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Difficulty: HardPercentage Calculations

A naval fleet has a certain number of vessels. Currently, 20%20\% of the fleet is undergoing long-term maintenance. Of the operational vessels remaining, 25%25\% are currently deployed on active missions. If there are exactly 3333 operational vessels remaining at the home port, what is the total number of vessels in the entire fleet?

  1. A
    4444
  2. B
    6060
  3. 5555Answer
  4. D
    165165

Answer

The total number of vessels in the entire fleet is 5555.
The correct answer is found by tracking the remaining percentages step-by-step. Since 20% of the fleet is in maintenance, 80% remains operational. The 25% deployment rate applies to this 80%, meaning 20% of the total fleet is deployed (0.25 * 0.80 = 0.20). Subtracting the deployed vessels leaves 60% of the original fleet at the port. Finally, dividing the 33 vessels by 0.60 yields the original total fleet size of 55.

Step-by-Step Solution

1
Determine the percentage of the fleet that is not in maintenance.
100%−20%=80%100\% - 20\% = 80\%
The 25%25\% deployment rate applies only to the remaining operational vessels.
2
Calculate the percentage of the total fleet that is deployed.
25%25\% of 80%=0.25×80%=20%80\% = 0.25 \times 80\% = 20\%
To find the deployed amount relative to the whole fleet, multiply the successive percentages.
3
Determine the percentage of the total fleet that remains at the home port.
80%−20%=60%80\% - 20\% = 60\%
Subtracting the deployed vessels from the operational vessels gives the portion remaining at port.
4
Set up an equation and solve for the total number of vessels in the fleet (xx).
0.60x=33⇒x=330.60=550.60x = 33 \Rightarrow x = \frac{33}{0.60} = 55
The 60%60\% of the total fleet is equal to the 3333 vessels explicitly counted at the port.

Key Concept

Successive Percentage Calculations and Reversing Percentages
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Topics

Percentage Calculations

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