Question

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?

Answer 1

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
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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 %