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Difficulty: HardPercents and Percent Change

The table below shows the number of employees in Division A and Division B of a company in 2024.

DivisionNumber of employees (2024)
Division A160
Division B240

In 2025, the number of employees in Division A increased by 35%, and the total number of employees in the company increased by 2%. What was the percent decrease in the number of employees in Division B from 2024 to 2025?

  1. A
    12%
  2. 20%Answer
  3. C
    25%
  4. D
    80%

Answer

The correct answer is 20%.
The correct answer is 20%. To find this, first calculate the total number of employees in 2024, which is 160+240=400160 + 240 = 400. In 2025, Division A's employees increase by 35% to 160×1.35=216160 \times 1.35 = 216, and the total number of employees increases by 2% to 400×1.02=408400 \times 1.02 = 408. The number of employees in Division B in 2025 is the difference: 408−216=192408 - 216 = 192. The decrease in Division B is 240−192=48240 - 192 = 48 employees. Finally, the percent decrease is calculated relative to Division B's original count of 240: 48240×100%=20%\frac{48}{240} \times 100\% = 20\%.

Step-by-Step Solution

1
Find the total number of employees in the company in 2024.
The total number of employees in 2024 is 160+240=400160 + 240 = 400.
To find changes in the total company size, we need to establish the baseline total.
2
Calculate the number of employees in Division A in 2025.
The number of employees in Division A in 2025 is 160×1.35=216160 \times 1.35 = 216.
Division A's workforce increased by 35% from its 2024 value of 160.
3
Calculate the total number of employees in the company in 2025.
The total number of employees in 2025 is 400×1.02=408400 \times 1.02 = 408.
The total company workforce increased by 2% from its 2024 value of 400.
4
Determine the number of employees in Division B in 2025.
The number of employees in Division B in 2025 is 408−216=192408 - 216 = 192.
The employees in Division B are the remaining employees after subtracting Division A's employees from the company total.
5
Calculate the percent decrease in Division B's employees from 2024 to 2025.
The decrease in Division B is 240−192=48240 - 192 = 48 employees. The percent decrease is 48240×100%=20%\frac{48}{240} \times 100\% = 20\%.
The percent decrease is the change divided by the initial value of Division B (240), multiplied by 100.

Key Concept

Solving multi-step percent problems with varying base values.

Alternative Method

Instead of calculating the absolute number of employees, you can use the weighted average of the percent changes. Since Division A represents 160400=40%\frac{160}{400} = 40\% of the company and Division B represents 240400=60%\frac{240}{400} = 60\%, the weighted percent change equation is: 0.40(35%)+0.60(x)=2%0.40(35\%) + 0.60(x) = 2\%, where xx is the percent change for Division B. Solving for xx gives: 14%+0.60x=2%⇒0.60x=−12%⇒x=−20%14\% + 0.60x = 2\% \Rightarrow 0.60x = -12\% \Rightarrow x = -20\%, representing a 20%20\% decrease.
Estimated Time:2m 0s
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Topics

Percents and Percent Change

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