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Three machines, individually, can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?
- a)11/30
- b)9/20
- c)3/5
- d)11/15
- e)5/6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Three machines, individually, can do a certain job in 4,5 and 6 hours,...
The two fastest machines will be able to do the greatest part of the job in one hour
The fastest machine, which can do the whole job in 4 hours, can do 1/4of the job in one hour
The next fastest machine, which can do the whole job in 5 hours, can do 1/5of the job in one hours Together, these machines can do
of the job in one hour
The fastest machine, which can do the whole job in 4 hours, can do 1/4of the job in one hour
The next fastest machine, which can do the whole job in 5 hours, can do 1/5of the job in one hours Together, these machines can do
of the job in one hourMost Upvoted Answer
Three machines, individually, can do a certain job in 4,5 and 6 hours,...
Understanding Machine Rates
To find the greatest part of the job that can be done in one hour by two machines working together, we first need to calculate the individual rates of each machine.
Machine Rates
- Machine A can complete the job in 4 hours:
Rate of Machine A = 1 job / 4 hours = 1/4 jobs per hour
- Machine B can complete the job in 5 hours:
Rate of Machine B = 1 job / 5 hours = 1/5 jobs per hour
- Machine C can complete the job in 6 hours:
Rate of Machine C = 1 job / 6 hours = 1/6 jobs per hour
Calculating Combined Rates
Now, we will calculate the combined rates of different pairs of machines:
- A and B:
Combined rate = 1/4 + 1/5
= (5 + 4) / 20 = 9/20 jobs per hour
- A and C:
Combined rate = 1/4 + 1/6
= (3 + 2) / 12 = 5/12 jobs per hour
- B and C:
Combined rate = 1/5 + 1/6
= (6 + 5) / 30 = 11/30 jobs per hour
Identifying the Greatest Rate
Now, we compare the combined rates of the pairs:
- A and B: 9/20
- A and C: 5/12 (which is approximately 0.4167)
- B and C: 11/30 (which is approximately 0.3667)
Among these, the greatest part of the job done in one hour by two machines working together is from A and B, which is 9/20.
Conclusion
Thus, the answer is option B: 9/20.
To find the greatest part of the job that can be done in one hour by two machines working together, we first need to calculate the individual rates of each machine.
Machine Rates
- Machine A can complete the job in 4 hours:
Rate of Machine A = 1 job / 4 hours = 1/4 jobs per hour
- Machine B can complete the job in 5 hours:
Rate of Machine B = 1 job / 5 hours = 1/5 jobs per hour
- Machine C can complete the job in 6 hours:
Rate of Machine C = 1 job / 6 hours = 1/6 jobs per hour
Calculating Combined Rates
Now, we will calculate the combined rates of different pairs of machines:
- A and B:
Combined rate = 1/4 + 1/5
= (5 + 4) / 20 = 9/20 jobs per hour
- A and C:
Combined rate = 1/4 + 1/6
= (3 + 2) / 12 = 5/12 jobs per hour
- B and C:
Combined rate = 1/5 + 1/6
= (6 + 5) / 30 = 11/30 jobs per hour
Identifying the Greatest Rate
Now, we compare the combined rates of the pairs:
- A and B: 9/20
- A and C: 5/12 (which is approximately 0.4167)
- B and C: 11/30 (which is approximately 0.3667)
Among these, the greatest part of the job done in one hour by two machines working together is from A and B, which is 9/20.
Conclusion
Thus, the answer is option B: 9/20.
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Three machines, individually, can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?a)11/30b)9/20c)3/5d)11/15e)5/6Correct answer is option 'B'. Can you explain this answer?
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Three machines, individually, can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?a)11/30b)9/20c)3/5d)11/15e)5/6Correct answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Three machines, individually, can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?a)11/30b)9/20c)3/5d)11/15e)5/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three machines, individually, can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?a)11/30b)9/20c)3/5d)11/15e)5/6Correct answer is option 'B'. Can you explain this answer?.
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