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

Question

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%

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

KanishkM · Accepted Answer

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

amanchandra17 · Answer

Above all are those of the bad explanations:

here is the easiest explanation

Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125
Now,
15% increment in raw materials cost and labor cost has gone up to 30% from 25 %
Raw material cost = 115 And
Labor cost = (115 × 30%) = 34.5
So, New net cost,
= 115 + 34.5 = 149.5
Difference of labor cost = 149.5 - 125 = 24.5
% reduction = 24.5×100149.5
 = 17%(approx.)

chetan2u · Answer

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%

Archit3110 · Answer

chetan2u  please see highlighted part it seems to be a typo error..

Archit3110 · Answer

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

JHTIPU18 · Answer

I need a shortcut method. Can anyone help me pleas!

Posted from my mobile device

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