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One fourth of a solution that was 10 percent sugar by weight

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One fourth of a solution that was 10 percent sugar by weight [#permalink] New post 21 Dec 2009, 05:17
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71% (02:19) correct 29% (02:20) wrong based on 59 sessions
One fourth of a solution that was 10 percent sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight ?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jun 2012, 06:13, edited 1 time in total.
Edited the question and added the OA
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Re: Tricky-mixture problem [#permalink] New post 21 Dec 2009, 06:00
EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of sugar in 2nd sol)=34%
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Re: Tricky-mixture problem [#permalink] New post 21 Dec 2009, 12:41
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Let the original solution be 100ml
It had 10ml of sugar
1/4 of this solution is removed
sugar remaining = 7.5 ML
25 ml of x% solution is added.
New volume of sugar = 7.5+25*x/100
Since resulting solution is 16% sugar by weight, volume of sugar = 16ml

equating the 2

x=(16-7.5)*4
=34

A
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Re: Tricky-mixture problem [#permalink] New post 21 Dec 2009, 16:52
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Answer A: 34%

Simply,
.75*.1+.25*y = .16
Solving for y would give the value 34%

Explanation:
.75% is still 10% solution
.25% is the y% solution

16% solution is 100%
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Re: Tricky-mixture problem [#permalink] New post 22 Dec 2009, 05:59
3/4 * 10 + 1/4 * x = 16
x = 16*4 - (30/4)*4
x = 64 - 30
x = 34

Therefore the answer is A
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Re: Tricky-mixture problem [#permalink] New post 22 Dec 2009, 12:57
A

Like ludwigfraboulet simpler approach.
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Re: Tricky-mixture problem [#permalink] New post 01 Jun 2012, 20:26
A

Total solution : 16 Liters

Initial Solution (V1) : 12 Liters
Concentration of Sugar (C1) = 10%

1/4 replaced with new solution (V2)= 4 liters
Concentration of Sugar (C2) = x% = ?

Final Solution (Vf): 16 Liters
Concentration of Sugar (Cf) = 16%



v1/v2 = (C2 - cf
) / (cf-c1)

12/4 = (x-16) / (16-10)

18 = (x-16)
34 = x
Re: Tricky-mixture problem   [#permalink] 01 Jun 2012, 20:26
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