A vessel is filled with a liquid in which 5 parts are milk and 3 parts are water. What fraction of mixture must be drawn off are replaced with water. So that the mixture may be half water and half milk.
a) 1/2
b) 1/3
c) 2/3
d) 1/5
e) 1/8
Mixture Question: A Vessel is Filled with a Liquid
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E.
hmmm Wrong Choice !!
d – You have to remove 1/8 of milk, and replace the milk with water because the mixture is currently 3/8 water and 5/8 milk. In order to remove 1/8 of milk:
x(5/8) = 1/8
which x=1/5
well said……..other way could be
5 – (5+3)X 5/8 = 4
=> X= 1/5
the answer is D :
5 parts are milk so let’s say 50 instead 100
3 parts are water so let’s say 30 instead 100
then 100-(50+30) = 20 because we must have 50% milk and 50% water, so 20% from 100% there’s 20/100 equal to 1/5, it’s D.
We have replace milk with water
So when we replace 1/8 of milk with 1/8 of water ratio of milk and water will be equal.
So we are replacing (1/8)/(5/8) (amount of milk/fraction of milk_
=1/5
Hence d..
milk is 5x and water 3x and total mixture is 8x.
when we remove ‘y’ litres of mixture we are removing 5y/8 milk and 3y/8 water and again replacing with y litres of water.
Hence, equation will become :
5x-5y/8=3x-3y/8+y
2x=10y/8
which gives y/8x=1/5 and hence D.
We have to replace
1/5 of the existing milk (that equals)
1/8 of the total mixture
The question asks “portion of mixture” and not “portion of milk”
hence
E
OA ?
It’s D.
In the original content: there’s 3/8 water, now you need to remove a fraction (which is also 3/8 of water) and add the same amount back to make it 1/2. This translates to simple algebra expressions:
3/8 – 3/8x + x = 1/2
solve for x, and x = 1/5 –> Choice D
Option D
D
d is correct.
1/5 * 5 =1, So water will be 3+1=4 and Milk will be 5-1=4
Ans D
Its 5 parts of milk and 3 parts of water. If we take out 1 part of the milk, and this part be replaced by water, we have 4 parts of milk and 4 parts of water.. hence this 1 part of water that has been added = the part of milk in the mixture that was removed. There 1part of water added/total mixture is the final answer.. Its E.
Heu…
Simple rule of 3
5/8 = 1
1/2 = x
=> 5/8 * x = 1/2
=> x = (1/2) / (5/8)
=> x = 8 / 10
to have a concentration of 0.5 you have to have 0.8 of the current mixture: you have to remove 20% of the current mixture and replace it with nothing, in that case water.
Hence 20% is the awnser = 1/5 = ‘D’
Here is my answer,
let V be the quantity of the mixture to be replaced with water.
before replacement, the quantity of milk in the mixture is :
(5/8)*(8-v) which must represent the half of the total volume.
==> (5/8)*(8-v) = 8/2
==> v = 8/5
so the fraction of mixture to be replaced is v/8 = 1/5