Karina is deciding whether to use Brand A or Brand B motor oil in her

Okay I am slightly confused about this question. How do you decide the percentage has to be taken with respect to brand A or brand B? It is slight confusion, but if I take percentage with respect to brand A, I get E as an answer which seems incorrect

The percentage decrease should be calculated with respect to Brand B's cost because you're comparing how much cheaper Brand A is than Brand B per kilometer.

The general formula for calculating percent increase or decrease (percent change) is: \(\frac{\text{Difference in values}}{\text{Reference value}}*100\). The reference value is the value you are comparing to.

Therefore, for the correct interpretation of 'The cost per kilometer driven is what percent less when using Brand A than when using Brand B?', would be \(\frac{\text{Brand B cost per kilometer} - \text{Brand A cost per kilometer}}{\text{Brand B cost per kilometer}} *100\). In this instance, Brand B serves as the reference point since the question asks how much less is cost per kilometer when using Brand A than when using Brand B.

Hope it's clear.

gmatophobia - I didn't understand something. How do we know what is the mileage in this question. Do we simple assume that if the cost of 1 litre of brand B oil is 100, then the mileage is also 1litre/km. What if the distance covered is 100km using brand B oil but its mileage is 50 km/litre. That would be mean the total cost incurred to cover that distance would be 200 bucks and not 100

 
Jayam12

The question mentions motor oil and not gasoline. Hence, mileage has no impact here. ­

 
We are dealing with motor oil here, not fuel, but the handling is no different. You need certain amount of fuel (petrol/diesel) for each km driven. Similarly, you need certain amount of motor oil which "gets used" as you drive and after some kms, it needs to be replaced. 

When dealing with confusing quantities such as 'mileage' or 'cost per km' etc  focus on the units. Here we are given: 

Brand A - Cost per litre = 1.5x , Distance per oil change = 2.5y km
Brand B - Cost per litre = x, Distance per oil change = y km
Same amount of oil will be filled at each change whether it is brand A or B so let's just assume its 1 ltr.

Cost per kilometer = Cost per litre/Distance per litre 

Cost per kilometer for Brand A = \(\frac{1.5x}{2.5y} = \frac{3x}{5y}\)

Cost per kilometer for Brand B = \(\frac{x}{y}\)

Hence, cost per km is 40% less for Brand A. 

Answer (B)

Check out another question in which using units to solve helps here:
https://youtu.be/_s5vZE-csgY 
­

Brand A Brand B
150 Rs/litre 100 Rs/litre
2.5x km x km


150/2.5x=60/x 100/x

100/x-60/x= 40/x ie. 40 %

Had a different approach but got the correct answer.
Since brand a is 50 percent greater that brand b I started my equations a=1.5b
Since brand a extends the amount of kilometers before oil change by 2.5 I divided this (2.5) by the price of a, new equation. a=1.5b/2.5 then solved.
2.5a=1.5b or 5a/2=3b/2
10a=6b
a=6b/10 or a=60% of b which is 40% less