8 liters of solution is removed from 20% milk solution and 8 liters of

Question

8 liters of solution is removed from 20% milk solution and 8 liters of water is added to the solution. The resulting solution has 16% milk in it. What was the initial quantity of the 20% milk solution?

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

A. 38 liters
B. 40 liters
C. 42 liters
D. 44 liters
E. 45 liters

RJ7X0DefiningMyX · Accepted Answer

Let the initial quantity of the 20% milk solution be X, of which 0.2X would be milk and the remaining (0.8X) be water

Now since 8 litres of this solution is removed and is dilated by adding 8 litres of water, amount of milk reduced would be = 20% of 8 litres, i.e. 1.6 litres

The remaining portion of milk in the solution = 0.2X - 1.6 litres

Now, it is given that the concentration of the resulting solution (or to simply put, % of milk in the resulting solution) = 16%

We can write this as (0.2X - 1.6)/X *100 = 16, solving which we get 4X = 160, or X = 40 (D)

MidhilaMohan · Answer

8 litres of mixture taken out also had 20% milk => milk taken out was 8 x 0.2=1.6 litres

milk/total mixture =0.2=> milk=0.2 total qty

as the total qty remains the same, substitute the above eq as shown below

=>(milk-1.6)/total qty=0.16
=>0.2 total qty - 0.16 total qty= 1.6
=>total qty= 1.6/0.04=40 
IMO option B

Lampard42 · Answer

Milk/total solution = 20% initially then 16%;
M=0.2T

16%= T; 
16%=(0.2T-1.6)/T
0.04T=1.6; T=40 IMO B

gracie · Answer

let x=initial quantity of 20% milk solution
.8x-8(.8)+8=.84x→
x=40 liters
B

Archit3110 · Answer

total qty of milk ; .2*8 ; 16 
milk /total = 20%
milk-1.6/total = 16%
milk = .2*total
.2*total-1.6/total = .16
solve for total = 40 
IMO B

ScottTargetTestPrep · Answer

When 8 liters of the solution is removed, the 8 liters consists of 0.2 x 8 = 1.6 L of milk, and 6.4 L or water. If we let s = the initial amount, in liters, of the solution, so originally there are 0.2s liters of milk and we can create the equation:

(0.2s - 1.6 + 0)/(s - 8 + 8) = 16/100

(0.2s - 1.6)/s = 4/25

25(0.2s - 1.6) = 4s

5s - 40 = 4s

s = 40

Alternate Solution:

We start with x liters of 20% milk. We remove 8 liters of this solution, so we are removing 8 liters of 20% milk. Then we add back 8 liters of water (which is 0% milk), and the result is x liters of 16% milk. We can summarize this in an equation as:

x(0.20) - 8(0.20) + 8(0) = x(0.16)

0.20x - 1.6 + 0 = 0.16x

0.04x = 1.6

4x = 160

x = 40

Answer: B

apurv09 · Answer

we can do witha allegations:

we see we have 80%water solution, 8 litre is removed and is replayed by 100% water solution to make a 84% water solution.
so

80 100
 84
16:4
=4:1
So, 1/5 of the total solution was repplaced with 8 litres.
so, total solution is 40

nissstheone · Answer

can we do it this way?

20/100 * x = 8 ltrs. 
upon solving, we get x = 40 ltrs. ?

(percentage method?)

Basshead · Answer

We are told 8 liters of a solution is removed from a 20% milk solution.

Of the 8 liters removed, 20% consists of milk. Thus, 1.6 liters of the 8 liters consists of milk.

We are then given that the resulting solution consists of 16% milk. From this piece of information, we can create the following formula:

(0.2X - 1.6) / X * 100 = 16

20X - 160 / X = 16
16X = 20X - 160
X = 40

Answer is B.

Please correct me if I'm wrong, but we did not need to know that '8 liters of water is added' to solve this question.

KhayatiK · Answer

KarishmaB could u explain the last line : " So, 1/5 of the total solution was repplaced with 8 litres.". i approached the problem thru alligations myself, reached 32 liters (or 4:1 = water : original mixture) , but wasnt able to get to 32+8 = 40. the only POV im able to look at it is , to make a 16% solution , we need the OG sol to be 32 ltrs to which we are going to add the 8 ltrs water. which means the 32 litrs is the total quantity from which 8 lit solution was removed and replaced with external 8 litr water. hence in my mind, 32 ltrs shud b the answer. Thanks for clarifying.

apurv09

we can do witha allegations:

we see we have 80%water solution, 8 litre is removed and is replayed by 100% water solution to make a 84% water solution.
so

80 100
84
16:4
=4:1
So, 1/5 of the total solution was repplaced with 8 litres.
so, total solution is 40

Bunuel · Answer

A simple example would be to take x = 1. If you square both sides, you get x^2 = 1, which gives x = 1 or -1. The extra root x = -1 appears because squaring can introduce an additional, invalid solution.

KarishmaB · Answer

Think of the steps. You had certain quantity of 20% milk solution. You removed 8 liters of it. Then you mixed the remaining with 8 liters water and got 16% milk solution. You use alligation here - mix some amount of 20% solution with 8 liters water to get 16% solution and you found that this amount of 20% solution is 32 liters. So 32 liters of 20% milk solution was mixed with 8 liters of water to get 16% milk solution. 
But remember that you had removed 8 liters from the 20% solution in the first step. This means that you had 32 + 8 = 40 liters of 20% milk solution to start with.

8 liters of solution is removed from 20% milk solution and 8 liters of

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