# The price of raw materials has gone up by 15% labour cost has also increased from25% 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 material so as to keep the cost same?

1
by cnirmalkar

2014-11-20T20:41:50+05:30

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Let the amount of raw material used be X units.
Let price of raw material be = 100 units.

cost of raw material = 100 X units
Labour cost,  previously = 25% of 100 X = 25 X units

Total cost, previously = 125 X units
=====

New price of raw material = 100 + 15% *100 = 115 units
Let the reduced amount of raw material be Y units

new raw material cost = (100 + 15/100) Y = 115 Y units

It is not clear to me if the increase in labour cost is with respect to the old raw material cost or the new raw material cost.

Case 1 : labour cost is 30% previous raw material cost

new labour cost = 30% * (100 X) = 30 X units

Total cost , new = 115 Y + 30 X units

If the total cost is kept same as before, then

125 X = 115 Y + 30 X
95 X = 115 Y
Y/X = 95/115 = 82.6
=>   raw material amount is to be reduced by (100 - 82.6) = 17.4 %

Case 2 :  labour cost is 30% of new raw material cost

New labour cost = 30% * 115 Y = 34.5 Y
New total cost = 115 Y + 34.5 Y = 149.5 Y

As the total costs are to be the same,  125 X = 149.5 Y
Y/X = 125/149.5 = 83.6%

Hence, the reduction in raw material consumption is to be 16.4 %

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