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# How many liters of water must be added to a 20 liter solution of water

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
How many liters of water must be added to a 20 liter solution of water  [#permalink]

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27 Jan 2017, 09:40
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Difficulty:

35% (medium)

Question Stats:

76% (01:56) correct 24% (02:21) wrong based on 314 sessions

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How many liters of water must be added to a 20 liter solution of water and acid, which is 24% acid, to make a solution that is 8% acid?

A. 20
B. 40
C. 48
D. 60
E. 170

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Re: How many liters of water must be added to a 20 liter solution of water  [#permalink]

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27 Jan 2017, 22:24
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Bunuel wrote:
How many liters of water must be added to a 20 liter solution of water and acid, which is 24% acid, to make a solution that is 8% acid?

A. 20
B. 40
C. 48
D. 60
E. 170

Volume of acid will remain unchanged as only water is being added.

$$\frac{24}{100}*20$$ = $$\frac{8}{100}*Final Volume$$
Thus, $$Final Volume$$ = 60

Change in Volume = Water added = 60-20 = 40 liters.
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How many liters of water must be added to a 20 liter solution of water  [#permalink]

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28 Jan 2017, 11:41
Amount of Acid in the new mix : 24/100* 20 + 0*X = 8/100*(X+20)

24/5 = 2/25X + 40/25 => 120 = 2X + 40

=> X = 40

You can also easily check because the acid required is 8% which is 1/3 of the first mix (24%), therefore we need 1/3 of the mix and 2/3 of water => 20* 3 * 2/3 = 40
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Re: How many liters of water must be added to a 20 liter solution of water  [#permalink]

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28 Jan 2017, 16:04
Bunuel wrote:
How many liters of water must be added to a 20 liter solution of water and acid, which is 24% acid, to make a solution that is 8% acid?

A. 20
B. 40
C. 48
D. 60
E. 170

let w=liters of water to be added
.76*20+w=.92(20+w)
w=40
B
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Re: How many liters of water must be added to a 20 liter solution of water  [#permalink]

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21 Apr 2017, 08:36
1
Choice:B
Time taken:1:26
here we go
Since currently acid is 24% in 20 liter mean 4.8 Litre
So
(4.8/20+x)*100=8(The new required level)
480=8(20+x)
480=160+8x
320=8x
x=40
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How many liters of water must be added to a 20 liter solution of water  [#permalink]

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08 May 2017, 19:30
Let x be amount of water to be added to the original 20 liters

x is 100% water, so there's an implied 1 before the first x in equation:

.24*20 + x = .08*(20+x)

4.8 + x = 1.6 + .08x
3.2 =.08x
x=40
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Re: How many liters of water must be added to a 20 liter solution of water  [#permalink]

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08 May 2017, 22:44
We are going to mix a 24% acid solution with water which is basically a 0% acid solution. And the result required is 8% acid. So we can apply weighted average concept here.

Ratio in which these two solutions (24% and 0%) should be mixed in order to get an 8% result can be found this way:

24-8 = 16 and 8-0 = 8. So the net result must be 16 steps away from 24 and 8 steps away from 0. OR we can say that ratio in which 24% and 0% solutions should be mixed (in order to get an 8% solution) has to be 8:16 or 1:2.

Since the ratio is 1:2, the amount of 0% solution (water in our case) must be double that of 24% solution.

So the amount of water must be = 2*20 = 40 litres.
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Re: How many liters of water must be added to a 20 liter solution of water  [#permalink]

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08 Oct 2018, 01:18
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Re: How many liters of water must be added to a 20 liter solution of water   [#permalink] 08 Oct 2018, 01:18
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