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An alloy of copper and zinc contains copper and zinc in the ratio 5 :

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An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 30 Jul 2015, 11:18
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An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3

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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 30 Jul 2015, 11:26
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Bunuel wrote:
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3

Kudos for a correct solution.


Alloy-1: Copper: Zinc = 5:3, Let Quantity = x
i.e. Copper in Alloy-1 = [5/(5+3)]*x = (5/8)x
and Zinc in Alloy-1 = [3/(5+3)]*x = (3/8)x


Alloy-2: Copper: Zinc = 1:7, Let Quantity = y
i.e. Copper in Alloy-2 = [1/(1+7)]*y = (1/8)y
and Zinc in Alloy-1 = [7/(1+7)]*y = (7/8)y


After Combining the two alloys
Copper = (5/8)x + (1/8)y
Zinc = (3/8)x + (7/8)y

Now, (5x + y)/8 = (3x + 7y)/8
i.e. 2x = 6y
i.e. x = 3y
i.e. x/y = 3/1

Answer: option D
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 30 Jul 2015, 15:16
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Bunuel wrote:
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3

Kudos for a correct solution.


IMO: D

Cu:zn = 5:3 Cu:zn = 1:7

Thus in 1st alloy in total of 8(5+3) parts 5 parts contain copper ==> Cu1 = 5/8
In 2nd alloy in total of 8(1+7) parts 1 part contains copper ==> Cu2 = 1/8

After combining Cu: Zn = 1:1
In final combination in total of 2 parts 1 part contain copper ==> 1/2
Attachment:
1.jpg
1.jpg [ 19.2 KiB | Viewed 35603 times ]


Thus Cu2 : Cu1 = 1:3

The ratio of Alloy1 : Alloy2 is asked = 3:1
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 31 Jul 2015, 02:01
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simple mixtures problem.

5x + y = 3x + 7y (since quantity of Cu and Zn in resultant mixture is equal)

2x = 6y
x = 3y

Ans. = D
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 31 Jul 2015, 07:31
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Let Alloy_1 be x units, and let Alloy_2 be y units.

So, fraction of copper in Alloy_1 = 5x/8, and fraction of zinc in Alloy_1 = 3x/8.

Similarly, fraction of copper in Alloy_2 = y/8, and fraction of zinc in Alloy_2 = 7y/8.

Mixing them, we get
copper = 5x/8 + y/8; zinc = 3x/8 + 7y/8.

So, 5x+y = 3x+7y
-> x = 3y
-> x/y = 3/1.

So, they must be mixed in the ratio 3 : 1. Ans (D).
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 31 Jul 2015, 14:48
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Putting together an equation with the numbers - 5x+y/ 3x+7y = 1

Solving it out - 2x=6y

Hence 3/1


Option D
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 05 Aug 2015, 23:23
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Bunuel wrote:
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3


Ans: D

Solution: While the ratio of Cu and Zn in both the mixture is given but not the quantity.
so we assume that M1 is x, and M2 is y.
now we know in M1= 5x/8 Cu, 3x/8 Zn
in M2 y/8 Cu and 7y/8

now we want to make the total quantity of Cu and Zn equal
use the following data and make equation

5x/8 + y/8 = 3x/8 + 7y/8
it gives x = 3y
so the ratio must be x:y = 3y:y = 3:1
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 15 Oct 2015, 00:56
let ratio of 1st alloy and 2nd alloy in 3rd mixture=k:1
5k+1=3k+7
k=3
ans 3:1 (D)
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An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post Updated on: 08 Mar 2018, 23:04
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3

let x=alloy 1
y=alloy 2
(5x/8)+y/8=4(x+y)/8
x/y=3
3:1
D

Originally posted by gracie on 23 Jan 2017, 10:44.
Last edited by gracie on 08 Mar 2018, 23:04, edited 1 time in total.
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 08 Mar 2018, 21:22
Hi All,

Beyond the algebra that can be used here, there are often other approaches that are fairly straight-forward (and sometimes faster/easier than doing "math"). Since the answers provide 5 ratios for us, we can use them "against" the information in the prompt to find the one ratio that gives us an equal proportion of copper and zinc. Let's TEST THE ANSWERS:

The two ratios…
C:Z
5:3

and

C:Z
1:7

Answer A: 1:5 gives us (5C + 3Z) + (5C + 35Z) --> 10C and 38Z --> NOT a match
Answer B: 7:3 gives us (35C + 21Z) + (3C + 21Z) --> 38C + 42Z --> NOT a match
Answer C: 5:3 gives us (25C + 15Z) + (3C + 21Z) --> 28C + 36Z --> NOT a match
Answer D: 3:1 gives us (15C + 9Z) + (1C + 7Z) --> 16C + 16Z --> This IS a match
Answer E: 4:3 gives us (20C + 12Z) + (3C + 21Z) --> 23C + 33Z --> NOT a match

Final Answer:

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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 : [#permalink]

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New post 12 Mar 2018, 16:33
Bunuel wrote:
An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?

A. 1 : 5
B. 7 : 3
C. 5 : 3
D. 3 : 1
E. 4 : 3


We can let the ratio of the first alloy of copper to zinc = 5x: 3x

We can let the ratio of the second alloy of copper to zinc = y : 7y

We can create the equation:

5x + y = 3x + 7y

2x = 6y

x = 3y

x/y = 3/1

Answer: D
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Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 :   [#permalink] 12 Mar 2018, 16:33
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