Two alloys containing zinc and copper in the ratio 3: 5 and 9: 7 respe

Question

Two alloys containing zinc and copper in the ratio 3: 5 and 9: 7 respectively are melted to form a new zinc copper alloy in which the ratio of zinc and copper is 1: 1. In what ratio were the two alloys mixed?
A. 1:1
B. 2:3
C. 1:2
D. 3:8
E. 1:3

anuhyadixit · Answer

Take any zinc or copper ratio to the total and follow the subtraction approach.

3/ 8---------9/16 
--------1/2------------
1/16--------1/8 --->>> 8 : 16 = 1:2

Gives us the ratio 1:2

san10789 · Answer

Alloy1 zinc:copper = 3:5
or zinc:Total = 3:8

Alloy2 zinc:copper = 9:7
or zinc:Total = 9:16

lets take x amount of Alloy1 and y amount of alloy2 to get 
zinc:cooper = 1:1 or zinc:Total = 1/2

3x/8 + 9y/16 = (x + y)/2
Alloy1 + Alloy2 = Mixture

x/y = 1/2 = 1:2 (Alloy1:Alloy2)

Same result we can get if we consider cooper:

5x/8 + 7y/16 = (x+y)/2

x/y = 1:2

ThatDudeKnows · Answer

Here's another approach.

Alloy1 is 3/8ths zinc, so 37.5%.
Alloy2 is 9/16ths zinc so 56.25%.

Let's just PITA (Plug In The Answers). I usually like testing B and D, but those look like more of a pain in the butt than C, so let's do C.
 \frac{(1*37.5) + (2*56.25)}{3}=150/3=50

That makes it 50%. Is that a ratio of 1:1? Yep.

Answer choice C.

ThatDudeKnowsPITA

Gmat860sanskar · Answer

Let the alloys be mixed in ratio x:y. Zinc and copper ratios are 3:5 and 9:7 for alloys 1 and 2, respectively, and 1:1 for the new alloy.
Equation: (3/8)x + (9/16)y = (5/8)x + (7/16)y
Simplify: -(1/4)x = -(1/8)y
Cross-multiply: 8x = 4y
Ratio x:y = 1:2
Answer: C. 1:2

DrAnkita91 · Answer

can please someone tell why 1:1 ratio is wrong??
option A and C both are right

Bunuel · Answer

Only 1:2 is correct, not 1:1.

Check it directly:

Alloy 1 (3:5), so fraction of zinc = 3/8 = 0.375 
 Alloy 2 (9:7), so fraction of zinc = 9/16 = 0.5625

We want the final alloy to be 1:1, i.e. 0.5 zinc fraction.

If you mix equal parts (1:1), the average zinc fraction = (0.375 + 0.5625)/2 = 0.46875, which is not 0.5.

Only when the alloys are mixed in 1:2 do we get exactly 0.5 zinc and 0.5 copper.

So option A is not correct, only C is.

Two alloys containing zinc and copper in the ratio 3: 5 and 9: 7 respe

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Two alloys containing zinc and copper in the ratio 3: 5 and 9: 7 respe

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