in D1 days, working T1 hours in a day and W2 work is done by M2 people in D2 days, working T2 hours in a day, then the relation between them will be
(M1 × D1 × T1 × W2) = (M2 × D2 × T2 × W1)
Solved Examples on Time and Work
Q1. A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is :
A. 1/12
B. 1/10
C. 5/12
D. 7/15
E. 8/15
Answer: C
Solution:
Man’s 1 day’s work = 1/20
Woman’s 1 day’s work = 1/15
(Man + woman)’s 1 day’s work = (1/20 + 1/15) = 7/60
(Man + woman)’s 5 day’s work = (7/60 × 5) = 7/12
Thus, Remaining work = 1 – 7/12 = 5/12
Q2. L can finish a work in 16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.
A. 48/5 days
B. 48/7 days
C. 48/11 days
D. 10 days
E. None of these
Answer: A
Solution:
(L + M + N)’s 1 day’s work =1/4
L’s 1 day’s work = 1/16
M’s 1 day’s work = 1/12
Therefore, N’s 1 day’s work
= 1/4 – (1/16 + 1/12)
= 1/4 – 7/48 = 5/48
So, N alone can do the work in 48/5 days.
Q3. P, Q and R can do a job in 20, 30 and 60 days respectively. In how many days can P do the job if he is assisted by Q and R every third day?
A. 11 days
B. 15 days
C. 17 days
D. 16 days
E. 18 days
Answer: B
Solution:
P’s 2 day’s work = 2/20 = 1/10
(P + Q + R)’s 1 day’s work
= (1/20 + 1/30 + 1/60)
= 6/60 = 1/10
Job done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 jobs is done in 3 days
Whole job will be done in (3 x 5) = 15 days.
Q4. M’s efficiency is three times N’s efficiency. M can finish a job in 60 days less than N. If they work together, then in how many days the job will be done.
A. 20 days
B. 22.5 days
C. 25 days
D. 30 days
E. 24.5 days
Answer: B
Solution:
Ratio of times taken by M and N = 1 : 3 (Since the efficiency of M is three times to N)
Time difference is (3 – 1) = 2 days, while N take 3 days and M takes 1 day.
- 2 units = 60 days
- 1 unit = 30 days
So, M takes 30 days to do the job.
And N takes (30×3) = 90 days to do the job.
M’s 1 day’s work = 1/30
N’s 1 day’s work = 1/90
(M + N)’s 1 day’s work =( 1/30 + 1/90) = 2/45
M and N together can do the job in 45/2 days = 22.5 days.
Q5. Ankit alone can do a piece of work in 6 days and Bishal alone in 8 days. Ankit and Bishal undertook to do it for Rs. 4800. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?
A. Rs. 1375
B. Rs. 1400
C. Rs. 1600
D. Rs. 600
E. Rs. 2000
Answer: D
Solution:
Ankit’s 1day work = 1/6
Bishal’s 1 day work = 1/8
(Ankit + Bishal + Dinesh)’s 1 day work =1/3
Dinesh’s 1 day work = 1/3 – (1/6+1/8) = 1/24
So, Dinesh’s 3 day work = 3 * 1/24= 1/8
If Dinesh contributed 8th part of work then he will receive 8th part of total payment
i.e., 4800 × 1/8 = 600
Q6. Vicky completes a job in 45/2 days. What part of the job will he do in 2 days?
A. 4/45
B. 1/45
C. 2/45
D. 8/45
E. 1/15
Answer: A
Solution:
We know, if a person does a job in n days, then his 1-day work = 1/n
Here, n = 45/2
Vicky’s 1-day work = 2/45
Thus, Vicky’s 2 days work = 2× 2/45 = 4/45
Q7. Karan completes 1/15 part of a certain job in 1 day. In how many, he will complete the full job.
A) 30 days
B) 15 days
C) 20 days
D) 5 days
E) 10 days
Answer: B
Solution:
Here, 1/n = 1/15
So, n = 15
Thus, the required days = 15
Q8. In a factory, 20 people can make 20 toys in 15 days working 10 hours per day. Then, in how many days can 25 persons make 30 toys working 20 hr per day?
A) 6 days
B) 9 days
C) 10 days
D) 12 days
E) 15 days
Answer: B
Solution:
Here, M1 = 20, M2 = 25, D1 = 15, D2 =? , T1 = 10 , T2= 20, W1 = 20 and W2 = 30.
We know,
M1 × D1 × T1 × W2 = M2 × D2 × T2 × W1
=> 20 × 15 × 10 × 30 = 25 × D2 × 20 × 20
=> D2 = 9
Thus, the required day = 9 days
Q9. P, Q and R together can complete a work in 16 days and R alone complete the work in 20 days. If P, Q and R started the work together and after 10 days P and Q left the work, in how many days R alone complete the remaining work?
A) 12½ days
B) 20½ days
C) 4 days
D) 7½ days
E) 15 days
Answer: D
Solution:
P + Q + R = 16 days
R =20 days
work (LCM of 16 and 20) = 80
( P + Q +R) ‘s work
= 80 /16
= 5 unit
Work done by R = 80 /20 = 4 unit
(P + Q + R) ‘s 10 days work
= 5 × 10
= 50 unit
Remaining work
= (80 – 50)
= 30 unit
Remaining work done by R
= 30/4
= 7½ days
Q10. M did a piece of work in 5 days. That piece of work was done by N in 9 days. If M and N worked together, they got total wages of Rs 4200. Find the share of N.
A) 1500
B) 2000
C) 1000
D) 1200
E) None of these
Answer: A
Solution:
M : N
Time = 5 : 9
Efficiency= 9 : 5
(Time and efficiency are inversely proportional)
N gets = 4200 × 5/14
= 1500
Thus, N gets the wages of Rs 1500.
