Time and Work Problems Question and Answers
Introduction
Nowadays, Aptitude time and work questions play an important role in competitive exams. It is very important to develop these skills. It determines your knowledge and values. One of the most important skills we want to know is time and work. It is a basic and common question that we see in every competitive exam. Practicing the time and work questions for competitive exams sum helps you to grow your mathematical knowledge. In this article, Nithra Jobs provides a time and work formula along with some time and work questions with solutions. Let's solve these below-given problems with the guidance of Nithra Jobs.
Time and workFormulas
1. Work from Days
If A can do a piece of work in 'n' days, then A's one day's work = 1/n
2. Days from work
If A's one day's work = 1/n, then A can finish the work in n days.
3. 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
Solved Problems
1. Praveen and Harish can finish a work 30 days if they work together. They worked together for 20 days and then Harish left. Praveen finished the remaining work in another 20 days. In how many days Praveen alone can finish the work?
Answer: 60 days.
Explanation:
Amount of work done by Praveen and Harish in 1 day = 1 / 30
Amount of work done by Praveen and Harish in 20 days = 20 *( 1 / 30 )
= 20 / 30
= 2 / 3
Remaining work = 1 - ( 2 / 3 )
= 1 / 3
Praveen completes ( 1 / 3 ) work in 20 days.
Amount of work Praveen can do in 1 day = ( 1 / 3 ) ( 1 / 20 )
= 1 / ( 3 * 20 )
= 1 / 60
Praveen can complete the work in 60 days.
2. Aswanth is twice as good a workman as Raja and is therefore able to finish a piece of work in 30 days less than Raja. In how many days they can complee the whole work, working together?
Answer: 20 days.
Explanation:
Ratio of times taken by Aswanth and Raja = 1 : 2.
The time difference is (2 - 1) 1 day while Raja take 2 days and Aswanth takes 1 day. If difference of time is 1 day, Raja takes 2 days.
If difference of time is 30 days, Raja takes 2 * 30 = 60 days.
So, Aswanth takes 30 days to do the work. Aswanth's 1 day's work = ( 1 / 30 )
Raja's 1 day's work = ( 1 / 60 ) (Aswanth + Raja)'s 1 day's work is
= ( 1 / 30 ) + ( 1 / 60 )
= ( 2 + 1 ) / 60
= ( 3 / 60 )
= ( 1 / 20 )
Aswanth and Raja together can do the work in 20 days.
3. Arjun, Bala and Karthi can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but Karthi left 4 days before the completion of the work. In how many days was the work completed?
Answer: 11 days.
Explanation:
One day's work of Arjun, Bala and Karthi is
= ( 1 / 24 ) + ( 1 / 30 ) + ( 1 / 40 )
= ( 5 + 4 + 3 ) / 120
= 12 / 120
= ( 1 / 10 )
Karthi leaves 4 days before completion of the work, which means only Arjun and Bala work during the last 4 days.
Work done by Arjun and Bala together in the last 4 days is
= 4 * ( 1 / 24 + 1 / 30 )
= 4 * ( ( 5 + 4 ) / 120 )
= 4 * ( 9 / 120 )
= ( 9 / 30 )
= ( 3 / 10 )
Remaining Work = 7/10, which was done by Arjun,Bala and Karthi in the initial number of days. Required days = Their one-day work / Remaining work
= ( 1 / 10 ) / ( 7 / 10 )
= ( 1 / 10 ) * ( 10 / 7 )
= ( 1 / 7 )
Number of days required for these initial work = 7 days. Thus, the total numbers of days required is
4 + 7 = 11 days.
The total numbers of days required is 11 days.
4. X and Y can do a piece of work in 15 days and 12 days respectively. X started the work alone and then after 3 days Y joined him till the completion of the work. How long did the work last?
Answer: 25 / 3 days
Explanation:
Work done by X in 3 days = ( 1 / 15 ) * 3
= 1 / 5
Remaining work = 1 - 1 / 5
= 4 / 5
( X + Y )'s 1 day's work = ( 1 / 15 ) + ( 1 / 12 )
= 27 / ( 15 * 12 )
= 3 / 20
Now, 3 / 20 work is done by X and Y in 1 day
So, 4 / 5 work will be done by X and Y = ( 20 / 3 ) * 4 / 5
= 16 / 3 days
Hence, total time taken = 3 + ( 16 / 3 ) days
= 25 / 3 days
The total work will last for 25 / 3 days.
5. A is 20 % more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 20 days?
Answer: 120 / 11 days
Explanation:
Given data, ratio of time taken by A and B = 100 : ( 100 + 20 )
= 100 : 120
= 10 : 12
Suppose B takes x days to do the work Then, 10 : 12 :: 20 : x
x = 20 * 12 / 10
= 24
A's 1 day's work = 1 / 20
B's 1 day's work = 1 / 24
( A + B )'s 1 day's work = ( 1 / 20 ) + ( 1 / 24 )
= 11 / 120 days
A and B together can complete the work in 120 / 11 days.
Conclusion
Nithra Jobs provides simple time and work aptitude questions to improve your aptitude skills. This site provides time and work questions for competitive exams. Time and work solved examples with solutions will be very helpful for future studies, exams, etc. Stay connected with us to get more questions with solved answers to score in your upcoming exams. Nithra Jobs wishes you a great future. It is the No.1 Job portal in Tamil Nadu. It is a very useful site for the Job seekers.
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