SOLUTION: Price of sugar is increased by 25%. The percentage of consumption to be decreased so that there would be no increase in the expenditure??
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Question 1122371: Price of sugar is increased by 25%. The percentage of consumption to be decreased so that there would be no increase in the expenditure??
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p is the current price of sugar.
q is the current quantity of sugar.
the total cost is equal to p * q.
when the price of sugar is increased by 25%, the price becomes 1.25 * p.
to keep the total cost the same, you will need to divide the quantity by 1.25.
you will get total cost is equal to 1.25 * p * q / 1.25 which becomes total cost is equal to p * q.
q / 1.25 is equal to 1/1.25 * q which is equal to .8 * q.
.8 * q is equal to q - .2 * q.
therefore, if the price goes up 25%, the quantity needs to come down 20% so that the total cost remains the same.
for example:
assume the price is 100 and the quantity is 100.
the total cost if 100 * 100 = 10,000.
when the price goes up 25%, the price becomes 125.
when the quantity comes down 20%, the quantity becomes 80.
125 * 80 = 10,000.
the total cost remains the same.
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