Math CentralQuandaries & Queries


Question from sujan, a student:

If the price of petrol increases by 25% and Rajesh intends to spend only 15% more on petrol then by how much % should he reduce the quantity of petrol he buys?

Suppose that Rajesh normally purchases $x$ liters of petrol at $d$ dollars per liter. Thus he normally pays $x \times d$ dollars for his petrol. He knows the price is going up but he wants his cost to only increase by 15% so he is only willing to pay $1.15 \times x \times d$ dollars.

The price of petrol is increasing by 25% so the new cost will be $1.25 \times d$ dollars per liter. He only plans to purchase a fraction of his normal amount. Suppose this fraction is $f$ so he plans to purchase $f \times x$ liters of petrol. At the increased price this will cost him $f \times x \times 1.25 \times d$ dollars.

Set the increased cost equal to the amount he is willing to pay and solve for $f.$ What percentage decrease is this in the amount of petrol he buys?


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