Question

Elmer's new car gets $50\%$ better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is $20\%$ more expensive per liter than the gasoline his old car uses. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

$20\%$

$26\tfrac23\%$

$27\tfrac79\%$

$33\tfrac13\%$

$41\tfrac23\%$

Answer: A

Concepts:rate percentage

Difficulty rating: 1280

Solution:

Let the old car's fuel efficiency be $M$ kilometers per liter and let gasoline cost $C$ dollars per liter. The old car therefore costs $\dfrac CM$ dollars per kilometer to fuel.

The new car gets $1.5M$ kilometers per liter and its fuel costs $1.2C$ dollars per liter, so its fuel cost per kilometer is $\dfrac{1.2C}{1.5M}=0.8\dfrac CM.$

The new fuel cost is $80\%$ of the old one, so Elmer saves $20\%.$

Thus, the correct answer is A .

2017 AMC 10B Problem 12

Answer: A

Difficulty rating: 1280

Solution:

Problem 12 in Other Years