The total cost to build a table is two-folds – one, the cost of raw material consumed and two, the labour cost. Further, the labour cost is calculated as a percentage of the cost of raw material consumed. Due to changes in the supply and labour situation, the price of raw material increased by 25% and also the labour cost increased from 20% of cost of raw material to 32% of cost of raw material. If the total cost to build a table needs to be the same, find the percentage reduction in consumption of raw material used.

27.2727…%

Approach 1: We have already seen, how to find the percentage increase in total cost of the table. Next, consider this as a stand-alone standard question ….. if the percentage increase in price is …%, by what percentage should consumption reduce to main the expenditure? I am sure, you would have done such a question.

Approach 1: We need to realise that this question has price and consumption, both. The price will be a sort of rate and total raw material cost will be price × consumption.

Let original price i.e. rate of raw material be Rs. 100/unit and original consumption be 100 units.

You can easily find the new price and let new consumption be x units.

Now, all you have to do is equate the original total cost and new total cost. Total cost can be found by finding the cost of raw material consumed as price × consumption; and then the labour cost can be added as a percentage of this raw material cost.

Let original price of raw material be Rs. 100/unit and original consumption be 100 units.

New raw material price will be Rs. 125/unit and let new consumption be x units

Equating total costs ….

120% of (100 × 100) = 132% of (125 × x)

Here we have added the labour cost to the raw material cost directly e.g. [raw material cost + 20% of raw material cost] is same as [120% of raw material cost]

Solving the equation, we get x = 800/11 i.e. 72.7272…

Thus, consumption reduced from 100 to 72.7272 … , a reduction of 27.2727…. %