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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
An alloy of copper and zinc contains copper and zinc in the ratio 5 :  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 72% (02:05) correct 28% (02:30) wrong based on 296 sessions

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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

Kudos for a correct solution.

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

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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

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GMAT 1: 710 Q50 V34 Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 :  [#permalink]

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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 [ 19.2 KiB | Viewed 58781 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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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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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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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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1
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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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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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An alloy of copper and zinc contains copper and zinc in the ratio 5 :  [#permalink]

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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

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

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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

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

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