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Zorluk: OrtaPercentages, Percent Change, and Interest

In Year 1, a software company had a total of 400 subscribers divided between a Basic plan and a Premium plan, with 70%70\% of the subscribers enrolled in the Basic plan. In Year 2, the number of Basic plan subscribers decreased by 20%20\%, while the total number of subscribers across both plans increased by 10%10\%. What was the percentage increase in the number of Premium plan subscribers from Year 1 to Year 2?

  1. A
    24%24\%
  2. B
    30%30\%
  3. C
    50%50\%
  4. 80%80\%Cevap
  5. E
    180%180\%

Cevap

The percentage increase in Premium plan subscribers from Year 1 to Year 2 was 80%80\%.
In Year 1, 70%70\% of the 400 subscribers were on the Basic plan (0.70×400=2800.70 \times 400 = 280), which leaves 120 subscribers on the Premium plan. In Year 2, the total subscriber count increased by 10%10\% to 440 (400×1.10=440400 \times 1.10 = 440), while Basic subscribers decreased by 20%20\% to 224 (280×0.80=224280 \times 0.80 = 224). Subtracting 224 Basic subscribers from the total 440 gives 216 Premium subscribers in Year 2. The increase in Premium subscribers is 216−120=96216 - 120 = 96. To find the percentage increase, divide the increase of 96 by the original Premium subscriber count of 120, yielding 96120=0.80\frac{96}{120} = 0.80, or 80%80\%.

Adım Adım Çözüm

1
Calculate the number of Basic and Premium subscribers in Year 1
Basic subscribers = 0.70×400=2800.70 \times 400 = 280; Premium subscribers = 400−280=120400 - 280 = 120
Determining the starting baseline values for each category is necessary to evaluate subsequent changes.
2
Calculate the total subscribers and Basic subscribers in Year 2
Total subscribers in Year 2 = 400×(1+0.10)=440400 \times (1 + 0.10) = 440; Basic subscribers in Year 2 = 280×(1−0.20)=224280 \times (1 - 0.20) = 224
Apply the given percentage changes to find the updated group totals in Year 2.
3
Find the number of Premium subscribers in Year 2 and the absolute increase
Premium subscribers in Year 2 = 440−224=216440 - 224 = 216; Absolute increase = 216−120=96216 - 120 = 96
Subtracting the Basic subscriber count from the total count yields the Premium subscriber count for Year 2.
4
Compute the percentage increase for Premium subscribers
Percentage increase = 96120×100%=80%\frac{96}{120} \times 100\% = 80\%
Divide the absolute increase by the initial Year 1 Premium subscriber count (the correct base value) and convert to a percentage.

Anahtar Kavram

Successive percentage changes and base shifting in multi-part totals
Tahmini Süre:1m 30s
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Konular

Percentages, Percent Change, and Interest

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