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Juice

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by Aman verma » Wed Aug 31, 2011 5:02 am
Q: There are 90 litres of grape juice and 150 litres of apple juice. The price of grape juice is $ 80 per litre and the price of apple juice is $ 75 per litre. Equal amounts of grape juice and apple juice is taken out and then grape juice is poured out in the vessel of apple juice and apple juice is poured out in the vessel of grape juice. Now the rates of both the mixtures is same. What is the amount of juice taken out from each of the vessel:

a)24.5 Litres

b)36 litres

c)45 litres

d)56.25 litres

e)68.5 litres
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by shankar.ashwin » Wed Aug 31, 2011 5:25 am
Since their final rates are equal, we could equate the per litre prices of both.

Consider x to be the amount removed and mixed in both, so we get:

[((90-x)80 + 75x)/90]=[((150-x)75+80x)/150]
Solving we get, 6750=120x
And x=56.25Ltrs
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by knight247 » Wed Aug 31, 2011 7:31 am
Once you get past equating this problem, half your battle is won.

Grape juice - 90 Litres costing $80/litre
Apple juice - 150 Litres costing $75/litre

Since equal quantities are taken out from both, let that amount equal x
After taking out x litres from both. 90-x and 150-x will be left respectively.

Grape juice .. 90-x litres will cost (90-x)80
Apple juice .. 150-x Litres will cost (150-x)75

Also,
Grape juice .. x litres will cost 80x
Apple juice .. x litres will cost 75x

(90-x)80+75x will be the total cost of the 90L mixture while (150-x)75+80x will be the total cost of the 150L mixture

Per litre cost of each mixture is {(90-x)80+75x}/90 and {(150-x)75+80x}/150

And both rates are now equal. So equating the above we get
{(90-x)80+75x}/90={(150-x)75+80x}/150
Calculation is pretty straight forward which gives you x=56.25 Hence D
Last edited by knight247 on Wed Aug 31, 2011 8:23 am, edited 3 times in total.
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by saketk » Wed Aug 31, 2011 8:19 am
Aman verma wrote:Q: There are 90 litres of grape juice and 150 litres of apple juice. The price of grape juice is $ 80 per litre and the price of apple juice is $ 75 per litre. Equal amounts of grape juice and apple juice is taken out and then grape juice is poured out in the vessel of apple juice and apple juice is poured out in the vessel of grape juice. Now the rates of both the mixtures is same. What is the amount of juice taken out from each of the vessel:

a)24.5 Litres

b)36 litres

c)45 litres

d)56.25 litres

e)68.5 litres
Let the amount of juice taken out =x

since the total quantity of juice in both the containers will remain same and the rate of the mixtures is also the same, our equation will look something like this.

90/[(90-x)*80+75x] = 150/[(150-x)*75+80x] --------equn 1

(90-x)*80 and (150-x)*75 are the prices of the juice remaining after we take out the X ltr of juice from both the containers. 75x and 80x is the value of the X amount of juice taken out of the container.


Solving equation 1, we will get X= 56.25.

Answer option D
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by Aman verma » Wed Aug 31, 2011 9:36 am
Many thanks to all the members for clarifying the underlying logic and solving the problem algebraically. I had a formula based solution but that was bit confusing: (3*150 + 5*90)/2*(3+5), I wasn't able to grasp the logic of the formula. OA[spoiler]d)56.25[/spoiler]
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