Q11. P and Q can do a job in 3 days. Q and R can do the same job in 9 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.
A) 72/19 days
B) 83/10 days
C) 61/3 days
D) 67/4 days
E) None of these
Answer: A
Solution:
Here, (P + Q)’s 1 day’s work = 1/3
(Q + R )’s 1 day’s work= 1/9
and (R + P)’s 1 day’s work = 1/12
Now, 2 (P + Q + R)’s 1 day’s work = (1/3+1/9+1/12) = 19/36
(P + Q + R)’s 1 day’s work = 19/(36 ×2)=19/72
Hence, (P + Q + R) complete the work in= 72/19 days
Q12. E and F are two friends working together to finish a work in 24 days and E alone can do the same work in 36 days. In how many days can F alone complete the work?
A) 36 days
B) 24 days
C) 72 days
D) 48 days
E) None of these
Answer: C
Solution:
(E+F)’s 1 days work = 1/24
E’s 1-day work = 1/36
F’s 1 day work = (1/24 – 1/36) = 1/72
Thus, the time is taken by F to finish the work alone= 72 days
Q13. If 12 men or 18 boys can build a wall in 48 days, then how long will 6 men or 9 boys build the wall?
A) 48 days
B) 36 days
C) 64 days
D) 72 days
E) 96 days
Answer: E
Solution:
12 men = 18 boys
2 men = 3 boys
Now, 12 men + 2×18/3 men = 24 Men
And, 6 men + 2× 9/3 men = 12 men
Here, M1 = 24, M2 = 12, D1 = 48, D2 =?
According to the formula,
M1 × D1 = M2 × D2
=> 24 × 48 = 12 × D2
=> D2 = 96
Q14. Akash can reap a field in 45 days and Vishal is 200% more expert than Akash to reap the field, then find total time taken to reap the field by Vishal.
A) 15
B) 20
C) 22
D) 25
E) 30
Answer: A
Solution:
According to the question, Vishal is more efficient than Akash. So, he takes less days to complete the work.
Let, Vishal takes time = x days
So, Akash takes time = 3x days
According to the question,
3x = 45
x = 15
Thus, Vishal takes time 15 days.
Q15. Two brothers(younger and older) can do a piece of work in 70 and 60 days respectively. They began to work together, but the younger brother leaves after some days and the older brother finished the remaining work in 47 days. After how many days did the younger brother leave?
A) 14 days
B) 16 days
C) 11 days
D) 12 days
E) 7 days
Answer: E
Solution:
Older brother would have done 47/60 work in 47 days.
Remaining work = (1 -47/60) = 13/60 must have done by them together.
Two brothers 1 day work = (1/70 + 1/60) = 13/420
So, they would have done 13/60 work in 420/13 × 13/60 = 7 days.
Therefore, The younger brother left the work after 7 days.
Unlock success in Government exams by delving into essential quantitative aptitude topics. Explore the links provided for a comprehensive understanding of key concepts.
As you prepare for the exam, it is essential to actively engage in solving a variety of questions to deepen your understanding of key concepts. Additionally, analyzing previous year’s papers is crucial to discerning patterns and gaining insights into the types of questions frequently asked. This dual approach will not only enhance your conceptual clarity but also provide valuable exam-specific knowledge, fostering a more comprehensive exam preparation strategy.
Practice Questions on Time and Work
Question 1. If 6 men can complete a work in 12 days, how many men are needed to complete the same work in 3 days?
Question 2. A can do a piece of work in 6 days and B can do the same work in 12 days. In how many days can they finish the work together?
Question 3. A can do a job in 10 days. B is 60% more efficient than A. How long will B take to do the same job?
Question 4. X and Y can do a piece of work in 4 days. Y and Z can do it in 3 days. Z and X can do it in 2 days. How long will it take if all three work together?
Question 5. If 15 men working 8 hours a day can finish a work in 10 days, how many days will it take for 12 men working 10 hours a day to finish the same work?
Question 6. A machine can fill 120 bottles in 6 minutes. How many bottles can it fill in 15 minutes?
Question 7. A tap can fill a tank in 6 hours. Due to a leak, it takes 8 hours to fill the tank. If the tank is full, in how many hours will it become empty due to the leak?
Question 8. A and B together can do a piece of work in 12 days. If A alone can do it in 20 days, in how many days can B alone do it?
Question 9. A does 1/3 of a job in 5 days. B finishes the rest of the job in 10 days. How long would it take B to do the entire job alone?
Question 10. If 10 men working 6 hours a day can complete a work in 15 days, how many hours a day should 15 men work to complete the same work in 8 days?
Time and Work – FAQs
What’s the basic principle behind solving Time and Work problems?
A: The fundamental principle is that Work = Rate × Time. This can be applied in various forms, such as (Number of workers × Time taken) = Constant, for a given amount of work.
How do I handle problems where workers have different efficiencies?
A: Convert different efficiencies to a common unit, often expressed as the time taken to complete the entire job. Then, use the concept of work done per unit time to solve the problem.
What’s the best way to improve speed in solving these problems?
A: Practice regularly, learn to quickly identify the type of problem, and memorize common formulas. Develop the habit of estimating answers to check your calculations.
Are these types of problems relevant in real-world scenarios?
A: Yes, they’re highly relevant in project management, resource allocation, and productivity analysis in various industries. Understanding these concepts can help in efficient planning and execution of tasks.
How do I approach problems involving pipes filling and emptying tanks?
A: Treat filling pipes as positive work rates and emptying pipes as negative work rates. The net rate of filling or emptying is the sum of these rates.
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