At a logistics company, fuel expenditure accounted for 40\% of total operational costs in … — GRE General Test

At a logistics company, fuel expenditure accounted for $40\%$ of total operational costs in Year 1, while maintenance expenditure accounted for the remaining $60\%$ . In Year 2, fuel expenditure increased by $25\%$ , and maintenance expenditure decreased by $15\%$ . If there were no other operational costs in either year, by what percentage did the total operational cost change from Year 1 to Year 2?

An increase of $1\%$ Answer
B
An increase of $5\%$
C
An increase of $9\%$
D
An increase of $10\%$
E
A decrease of $1\%$

Answer

An increase of

1\%

The total operational cost increases by

1\%

because fuel cost increases by

0.40 \times 25\% = +10\%

of the total cost, while maintenance cost decreases by

0.60 \times 15\% = -9\%

of the total cost, yielding a net change of

+10\% - 9\% = +1\%

Step-by-Step Solution

Assign an arbitrary base value or variable for Year 1 total cost

Let the total operational cost in Year 1 be

C = 100

. Thus, fuel expenditure is

40

and maintenance expenditure is

60

Choosing a concrete baseline value makes multi-step percentage change calculations clear and straightforward.

Calculate Year 2 cost for each component

Year 2 fuel cost

= 40 \times (1 + 0.25) = 50

. Year 2 maintenance cost

= 60 \times (1 - 0.15) = 51

Apply the individual percentage increase (

+25\%

) and decrease (

-15\%

) to the respective Year 1 component values.

Sum the Year 2 component costs and compute total percentage change

Total Year 2 cost

= 50 + 51 = 101

. Percent change

= \frac{101 - 100}{100} \times 100\% = +1\%

Compare the new total operational cost to the original baseline cost to determine net percentage change.

Key Concept

Weighted Percentage Change

Estimated Time:1m 30s

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