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06 Jun 2019, 00:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
73% (03:08) correct
27%
(02:52)
wrong
based on 193
sessions
History
Date
Time
Result
Not Attempted Yet
Each of 60 mineral water bottles in a certain shipment is either 500ml or 1 litre and the average volume of the bottles in the shipment is 800ml. If the average volume of bottles is to be reduced to 600ml by removing some 1 litre bottle, how many 1 litre bottles must be removed?
A) 24
B) 36
C) 20
D) 30
E) 40
A) 24
B) 36
C) 20
D) 30
E) 40
06 Jun 2019, 11:08
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Since this is a question on weighted averages (all mixtures and alligation questions, essentially, are applications of weighted average), we CAN use the weighted average formula to solve this question. However, the quicker method will be to use the alligation diagram.
The diagrams representing the first situation is shown below:
06th June 2019 - Reply 2 - 1.JPG [ 19.93 KiB | Viewed 9338 times ]
So we gather that the two types of bottles should be mixed in the ratio of 2:3 to obtain an average quality of 800 ml for the mixture. This means that, there should be 24 bottles of 500ml and 36 bottles of 1000 ml.
For the second situation, the diagram can be drawn as shown below:
06th June 2019 - Reply 2 - 2.JPG [ 22.21 KiB | Viewed 9152 times ]
We have only removed the 1 litre bottles. So, the 4 parts of the ratio should still represent 24 bottles. This means that 1 part will represent 6 bottles.
But there were 36 bottles of 1000 ml earlier. This means 30 bottles were removed.
The correct answer option is D.
If you have practiced the alligation diagram enough and are good with it, this question should take you about a minute to solve.
Hope this helps!
The diagrams representing the first situation is shown below:
Attachment:
06th June 2019 - Reply 2 - 1.JPG [ 19.93 KiB | Viewed 9338 times ]
So we gather that the two types of bottles should be mixed in the ratio of 2:3 to obtain an average quality of 800 ml for the mixture. This means that, there should be 24 bottles of 500ml and 36 bottles of 1000 ml.
For the second situation, the diagram can be drawn as shown below:
Attachment:
06th June 2019 - Reply 2 - 2.JPG [ 22.21 KiB | Viewed 9152 times ]
We have only removed the 1 litre bottles. So, the 4 parts of the ratio should still represent 24 bottles. This means that 1 part will represent 6 bottles.
But there were 36 bottles of 1000 ml earlier. This means 30 bottles were removed.
The correct answer option is D.
If you have practiced the alligation diagram enough and are good with it, this question should take you about a minute to solve.
Hope this helps!
General Discussion
06 Jun 2019, 00:55
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Equation 1 : 500X+1000Y=800*60 divide by 500 to obtain x+2y=8*12
Equation 2 = x+y=60
Solving both X= 24 and Y = 36; So 500*24+1000y=600*(24+y) solving this Y=6; So 30 bottles must be removed IMO Option D
Equation 2 = x+y=60
Solving both X= 24 and Y = 36; So 500*24+1000y=600*(24+y) solving this Y=6; So 30 bottles must be removed IMO Option D
