Understanding the concept of "Time & Work" is crucial for students preparing for various exams. This topic not only helps in solving practical problems but also enhances your analytical skills. Practicing MCQs and objective questions on Time & Work can significantly boost your exam preparation and improve your scores. By tackling important questions, you can gain clarity and confidence in this essential area of mathematics.
What You Will Practise Here
Basic definitions and concepts of Time & Work
Formulas related to work done, time taken, and efficiency
Problems involving multiple workers and their combined efforts
Concept of work done in fractions and ratios
Applications of Time & Work in real-life scenarios
Diagrams illustrating work distribution among workers
Common tricks and shortcuts for solving Time & Work problems
Exam Relevance
The topic of Time & Work is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to calculate the time taken by individuals or groups to complete a task. Common question patterns include direct application of formulas, word problems, and scenarios involving efficiency comparisons. Mastering this topic can give you an edge in both school and competitive exams.
Common Mistakes Students Make
Confusing the relationship between time, work, and efficiency
Neglecting to convert units when necessary
Misinterpreting the problem statement, leading to incorrect assumptions
Failing to account for the contribution of multiple workers accurately
Overlooking the importance of practice in mastering problem-solving techniques
FAQs
Question: What is the formula for calculating work done? Answer: Work done can be calculated using the formula: Work = Time × Efficiency.
Question: How can I improve my speed in solving Time & Work problems? Answer: Regular practice of MCQs and understanding key concepts can significantly enhance your speed and accuracy.
Question: Are there any shortcuts for solving Time & Work problems? Answer: Yes, learning specific tricks and shortcuts can help you solve problems more efficiently, especially in competitive exams.
Now is the time to take charge of your exam preparation! Dive into our practice MCQs on Time & Work and test your understanding. The more you practice, the better you will perform!
Q. A can complete a work in 10 days, while B can complete the same work in 15 days. If both work together, how many days will they take to complete the work?
A.
5
B.
6
C.
7
D.
8
Solution
A's work rate = 1/10, B's work rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. They will complete the work in 6 days.
Q. A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days. If they work together, how long will they take to complete the work?
A.
4
B.
5
C.
6
D.
7
Solution
A's rate = 1/12, B's rate = 1/18, C's rate = 1/24. Combined rate = 1/12 + 1/18 + 1/24 = 1/4. They will complete the work in 4 days.
Q. A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days. If all three work together, how long will it take to complete the work?
A.
5
B.
6
C.
7
D.
8
Solution
A's rate = 1/15, B's rate = 1/20, C's rate = 1/30. Combined rate = 1/15 + 1/20 + 1/30 = 1/6. They will complete the work in 6 days.
Q. A can do a work in 18 days, B can do it in 24 days, and C can do it in 36 days. If they all work together, how long will it take to complete the work?
A.
6
B.
8
C.
10
D.
12
Solution
A's rate = 1/18, B's rate = 1/24, C's rate = 1/36. Combined rate = 1/18 + 1/24 + 1/36 = 1/6. They will complete the work in 6 days.
Q. A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days. If all three work together, how long will they take to complete the work?
A.
5
B.
6
C.
7
D.
8
Solution
A's rate = 1/20, B's rate = 1/30, C's rate = 1/60. Combined rate = 1/20 + 1/30 + 1/60 = 1/10. They will complete the work in 10 days.
Q. If 4 men can complete a work in 10 days, how many men are required to complete the same work in 5 days?
A.
6
B.
8
C.
10
D.
12
Solution
Work done by 4 men in 10 days = 1 work unit. Work done by 1 man in 40 days = 1/40 work unit/day. To complete in 5 days, required rate = 1/5 work unit/day. Number of men = 1/(1/40) * 5 = 8.
Q. If 5 workers can complete a task in 12 days, how many days will it take for 10 workers to complete the same task?
A.
6
B.
8
C.
10
D.
12
Solution
Work done by 5 workers in 12 days = 1 work unit. Work done by 1 worker in 60 days = 1/60 work unit/day. For 10 workers, rate = 10/60 = 1/6 work unit/day. Time = 1/(1/6) = 6 days.
Q. If a pipe can fill a tank in 15 hours and another pipe can empty it in 20 hours, how long will it take to fill the tank if both pipes are opened together?
Q. If a pipe can fill a tank in 8 hours and another pipe can empty it in 12 hours, how long will it take to fill the tank if both pipes are opened together?
A.
4
B.
6
C.
8
D.
10
Solution
Filling rate = 1/8, emptying rate = 1/12. Combined rate = 1/8 - 1/12 = 1/24. Time to fill = 24 hours.
