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# The price of raw materials has gone up by 15%, labour cost has also in

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Joined: 18 Jul 2017
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The price of raw materials has gone up by 15%, labour cost has also in  [#permalink]

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27 Jan 2019, 05:33
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Difficulty:

65% (hard)

Question Stats:

50% (03:03) correct 50% (02:43) wrong based on 25 sessions

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The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

A. 30%
B. 24%
C. 28%
D. 25%
E. 17%
Math Expert
Joined: 02 Aug 2009
Posts: 7335
The price of raw materials has gone up by 15%, labour cost has also in  [#permalink]

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27 Jan 2019, 07:51
wishalsp333 wrote:
The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

A. 30%
B. 24%
C. 28%
D. 25%
E. 17%

Let the initial quantity be n and the initial cost be c, so labour charges = 0.25c.... Total cost = c+0.25c=1.25c
The changed price = 1.15c and therefore, the labour price = 0.30*1.15c..... Total cost = 1.15c+0.3*1.15c=1.15c*(1+0.3)=1.15c*1.3 = 1.495 c or 1.5c
Let the changed quantity be r..

the total money spent has to be the same, so $$1.25c*n=1.5c*r.......\frac{r}{n}=\frac{1.25}{1.5}=\frac{125}{150}$$..
r as a % of n = $$\frac{125}{150}*100=\frac{250}{3}=83$$%

Thus reduction is 100-83=17%
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Re: The price of raw materials has gone up by 15%, labour cost has also in  [#permalink]

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27 Jan 2019, 08:15
wishalsp333 wrote:
The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

A. 30%
B. 24%
C. 28%
D. 25%
E. 17%

Inline is my approach

Initial price of raw materials = 100
New price of raw materials = 115

Initial labor cost = 125
New labor cost = 130

By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same

For me this meant that

115* 130 * x( % decrease) = 125 * 100

So i just calculated the individual percentage decrease and added it

((130- 125) / 125) * 100 = 5/125 * 100 = 4

((115- 100) / 115) * 100 = 13

Total % = 17

E
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Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The price of raw materials has gone up by 15%, labour cost has also in  [#permalink]

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27 Jan 2019, 10:01
chetan2u wrote:
wishalsp333 wrote:
The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

A. 30%
B. 24%
C. 28%
D. 25%
E. 17%

Let the initial quantity be n and the initial cost be c, so labour charges = 0.25c.... Total cost = c+0.25c=1.25c
The changed price = 1.15c and therefore, the labour price = 0.30*1.15c..... Total cost = 1.15c+0.3*1.15c=1.15c*(1+0.3)=1.15c*1.3 = 1.495 c or 1.5c
Let the changed quantity be r..

the total money spent has to be the same, so $$1.25c*n=1.5c*r.......\frac{r}{n}=\frac{1.25}{1.5}=[fraction]125/100[/fraction]$$..
r as a % of n = $$\frac{125}{150}*100=\frac{250}{3}=83$$%

Thus reduction is 100-83=17%

chetan2u please see highlighted part it seems to be a typo error..
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Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
The price of raw materials has gone up by 15%, labour cost has also in  [#permalink]

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27 Jan 2019, 10:06
wishalsp333 wrote:
The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

A. 30%
B. 24%
C. 28%
D. 25%
E. 17%

really a great question;
let cost of raw material be x
new price of raw materials 15% increase : 1.15x
and labor cost has become 30% of the raw material ; 0.30*1.15x
new cost : 1.15x+0.3*1.15x
new cost : 1.5x

earlier cost would have been 25% of raw material cost i.e x so 1.25x
so we can say goods purchased at earlier price 1.25x* n
and new price 1.5x*r
1.25x *n = 1.5x*r
r/n = 1.25/1.5
= ~ 83% or say 17% reduction is required..

IMOE
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The price of raw materials has gone up by 15%, labour cost has also in   [#permalink] 27 Jan 2019, 10:06
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