Question : The strength of a school increases and decreases every alternate year by 10%. It started with an increase in 2000. Then, the strength of the school in 2003, as compared to that in 2000, was:
Option 1: Increased by 8.9%
Option 2: Decreased by 8.9%
Option 3: Increased by 9.8%
Option 4: Decreased by 9.8%
Correct Answer: Increased by 8.9%
Solution :
Given: The strength of a school increases and decreases every alternate year by 10%. It started with an increase in 2000.
Let the strength of the school in 2000 be 100.
Till the year 2003, it first increases, then decreases, and then increases again.
The increase and decrease are by 10%.
So, in the year 2003, the strength of the school is = 100 × ($\frac{100+10}{100}$) × ($\frac{100–10}{100}$) × ($\frac{100+10}{100}$)
= 100 × ($\frac{110}{100}$) × ($\frac{90}{100}$) × ($\frac{110}{100}$) = ($\frac{11×9×11}{10}$) = 108.9
Therefore, compared to the year 2000, the strength of the school increased by (108.9 – 100) = 8.9%.
Hence, the correct answer is 'Increased by 8.9%'.
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