Time and Work is an important topic in Quantitative Aptitude which often appears in government exams. Many candidates are familiar with the basic concepts even before starting their preparation. This subject is relevant not only in Mathematics but also in Physics and is commonly tested in government competitive jobs examinations. By mastering these subjects, candidates can improve their scores significantly, as it is a favorite subject for the examiners. To perform well, candidates need to understand the main formulas and practice solving problems regularly. In exams like banking, questions related to time and work assess the candidate’s ability to manage tasks and resources efficiently. Regular practice can help candidates perform well in this section.
time and work
Problems of time and work are prominent in many competitive examinations including bank examinations. These problems assess the candidate’s ability to analyze the relationships between time, work and efficiency. Mastering this subject can significantly improve your performance in the quantitative section of bank exams. This article will highlight the basic concepts, essential formulas, and typical aptitude questions you may face.
concept of time and work
Relation of work and time:
- Work: Generally it is considered as a task or job that needs to be completed.
- Time: Period required to complete the work.
Efficiency (rate of work): This is usually the amount of work done per unit of time. Higher efficiency means less time is required to complete the task.
basic principles:
- If a person or a machine can complete a work in ‘n’ days, the amount of work done in a day is 1/n of the total work.
- Conversely, if a person or machine can complete 1/n work in a day, then they can complete the work in ‘n’ days.
joint work:
When several people or machines work together, their combined rate of work is the sum of their individual rates.
essential formula
Individual Work Rate:
- Work rate of A = 1\time taken by A to complete the work
Combined work rate:
- Work rate of A and B = Work rate of A + Work rate of B
Time taken by joint workers:
Time taken by A and B = 1(A’s work rate + B’s work rate)
Functional equivalence:
- If A is ‘k’ times as efficient as B, then A will take ‘1/k’ times the time taken by B to complete the work.
Work done by multiple institutions:
- If A, B, and C can do a piece of work in x, y, and z days respectively, then the joint work rate is:
combined work rate = 1/x + 1/y + 1/z
- The time taken by A, B and C together to complete the work is:
Time taken = 1\Joint work rate
qualifying questions for practice
Question 1:
A can complete a work in 12 days, and B can complete the same work in 16 days. How much time will A and B together take to complete the work?
Solution:
Work rate of A = 1/12
Work rate of B = 1/16
Combined work rate = 1/12 + 1/16 = (4 + 3)/48 = 7/48
Time taken = 48/7 (approximately 6.86) days.
Question 2:
If A is twice as efficient as B and together they can complete a work in 18 days, then how much time will each take individually to complete the work?
Solution:
Let the work rate of B be 1/x. Then, the work rate of A is 2/x
Combined work rate = 1/x} + 2/x = 3/x.
3/x = 1/18
x = 54
Time taken by B = 54 days, and time taken by A = 54/2 = 27 days.
Question 3:
C can do a work in 10 days. B is 50% more efficient than C, and A is twice as efficient as B. How much time will A, B and C together take to complete the work?
Solution,
Work rate of C = 1/10.
Work rate of B = 1.5 × (1/10) = 3/20
Work rate of A = 2 × (3/20) = 3/10
Combined work rate = 1/10 + 3/20 + 3/10 = 2/20 + 3/20 + 6/20 = 11/20
Time taken = 20/11 (approximately 1.82) days.
Tips for Solving Time and Work Problems
Understand the question: Read the problem carefully to identify who is doing the work, their individual work rates, and how these rates combine.
Use Ratio and Proportion: Many problems can be simplified by using ratios, especially when comparing efficiencies.
Work with fractions: Be comfortable converting work and time into fractions, as most solutions involve fractional rates of work.
Practice regularly: Consistent practice helps to recognize patterns and improve speed and accuracy.
By mastering these concepts, formulas and practicing different types of questions, you will be well prepared to tackle time and task problems in your bank exams.
