byRituparna Nath Content Writer at Study Abroad Exams
Question: Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
(A) 22
(B) 25
(C) 28
(D) 32
(E) 56
“Machine A produces bolts at a uniform rate of 120 every 40 seconds” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review".
In the GMAT Problem Solving section, examiners measure how well the candidates make analytical and logical approaches to solve numerical problems. In this section, candidates have to evaluate and interpret data from a given graphical representation. In this section, mostly one finds out mathematical questions. Five answer choices are given for each GMAT Problem solving question.
Solution and Explanation:
Approach Solution 1:
This above-given sum can be solved using the basic arithmetic formula for time and work. Let, Machine A produce 120 bolts every 40 seconds. So, Machine A produces 120/40 which is 3 bolts every second. Whereas, Machine B produces 100 bolts every 20 seconds. Therefore, Machine B produces 100/20 and makes 5 bolts every second. So, both the machines together produce 3+5 = 8 bolts every second.
Therefore, 8 bolts / 1 sec = 200 bolts / x sec
Doing Cross multiplication , we get 200 = 8x; x=25.
So it takes 25 seconds to produce 200 bolts when Machine A and Machine B work together.
Correct Answer: B
Approach Solution 2:
This above-given sum can be solved using the basic arithmetic formula for work and efficiency.
We are given that machine A produces bolts at a uniform rate of 120 every 40 seconds. Thus, the rate of Machine A is 120/40 = 3 bolts/second. We are also given that Machine B produces bolts at a uniform rate of 100 every 20 seconds. Thus, the rate of Machine B is 100/20 = 5 bolts/second. To determine the time it will take to produce 200 bolts when the two machines run simultaneously. For the time to produce 200 bolts, we can use the combined work formula:
Work by Machine A + Work by Machine B = 200 bolts (the total work completed).
As both machines are working simultaneously, we can say that they both work together for t seconds. We now can define the individual work done by Machine A and by Machine B. We must determine that work = rate x time.
Work done by Machine A = 3t
Work done by Machine B = 5t
This implies, 3t + 5t = 200
This implies,8t = 200
This implies, t = 200/8 = 25
Hence, option B is the most appropriate answer.
Correct Answer: B
Approach Solution 3:
In the problem, it is given that Machine a produces bolts at a uniform rate of 120/ 40 seconds.
So the machine b produces bolts at a uniform rate of 100/ 20 seconds.
Now, if the two machines run simultaneously, to produce a total of 200 bolts, the time required:
machine a produces 120/40 = 3 bolts/ second
machine b produces 100/20 = 5 bolts/ second
So, machines a and b produce 3 + 5 = 8 bolts/ second while running simultaneously
Hence, for 200 bolts the time required is 200 /8 = 25 seconds
Therefore if two machines run simultaneously then it takes 25 seconds to produce 200 bolts.
Correct Answer: B
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