Question

A car rental agency is considering a modification in its oil change procedure. currently, it uses a type X filter, which cost $4.25 and must be changed every 9,000 miles along with oil (4 quarts.) Between each oil change , one quart of oil must be added after each 500 miles. The proposed filter (typeY) has to be replaced every 4,000 miles (along with 4 quarts of oil) but does not require any additional oil between filter changes. If the oil costs $1.14 per quart, what is the maximum acceptable price for the Type Y filter?

A. $7.97

B. $15.94

C. $17.93

D. 58.87

Answer 1

Answer : The answer is option C.

For type X filter : After 500 miles 1 quart of oil have to be added. So, for 9000 miles (9000/500) = 18 quart of oil have to be added additionally. Given that type X filter requires 4 quart of oil for 9000 miles. So, type X filter requires total (18 + 4) = 22 quart of oil. Per quart oil price is $1.14. Therefore, cost of 22 quart of oil = 22 * 1.14 = $25.08. As the cost of type X filter is $4.25, hence the total cost for this filter = 25.08 + 4.25 = $29.33 .

For type Y filter : There is no need to add additional quart of oil. But it have to be changed for every 4000 miles. This filter requires 4 quart of oil for 4000 miles. So, for 1000 miles it requires 1 quart of oil. Hence, for 9000 miles it requires 9 quart of oil. As the price of per quart of oil is $1.14, hence the cost for 9 quart of oil = 9 * 1.14 = $10.26 .

Now, for 9000 miles the cost difference between type X filter and type Y filter = 29.33 - 10.26 = $19.07.

So, the maximum acceptable price for type Y filter have to be either less than $19.07 or equal to $19.07 . Based on given options, options A, B and C are acceptable. But the maximum acceptable price is $17.93. Therefore, option C is correct.