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# A bottle contains a certain solution. In the bottled solution, the rat

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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05 Apr 2016, 06:44
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Difficulty:

65% (hard)

Question Stats:

64% (02:33) correct 36% (02:41) wrong based on 225 sessions

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A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

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Joined: 02 Aug 2009
Posts: 8283
Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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05 Apr 2016, 07:01
Bunuel wrote:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

Hi,
W:Soap = 3:2 and
Soap :Salt = 9:2..

however the ratio of W:S is halved due to evaporation = 3:4..
so Multiply W:S by 9 and S:Salt by 4 to get combined ratio
so W:S:Salt = 3*9 : 4*9 : 2*4 = 27 : 36 : 8
so Ratio of W: Salt = 27 : 8..
ans E
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Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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05 Apr 2016, 07:07
1
2
Water:soap = 3:2

Soap:Salt=9:2

=> For 9 soap, salt = 2
=> For 2 Soap, salt = (2/9)*2 = 4/9

So, water:soap:salt = 3:2:4/9 = 27:18:4

After open container, water:soap:salt = 13.5:18:4

So, water:salt = 13.5:4 = 27:8
Intern
Joined: 09 Dec 2016
Posts: 1
Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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23 Feb 2017, 05:50
Bunuel wrote:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

Hi,

Could you please explain why are we not considering evaporation of salt and soap?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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23 Feb 2017, 05:59
ashupatil wrote:
Bunuel wrote:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

Hi,

Could you please explain why are we not considering evaporation of salt and soap?

Thanks

It is assumed that only water evaporates. .
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Joined: 07 Dec 2014
Posts: 1218
A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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23 Feb 2017, 10:10
2
Bunuel wrote:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

original water:soap ratio=3:2=27:18
and original soap:salt ratio=3*3:2=9:2=18:4
thus original water:salt ratio=27:4
half the water is lost during evaporation
thus new water:salt ratio=27/2:4=27:8
E
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Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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27 Feb 2017, 11:50
1
1
Bunuel wrote:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

We are given that in a bottled solution, the ratio of water to soap is 3 : 2. Since the ratio of soap to salt is three times this ratio, the ratio of soap to salt is 9 : 2. We see the number for soap in the first ratio is 2 while that in the second is 9. We can make them the same number by using their LCM. Since the LCM of 2 and 9 is 18, we can say the ratio of water to soap is 27 : 18 and the ratio of soap to salt is 18 : 4. Thus:

water : soap : salt = 27 : 18 : 4

If the ratio of water to soap is halved by water evaporation, the new ratio of water to soap is 13.5 : 18 and the new ratio of water : soap : salt is 13.5 : 18 : 4. Thus, the ratio of water to salt after water evaporation is 13.5 : 4 or 27 : 8.

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Re: A bottle contains a certain solution. In the bottled solution, the rat  [#permalink]

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20 Jun 2019, 06:17
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Re: A bottle contains a certain solution. In the bottled solution, the rat   [#permalink] 20 Jun 2019, 06:17
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