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Total cost of an item is formed out of three costs: Material cost, Lab

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Bunuel
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Total cost of an item is formed out of three costs: Material cost, Lab [#permalink] New post   25 Sep 2018, 05:14
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Total cost of an item is formed out of three costs: Material cost, Labour cost, Factory overhead cost, and Office overhead cost. If Material cost and Labour cost constitute 3/7 part of the total cost, Labour cost and Factory overhead cost constitute 1/2 part of the total cost, Factory overhead cost and Office overhead cost constitute 4/7 part of the total cost, and Material cost and Office overhead cost constitute 1/2 part of the total cost, which of the four cost is the highest among all?

(A) Material cost
(B) Labour cost
(C) Factory overhead cost
(D) Office overhead cost
(E) Factory overhead cost or Office overhead cost
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chetan2u
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Re: Total cost of an item is formed out of three costs: Material cost, Lab [#permalink] New post   29 Sep 2018, 18:58
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Bunuel wrote:
Total cost of an item is formed out of three costs: Material cost, Labour cost, Factory overhead cost, and Office overhead cost. If Material cost and Labour cost constitute 3/7 part of the total cost, Labour cost and Factory overhead cost constitute 1/2 part of the total cost, Factory overhead cost and Office overhead cost constitute 4/7 part of the total cost, and Material cost and Office overhead cost constitute 1/2 part of the total cost, which of the four cost is the highest among all?

(A) Material cost
(B) Labour cost
(C) Factory overhead cost
(D) Office overhead cost
(E) Factory overhead cost or Office overhead cost


Material cost, Labour cost, Factory overhead cost, and Office overhead cost.
If Material cost and Labour cost constitute 3/7 part of the total cost, so M+L=3/7 *T Labour cost and Factory overhead cost constitute 1/2 part of the total cost, so L+F=1/2*T....
Since 1/2*T>3/7*T... L+F>M+L..... F>M

Material cost and labour cost constitute 3/7 part of the total cost, so M+L=3T/7
and Material cost and Office overhead cost constitute 1/2 part of the total cost, so M+O=T/2
Since 1/2*T>3/7*T... M+0>M+L..... O>L

So any of the two - F or O

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Total cost of an item is formed out of three costs: Material cost, Lab [#permalink] New post   17 Mar 2021, 04:06
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Bunuel wrote:
Total cost of an item is formed out of three costs: Material cost, Labour cost, Factory overhead cost, and Office overhead cost. If Material cost and Labour cost constitute 3/7 part of the total cost, Labour cost and Factory overhead cost constitute 1/2 part of the total cost, , which of the four costs is the highest among all?

(A) Material cost
(B) Labour cost
(C) Factory overhead cost
(D) Office overhead cost
(E) Factory overhead cost or Office overhead cost


Let the total cost = 14

Material cost and Labour cost constitute 3/7 part of the total cost.
\(M+L = \frac{3}{7}*14 = 6\)
Labour cost and Factory overhead cost constitute 1/2 part of the total cost.
\(L+F = \frac{1}{2}*14 = 7\)
Factory overhead cost and Office overhead cost constitute 4/7 part of the total cost.
\(F+O = \frac{4}{7}*14 = 8\)
Material cost and Office overhead cost constitute 1/2 part of the total cost.
\(M+O = \frac{1}{2}*14 = 7\)

The smallest sum is yielded by M+L, suggesting that neither M nor L is the greatest cost.
Strategy:
Test small values for M and L to see whether F, O, or both can be the greatest.

Case 1: M=1 --> the equations above yield L=5, F=2 and O=6
In this case, O is greatest.
Eliminate A, B and C.

Case 2: L=1 --> the equations above yield M=5, F=6 and O=2
In this case, F is greatest.
Eliminate D.

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Total cost of an item is formed out of three costs: Material cost, Lab [#permalink]
17 Mar 2021, 04:06
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