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water in a potion

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by sanju09 » Tue Feb 16, 2010 6:24 am
Ratio of syrup to water in a potion contained in a jar is 7:5. What fraction of potion in the jar must be swapped by water so as to obtain syrup to water in the potion as one to one?
(A) ¼
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8



[spoiler]Any problem in the wording?[/spoiler]
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by ajith » Tue Feb 16, 2010 6:31 am
sanju09 wrote:Ratio of syrup to water in a potion contained in a jar is 7:5. What fraction of potion in the jar must be swapped by water so as to obtain syrup to water in the potion as one to one?
(A) ¼
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8

[spoiler]Any problem in the wording?[/spoiler]
Say the capacity of jar is 1.2 Liters

It contains 700 ml of Syrup and 500 ml of water

now say a portion, y is taken from the jar and replaced by same amount of water

the syrup removed = 7/12*y and water added is 7/12*y

700 - 7/12y = 600
7y = 1200
y= 1200/7

y as a fraction of original size =[spoiler] (1200/7)/1200 = 1/7, D[/spoiler]
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by djkvakin » Tue Feb 16, 2010 7:36 am
There is also a very simple and fast approach: total parts=12. 1:1 would mean that there are 6 parts of syrup and 6 parts of water. Therefore we need to swap one part of syrup for the water (to make 7 a 6) - this will increase 5 by 1 and make it 6.
Since there are 7 parts of syrup and 1 part has to be swapped, then we know that it's 1/7, hence D is our answer.
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by anki_jain » Thu Feb 25, 2010 12:02 am
as per my understanding it should be 1/6.

To remove the 1/7th part of the syrup you need to remove 1/7th part of the water and then you put the same fraction of water to make it 1:1.

say, 700g syrup 500g water
First, you have to remove 200g mixture from 1200g to remove 100g of syrup, so we will have 600g syrup and 400g water. then you will refill it with 200g of water that would make it 600g syrup and 600g water.

So as per the question "What fraction of potion in the jar must be swapped by water", it should be 200g of potion should be swapped with water i.e 200/1200=1/6.

in brief, we are not swapping the syrup with water, we are swapping the mixture of syrup+water with water.

OA??
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