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

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!

Please suggest simpler solution.

Posted from my mobile device

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:

GMAT assassins aren't born, they're made,
Rich

How am I still not clear? Can someone simplify it further?

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