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Concrete mixture A is composed of 35 percent cement, 40 pecent sand an

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Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post Updated on: 17 Jul 2018, 11:46
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Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%

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Originally posted by Harshgmat on 16 Jul 2018, 08:45.
Last edited by Harshgmat on 17 Jul 2018, 11:46, edited 1 time in total.
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Re: Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 16 Jul 2018, 19:33
Harshgmat wrote:
Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%


.35A+.15B=.25(A+B)
.10A=.10B
A=B
50%
D
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Re: Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 16 Jul 2018, 23:16
I'm a bit confused - the response to this question is D and the spoiler says C... can someone help me figure out which one is correct? I got D but don't know if that is right.
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Re: Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 17 Jul 2018, 11:48
sdilley wrote:
I'm a bit confused - the response to this question is D and the spoiler says C... can someone help me figure out which one is correct? I got D but don't know if that is right.


Thanks sdiley for pointing out the error. :(

It is being rectified now. :angel:
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Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 17 Jul 2018, 12:44
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Harshgmat wrote:
Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%

We need to track only on cement percents, and we need either the ratio of A to B (part-part) or the ratio of A to (A + B) (part-whole) to answer the question.

Let % = percent cement in a mixture
A = volume / weight of A
B = volume / weight of B

(% A)(Vol A) + (% B)(Vol B) = (% A+B)(Vol A+B)

\((.35*A)+(.15*B)=.25(A+B)\)
\(35A+15B=25A+25B\)
\(10A=10B\)

\(A=B\) in the final mixture

\(A\) is what percent of final mixture's weight?

Part-whole.
Percent A is \(\frac{A}{A+B}*100\)
From above \(A=B\)
Percent A:
\(\frac{A}{A+A}=\frac{1A}{2A}=\frac{1}{2}=(.50*100) = 50\) percent

Answer D

Part-Part
From above, \(A=B\)
Part + Part = Whole
Half + Half = Whole
A is half = 50%

That is, logically, a mixture containing only A and B and equal parts A and B is 50% A.

Answer D
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Re: Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 17 Jul 2018, 13:18
Harshgmat wrote:
Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%


i have used an alligator method :-)

...35....………….15...

…………...25...………...

25-15..........35-15

…….. 10.......10...….

………...\(\frac{10}{10}\)

so D :grin:

is my solution correct :)
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Re: Concrete mixture A is composed of 35 percent cement, 40 pecent sand an  [#permalink]

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New post 17 Jul 2018, 19:10
1
Harshgmat wrote:
Concrete mixture A is composed of 35 percent cement, 40 pecent sand and 25 percent gravel; concrete mixture B is composed of 15 percent cement, 30 percent sand and 55 percent gravel. If a mixture of A and B contains 25 percent cement, what percent of the weight of the mixture is A?

A 20%
B 33 1/3%
C 45%
D 50%
E 55 1/3%



One of the best way to do this is by weighted average method
1) Here since presence of cement in final solution is being talked of, we require to concentrate only on cement.
2) the question becomes much easier when we see the % in three solutions..
A- 35
B- 15
Mix of A and B - 25
25 is half way between 15 and 35, so 50% of each

D
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