In January, a logistics company's total monthly operational expenditure for its electric d… — GMAT

In January, a logistics company's total monthly operational expenditure for its electric delivery fleet was $\$C$ . In February, the number of vehicles in the fleet increased by $25\%$ , while the monthly operational cost per vehicle decreased by $10\%$ due to optimized charging schedules. If the fleet's total operational expenditure in February was $\$33,750$ , what was the total operational expenditure, in dollars, in January?

Answer: 30000 dollars

Answer

The total operational expenditure in January was $30,000.

The total expenditure is the product of the number of vehicles and the cost per vehicle. An increase of

25\%

in fleet size introduces a multiplier of

1.25

, while a

10\%

decrease in unit cost introduces a multiplier of

0.90

. The net multiplier for the total expenditure is

1.25 \times 0.90 = 1.125

(or

\frac{9}{8}

). Dividing the February total of

\$33,750

1.125

yields the January expenditure of

\$30,000

Step-by-Step Solution

Define variables for January's components and express January's total cost

Let

N

be the number of vehicles in January and

V

be the operational cost per vehicle in January. Total January expenditure

C = N \times V

Total cost is the product of quantity and unit cost.

Determine the updated fleet size and unit cost for February

February fleet size

= N \times (1 + 0.25) = 1.25 N = \frac{5}{4} N

. February unit cost

= V \times (1 - 0.10) = 0.90 V = \frac{9}{10} V

25\%

increase corresponds to a factor of

1.25

, and a

10\%

decrease corresponds to a factor of

0.90

Calculate February's total expenditure in terms of

C

February total cost

= \left(\frac{5}{4} N\right) \times \left(\frac{9}{10} V\right) = \frac{45}{40} NV = 1.125 C = \frac{9}{8} C

The total cost in February is the product of the updated fleet size and the updated unit cost.

Solve for January's total cost

C

\frac{9}{8} C = 33,750 \implies C = 33,750 \times \frac{8}{9} = 3,750 \times 8 = 30,000

Divide February's known cost by the net multiplier

1.125

(or

\frac{9}{8}

) to reverse the percent change.

Key Concept

Net percentage change on a product of variables and reverse calculation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic