The strength of a school increases and decreases every alternate year by 20%. It started with an increase in 2018. What is the strength of the school at the start of 2021 as compared to that of 2017?
- AIncrease by 15.2%
- BDecrease by 15.2%
- CIncrease by 16.2%
- DDecrease by 16.2%
Solution & Step-by-step Explanation
Let the strength of the school at the start of 2017 be x.
The transitions happen over three intervals up to the start of 2021:
2017 to 2018 (1st year - Increase): +20%
2018 to 2019 (2nd year - Decrease): −20%
2019 to 2020 (3rd year - Increase): +20%
Let's compute the net effective change step by step using multiplier factors:
Final Strength=x×(1+
100
20
)×(1−
100
20
)×(1+
100
20
)
Final Strength=x×1.2×0.8×1.2
Multiplying the scale factors:
1.2×0.8=0.96
0.96×1.2=1.152
So, the strength becomes 1.152x.
Percentage change=(1.152−1)×100=+15.2%
This implies a net increase by 15.2%.
The transitions happen over three intervals up to the start of 2021:
2017 to 2018 (1st year - Increase): +20%
2018 to 2019 (2nd year - Decrease): −20%
2019 to 2020 (3rd year - Increase): +20%
Let's compute the net effective change step by step using multiplier factors:
Final Strength=x×(1+
100
20
)×(1−
100
20
)×(1+
100
20
)
Final Strength=x×1.2×0.8×1.2
Multiplying the scale factors:
1.2×0.8=0.96
0.96×1.2=1.152
So, the strength becomes 1.152x.
Percentage change=(1.152−1)×100=+15.2%
This implies a net increase by 15.2%.