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11. In 2022, a train carried 8% more passengers than in 2021. In 2023, it carried 8% more passengers than in 2022. Find the percentage increase in the number of train passengers from 2021 to 2023.



Answer :

GinnyAnswer
To solve this problem, let's follow a step-by-step approach:

1. Step 1: Determine the number of passengers in 2022 and 2023 based on the increments given.
3. Step 2: Calculate the percentage increase from 2021 to 2023.

### Step-by-Step Solution:
1. Initial Assumptions:
- Let's assume the number of train passengers in 2021 is 100 (this simplifies calculations without loss of generality, as percentages are ratios).

2. Finding the number of passengers in 2022:
- In 2022, the number of passengers increased by 8% compared to 2021.
- New number of passengers in 2022 = (Original number in 2021) \ (1 + Percentage increase)
- Number of passengers in 2022 = 100 \ (1 + 0.08)
- Number of passengers in 2022 = 100 \ 1.08
- Number of passengers in 2022 = 108

3. Finding the number of passengers in 2023:
- In 2023, the number of passengers increased again by 8% compared to 2022.
- New number of passengers in 2023 = (Number of passengers in 2022) \ (1 + Percentage increase)
- Number of passengers in 2023 = 108 \ (1 + 0.08)
- Number of passengers in 2023 = 108 \ 1.08
- Number of passengers in 2023 = 116.64

4. Calculate the percentage increase from 2021 to 2023:
- The percentage increase = [tex]\(\frac{(\text{Number of passengers in 2023} - \text{Number of passengers in 2021})}{\text{Number of passengers in 2021}} \times 100\)[/tex]
- Substitute the values:
- Percentage increase = [tex]\(\frac{(116.64 - 100)}{100} \times 100\)[/tex]
- Percentage increase = [tex]\(\frac{16.64}{100} \times 100\)[/tex]
- Percentage increase = 16.64

So, the percentage increase in the number of train passengers from 2021 to 2023 is 16.64%.

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