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The value of an alloy varies directly with the concentration of metal

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The value of an alloy varies directly with the concentration of metal [#permalink]

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The value of an alloy varies directly with the concentration of metal A and inversely with the square of the concentration of metal B. If the concentration of metal B has been increased by 30%, by approximately what percentage should the concentration of metal A be increased to avoid a drop in the value of the alloy?

A. 15%
B. 30%
C. 60%
D. 70%
E. 80%
[Reveal] Spoiler: OA

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Re: The value of an alloy varies directly with the concentration of metal [#permalink]

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New post 22 Oct 2017, 23:42
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IMO option D.
Let the value = V
v=k*x/\(y^{2}\)
The concentration of y has increased by 30%
New value =v=k*x/1.69 \(y^{2}\)
So to compensate the drop in value the concentration of A should approximately increase by 70%.
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Re: The value of an alloy varies directly with the concentration of metal [#permalink]

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New post 14 Nov 2017, 06:20
Plug in numbers
As per the question
V=value is directly proportional to conc of A and inversely prop of square of B or V=kA/B^2. (k is constant)
Let A=10 and B=10
we have V=10/(10)^2=10/100=1/10.
We have value of V =1/10
and
the new value of Y which is 30% more ie it is 13 now (10+30% of 10)
and
we now need to find the new A so that V remains=1/10
(1/10)=A/(13)^2=1/10=A/(169) or New A=16.9 which is 6.9 more than earlier A or approx 70% more. Answer D

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Re: The value of an alloy varies directly with the concentration of metal [#permalink]

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New post 14 Nov 2017, 06:36
let the initial concentration of A & B = 100 each
Value = K *100/ 100^2
New value = K * x /130^2
Equating we get x = 169
increase required in A = 69% that is approx 70%. Hence Answer is D

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The value of an alloy varies directly with the concentration of metal [#permalink]

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New post 18 Nov 2017, 13:35
nkmungila wrote:
The value of an alloy varies directly with the concentration of metal A and inversely with the square of the concentration of metal B. If the concentration of metal B has been increased by 30%, by approximately what percentage should the concentration of metal A be increased to avoid a drop in the value of the alloy?

A. 15%
B. 30%
C. 60%
D. 70%
E. 80%



hi

former expression

B^2
_____
A

later expression

(1.3 B)^2
_________
A

to keep the later expression approximately the same in value as the former expression, A should be increased by 70% , as (1.3)^2 = 1.69

cheers through the kudos button if this helps
thanks :cool:

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The value of an alloy varies directly with the concentration of metal   [#permalink] 18 Nov 2017, 13:35
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