Understanding the School Strength Problem
This problem asks us to determine the final percentage change in a school's strength from the start of 2017 to the start of 2021. We are told the strength changes by 20% every alternate year, and the first change (starting in 2018) was an increase.
Step-by-Step Calculation of Strength Changes
Let the strength of the school at the start of 2017 be represented by '$S$'. We need to track the changes year by year:
- Start of 2017: Strength = $S$
- Start of 2018: No change has occurred yet. Strength = $S$
- During 2018 (Increase): The strength increases by 20%.
- Calculation: $S \times (1 + \frac{20}{100}) = S \times (1 + 0.20) = 1.20S$
- Strength at the end of 2018 / Start of 2019: $1.20S$
- During 2019 (Decrease): Since the changes alternate, and the previous was an increase, this year involves a decrease of 20%.
- Calculation: $(1.20S) \times (1 - \frac{20}{100}) = (1.20S) \times (1 - 0.20) = 1.20S \times 0.80 = 0.96S$
- Strength at the end of 2019 / Start of 2020: $0.96S$
- During 2020 (Increase): The changes alternate again. The previous was a decrease, so this year involves an increase of 20%.
- Calculation: $(0.96S) \times (1 + \frac{20}{100}) = (0.96S) \times (1 + 0.20) = 0.96S \times 1.20 = 1.152S$
- Strength at the end of 2020 / Start of 2021: $1.152S$
Comparing Strengths and Calculating Percentage Change
Now, we compare the strength at the start of 2021 to the strength at the start of 2017:
- Strength at Start of 2017 = $S$
- Strength at Start of 2021 = $1.152S$
To find the percentage change, we use the formula:
Percentage Change = $ \frac{\text{Final Strength} - \text{Initial Strength}}{\text{Initial Strength}} \times 100\% $
Plugging in the values:
Percentage Change = $ \frac{1.152S - S}{S} \times 100\% $
Percentage Change = $ \frac{0.152S}{S} \times 100\% $
Percentage Change = $ 0.152 \times 100\% $
Percentage Change = $ 15.2\% $
Since the final strength ($1.152S$) is greater than the initial strength ($S$), the change is an increase.
Conclusion on Strength Comparison
The strength of the school at the start of 2021 is increased by 15.2% compared to the strength at the start of 2017.
Similar Questions
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Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?
