A logistics company maintains a fleet consisting of three types of delivery vehicles: Vans… — GMAT

A logistics company maintains a fleet consisting of three types of delivery vehicles: Vans, Medium Trucks, and Heavy Trucks. The ratio of the number of Vans to Medium Trucks is $3 : 2$ , and the ratio of the number of Medium Trucks to Heavy Trucks is $4 : 1$ . If the average fuel efficiency is $24$ miles per gallon for the Vans and $15$ miles per gallon for the Medium Trucks, and the average fuel efficiency for the entire combined fleet is $19$ miles per gallon, what is the average fuel efficiency, in miles per gallon, of the Heavy Trucks?

Answer: 5 miles per gallon

Answer

The average fuel efficiency of the Heavy Trucks is 5 miles per gallon.

Combining the given vehicle ratios gives a unified proportion of 6 Vans to 4 Medium Trucks to 1 Heavy Truck (total 11 units). The total weighted efficiency sum is

6(24) + 4(15) + 1(x) = 144 + 60 + x = 204 + x

. Setting this equal to the combined fleet total of

11 \times 19 = 209

yields

x = 5

miles per gallon.

Step-by-Step Solution

Unify the two relative ratios into a single compound ratio for all three vehicle groups.

Vans : Medium Trucks : Heavy Trucks = 6 : 4 : 1, giving a total of 11 ratio units.

Both individual ratios share Medium Trucks as a common element (

2

units in the first ratio and

4

units in the second). Multiplying the first ratio by

2

aligns the Medium Truck count.

Set up the weighted mean equation using group weights and individual group averages.

Weighted Sum = 6(24) + 4(15) + 1(x) = 204 + x, where total elements = 11.

The sum of (group quantity × group mean) divided by total quantity equals the combined average.

Equate to total fleet mean and solve for the unknown average fuel efficiency x.

204 + x = 11 × 19 = 209, so x = 5 miles per gallon.

Multiplying total items (11) by total mean (19) gives total combined miles per gallon units (209).

Key Concept

Weighted Average of Multiple Combined Subgroups

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