Percentages Question
Question:
An alloy of copper and aluminum has 40%
copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7.
These two alloys are mixed in such a way that in the overall alloy, there is
more aluminum than Zinc, and copper constitutes x% of this alloy. What is the
range of values x can take?
A. 30%
< x < 40%
B. 32.5%
< x < 42%
C. 33.33%
< x < 40%
D. 32.5%
< x < 40%
Correct Answer : (A)
Explanation:
Alloy 1

Copper

Aluminium

2x

3x


Alloy 2

Copper

Zinc

2y

7y

If
Aluminium and Zinc have to be equal, 3x = 7y. The simplest case occurs at the
LCM, when both Aluminium and Zinc are 21kg.
Alloy 1

Copper

Aluminium

14

21


Alloy 2

Copper

Zinc

6

21

Even
a gram of alloy 1 above this level would mean that there is more Aluminium than
Zinc in the total alloy. So, this table is a limit on the percentages of
different metals.
The
percentage of Copper in the total alloy would be (14 + 6)* = 32.25%
On
the other hand, if we want more Aluminium than Zinc, we can use tons and tons
of alloy 1, and only a microgram of Alloy 2. The quantity of alloy 2 can be
made so small that its presence can be almost neglected, as it will have as
good as zero impact on the overall percentage of copper. This is another
extreme case, in which Copper will have 40% weight in the alloy.
Thus,
the percentage of Copper ranges from 32.25% to 40% in this alloy.
Answer Choice (A)
Level
of difficulty 2
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