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Working together at their respective constant rates, Machine A and Machine B can produce 1,200 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,200 unit total would it produce?
A. 25
B. 33
C. 50
D. 67
E. 75
A. 25
B. 33
C. 50
D. 67
E. 75
08 Jun 2022, 01:57
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Machine A and Machine B can produce 1,200 units in 8 hours.
Working alone, Machine B would complete that same output in 50% more time.
=> machine B would need 8hrs + 50% of 8 hrs = 8 + 4 = 12hrs to produce 1,200 units
i.e., Production capacity of Machine B: 12hrs - 1,200 unit
Therefore, in 8 hrs machine B produces 800 units.
In 8 hrs both A & B produce 1,200 units, out of which B produces 800 units.
Therefore, Machine A produces 1,200 - 800 = 400 units in 8 hrs.
We need to find: % of 1,200 unit total that Machine A would produce working on its own for 8 hrs
=> what % of 1,200 = 400
Let the % be x => x*\(\frac{1200}{100}\) = 400
=> x = \(\frac{100}{3}\) ~ 33
Answer: B
Working alone, Machine B would complete that same output in 50% more time.
=> machine B would need 8hrs + 50% of 8 hrs = 8 + 4 = 12hrs to produce 1,200 units
i.e., Production capacity of Machine B: 12hrs - 1,200 unit
Therefore, in 8 hrs machine B produces 800 units.
In 8 hrs both A & B produce 1,200 units, out of which B produces 800 units.
Therefore, Machine A produces 1,200 - 800 = 400 units in 8 hrs.
We need to find: % of 1,200 unit total that Machine A would produce working on its own for 8 hrs
=> what % of 1,200 = 400
Let the % be x => x*\(\frac{1200}{100}\) = 400
=> x = \(\frac{100}{3}\) ~ 33
Answer: B
08 Jun 2022, 03:59
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If machine B can complete the task in 50% more time,i.e. in 3/2 of total time, it must have completed 2/3 of 1200 units in 8 hours.
Thus, in 8 hours, B can produce 1200*2/3 = 800 units.
In 1 hour, B will produce 100 units.
Similarly, machine A will produce 400 units in 8 hours.
Thus, A will complete 33.33% of the work in 8-hour shift.
The closest answer is option B.
Thus, in 8 hours, B can produce 1200*2/3 = 800 units.
In 1 hour, B will produce 100 units.
Similarly, machine A will produce 400 units in 8 hours.
Thus, A will complete 33.33% of the work in 8-hour shift.
The closest answer is option B.
