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Two alloys of iron having 85% and 67% iron respectively are fused toge

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Bunuel
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Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   31 Dec 2019, 03:14
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Two alloys of iron having 85% and 67% iron respectively are fused together to form another alloy having 71% iron in it. If 14 kgs of the first alloy is taken, find the weight of the second alloy.

A. 28 kgs
B. 34 kgs
C. 35 kgs
D. 42 kgs
E. 49 kgs
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E
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Re: Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   07 Jan 2020, 08:24
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Bunuel wrote:
Two alloys of iron having 85% and 67% iron respectively are fused together to form another alloy having 71% iron in it. If 14 kgs of the first alloy is taken, find the weight of the second alloy.

A. 28 kgs
B. 34 kgs
C. 35 kgs
D. 42 kgs
E. 49 kgs


Method: Mixtures and Allegations

Let the weights of 1st and 2nd alloy respectively be \(w_1\) & \(w_2\)

1st alloy ———— 2nd alloy
— 85 ——————— 67 —
————— 71 ——————
(71-67) —————(85-71)—
— 4 ——————— 14 ——

So, \(w_1\) : \(w_2\) = 4 : 14
—> 14/\(w_2\) = 2/7
—> \(w_2\) = 14*7/2 = 49

IMO Option E

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Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   07 Jan 2020, 15:00
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Bunuel wrote:
Two alloys of iron having 85% and 67% iron respectively are fused together to form another alloy having 71% iron in it. If 14 kgs of the first alloy is taken, find the weight of the second alloy.

A. 28 kgs
B. 34 kgs
C. 35 kgs
D. 42 kgs
E. 49 kgs


let x-14=weight of second alloy
.85(14)+.67(x-14)=.71x→
x-14=49 kgs
E
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Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   08 Jan 2020, 03:34
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First Alloy Second alloy
85 67


71

4 (71-67) 14(85-71)

The ratio of First alloy and the Second alloy = 4:14
= 2 :7
As there is 14(2 X 7) kg of first alloy, Second alloy = 7X7 = 49 kgs(E)
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Re: Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   10 Jan 2020, 09:24
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Bunuel wrote:
Two alloys of iron having 85% and 67% iron respectively are fused together to form another alloy having 71% iron in it. If 14 kgs of the first alloy is taken, find the weight of the second alloy.

A. 28 kgs
B. 34 kgs
C. 35 kgs
D. 42 kgs
E. 49 kgs


Solution:

Let’s let n = the weight of the second alloy. We can create the equation:

0.85(14) + 0.67n = 0.71(14 + n)

11.9 + 0.67n = 9.94 + 0.71n

1.96 = 0.04n

49 = n

Alternate solution:

We see that 71 is 14 away from 85 and 4 away from 67, so we can create the equation:

14/4 = n/14

4n = 196

n = 49

Answer: E
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Re: Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink] New post   10 Jan 2020, 09:59
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This question can be done easily using alligation:


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Re: Two alloys of iron having 85% and 67% iron respectively are fused toge [#permalink]
10 Jan 2020, 09:59
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