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Two brands of detergent are to be combined. Detergent X contains 20 pe

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Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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Two brands of detergent are to be combined. Detergent X contains 20 percent bleach and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent soap. If the combined mixture is to be 35 percent bleach, what percent of the final mixture should be Detergent X?

(A) 10%
(B) 32 1/2 %
(C) 35%
(D) 40%
(E) 60%
[Reveal] Spoiler: OA

Originally posted by Gmatdecoder on 23 Dec 2014, 23:31.
Last edited by Bunuel on 24 Dec 2014, 02:00, edited 1 time in total.
Edited the question.
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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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New post 24 Dec 2014, 01:46
Let we mix x units of detergent X and y units of detergent Y
Bleach Soap Total
Detergent X 0.20x 0.80x x
Detergent Y 0.45y 0.55y y
Combined 0.20x+0.45y 0.80x+0.55y x+y

Percentage of bleach in combined mixture = (0.20x+0.45y)/(x+y) = 35/100

20x + 45y = 35x + 35y
10y = 15x
x/y = 2/3

So, percentage of detergent x = x*100/(x+y) = (x/y)*100/ ((x/y)+1)
= (2/3)*100/((2/3)+1)
= 200/5 = 40%

So, Answer will be D

Hope it helps!


Gmatdecoder wrote:
Two brands of detergent are to be combined. Detergent X contains 20% bleach and 80% soap, while detergent Y contains 45% bleach and 55% soap. If the combined mixture is to be 35 % bleach, what % of the final mixture should be of detergent X?
A 10%
B 32-1/2 %
C 35%
D 40%
E 60%

Looking for process solution pls.

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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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New post 24 Dec 2014, 09:36
Please suggest simpler solution.

Posted from my mobile device
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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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New post 24 Dec 2014, 09:38
Hi Gmatdecoder,

In mixture questions, if you're not given amounts of each item to work with (in this case, the amount of the 2 detergents), then you can TEST VALUES and use real numbers to solve the problem.

Here, we're told about 2 detergents:
Detergent X = 20% bleach
Detergent Y = 45% bleach

We're told to mix some of each detergent together and end up with a 35% bleach mixture.

Here's how you can TEST VALUES:

Let's say you have 10 oz of Detergent X...
10(20%) = 2 oz bleach

We'll have to mix that with a certain amount of Detergent Y (let's call that Y oz.)
Y(45%) = .45Y oz bleach

Bleach/All = (2+.45Y)/(10 + Y) = .35

2+.45Y = 3.5 + .35Y
.1Y = 1.5
Y = 15

So, we need 15 oz. of Detergent Y to be mixed with 10 oz. of Detergent X to get a combined mixture that is 35% bleach.

The question asks what percent of the final mixture is X?

10/25 = 40%

Final Answer:
[Reveal] Spoiler:
D


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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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Gmatdecoder wrote:
Please suggest simpler solution.

Posted from my mobile device



Best is the allegation method. Refer diagram below:

Attachment:
ble.png
ble.png [ 5.86 KiB | Viewed 3067 times ]


X percentage \(= \frac{10}{25} * 100 = 40%\)
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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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Gmatdecoder wrote:
Two brands of detergent are to be combined. Detergent X contains 20 percent bleach and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent soap. If the combined mixture is to be 35 percent bleach, what percent of the final mixture should be Detergent X?

(A) 10%
(B) 32 1/2 %
(C) 35%
(D) 40%
(E) 60%


.2x+.45y=.35(x+y)
x/y=2/3
2/(3+2)=2/5=40%
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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe [#permalink]

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New post 19 Mar 2018, 10:49
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Re: Two brands of detergent are to be combined. Detergent X contains 20 pe   [#permalink] 19 Mar 2018, 10:49
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