Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]
(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%
TL;DR
Total Cost ($) = Unit Price ($/unit) * Quantity (units)
Cost ($) = Fuel Price ($/litre) * 1/Mileage (litre/km) * Distance (km)
1 = (6/5) * 1/m * 1 => m = 6/5
Increase in m = 6/5 - 1 = 1/5 = 20%
ANSWER: C
Veritas Prep Official Solution
The problem here is ‘how is mileage related to fuel price?’
Total fuel cost = Fuel price * Quantity of fuel used
Since the ‘total fuel cost’ needs to stay the same, ‘fuel price’ varies inversely with ‘quantity of fuel used’.
Quantity of fuel used = Distance traveled/Mileage
Distance traveled = Quantity of fuel used*Mileage
Since the same distance needs to be traveled, ‘quantity of fuel used’ varies inversely with the ‘mileage’.
We see that ‘fuel price’ varies inversely with ‘quantity of fuel used’ and ‘quantity of fuel used’ varies inversely with ‘mileage’. So, if fuel price increases, quantity of fuel used decreases proportionally and if quantity of fuel used decreases, mileage increases proportionally. Hence, if fuel price increases, mileage increases proportionally or we can say that fuel price varies directly with mileage.
If fuel price becomes 6/5 (20% increase) of previous fuel price, we need the mileage to become 6/5 of the previous mileage too i.e. mileage should increase by 20% too.
Another method is that you can directly plug in the expression for ‘Quantity of fuel used’ in the original equation.
Total fuel cost = Fuel price * Distance traveled/Mileage
Since ‘total fuel cost’ and ‘distance traveled’ need to stay the same, ‘fuel price’ is directly proportional to ‘mileage’.
Answer (C)