Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
- 648
- 1800
- 2700
- 10800
Hint: Focus on the point that says that the work rate of machines is constant. Let the number of bottles produced by each machine be x bottles per minute and find the value of x using the data that 270 bottles are produced per minute by 6 machines.
Correct Answer: B
Solution and Explanation
Approach Solution 1:
Let us consider the number of bottles produced by a machine per minute to be x bottles. The number of bottles produced in k minutes is given by:
k×∑(work capacity of each machine per minute).
k×∑(work capacity of each machine per minute).
So, to solve the given information in the question using mathematical terms and the above formula, we conclude:
Total number of bottles produced by 6 machines in 1 minute=6*x
Total number of bottles produced by 6 machines in 1 minute=6*x
Therefore, 270=6*x
⇒x=45 bottles per minute.
⇒x=45 bottles per minute.
Therefore, the total number of bottles produced by 10 machines in 4 minute=10×4*x
Now we will put the value of x from the above equation.
We get, 10*4*45 =1800 bottles
Total number of bottles produced by 10 machines in 4 minute=1800 bottles
Hence, 10 machines can produce a total of 1800 bottles in 4 minutes. Hence, the answer to the above question is option B.
Note: For the questions that include the work of machines, have two things that must be selected wisely. One is the variables, and the other is the unit.
Approach Solution 2:
6 machines produce 270 bottles per minute
1 machine will produce 270/6 = 45 bottles per minute
10 machines will produce 45*10 = 450 bottles per minute
in 4 minutes, those 10 machines will product 450*4 = 1800 bottles
Approach Solution 3:
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6:10}
Time(inminutes) 1:4 }::270:x
Therefore
6×1×x=10×4×270
⇒x= (10×4×270)/(6)
⇒x= 1800
“Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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