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Mixture and Alligation #1

1. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
A. 29.16 litresB. 28 litres
C. 28.2 litresD. 26 litres

Answer: Option A

Explanation:

Suppose a container contains $x$ units of a liquid from which $y$ units are taken out and replaced by water. After $n$ operations, quantity of pure liquid
$=x\left(1-\dfrac{y}{x}\right)^n$ units.

milk contained by the container now
$=40\left(1-\dfrac{4}{40}\right)^3\\= 40\left(1-\dfrac{1}{10}\right)^3 \\=40×\dfrac{9}{10}×\dfrac{9}{10}×\dfrac{9}{10}\\= \dfrac{4×9×9×9}{100}\\= 29.16$

Comments(7)

profileprince
2014-12-16 18:28:30 
they have taken 4 ltr of water each time that means totally 12 ltr right ?
40-12 =28

how come that is 29.16
plz explain
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profileVaijayanti
2014-12-20 19:53:25 
each time 4 L milk is taken and replaced with water.

Initially when 4 litre of milk is taken and replaced with water, the solution will have 36 litre of milk and 4 litre of water.

Next time when 4 litre is taken from this solution,  milk component removed = 4*36/40 = 3.6
after this process,  the solution will contain 32.4 litre of milk and 7.6 litre of water

next time, 4*32.4/40= 3.24 litre of milk gets removed.
Total quantity of milk becomes 32.4 - 3.24 = 29.16
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profileHarini
2014-01-16 06:59:15 
RAKESH:

From 40 liters 4 liters of milk is replaced by water three times.
then,
        practically 40-(4*3) =   40-12 = 28.
 .
.  .       ans is 28liters.
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profileJay
2014-01-19 19:35:41 
case 1: After 4 litre milk is taken out and replaced by water
water and milk are 4 litre and 36 litre respectively (ratio is 1:9)

case2: when 4 litre are removed in that mixture
quantity of water removed = 4 * (1/10) = 2/5
quantity of milk removed = 4 * (9/10) = 18/5
New quantity of Milk=36-18/5=162/5
New quantity of Water = 4-2/5=18/5

After addition of water,milk is same quantity (162/5)
New quantity of water = 18/5 + 4 =38/5
(ie, now ratio of  water and milk is 38 : 162 = 19 : 81)

case3: when 4 litre are removed in that mixture
quantity of water removed = 4 * (19/100) = 19/25
quantity of milk removed = 4 * (81/100)  = 81/25

New quantity of Milk=162/5-81/25=29.16 litre
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profilenaveed
2013-11-15 19:36:29 
10*10*10 = 1000 bt in above y it is 100?

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profilesandeep
2013-11-19 12:26:54 
bcz 40/10=4
thts why eqution is (4*9*9*9)/100
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profileRaj
2013-11-16 11:31:06 
40/10 is also done in the same step and hence it is 4. Remaining is 10*10 which is 100.
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