A petrol manager was told that 20% of the diesel oil had leaked on the journey to the petrol pump. Considering this he decides to increase the price of his diesel oil by 20% so that the same amount of money will be taken for the lost petrol. Was the petrol manager correct? I've been stuck on this question for a while. Working out would be great thanks.
+130516 I always find that setting up a hypothetical situation in these kinds of problems helps to see the correct answer.....
Let's suppose that the petrol manager was suppose to receive 100 gallons of petrol which he is going to sell at $1 per gallon......so......the expected revenue would be $100
However......he now only receives 80 gallons [ 20% of the 100 was lost] and if he increases the price by 20%....the new cost for a gallon = $1.20
But......the new revenue will only be 80 * $1.20 = $96 .....$4 less than before
So.....to determine the percentage that will bring in the same revenue, we can solve this
80 (1 + x) = 100 where x is the percentage increase that will generate the same revenue
Divide both sides by 80
1 + x = 100/80
1 + x = 5/4 subtract 1 from both sides
x = 1/4 = .25 = 25%
So....the cost for a gallon of petrol will have to be increased by 25% [ to $1.25] to provide the same revenue!!!
Proof : 80 * $1.25 = $100
