Question : During the first year, the strength of a school increased by 12%, in the second year it decreased by 12%, and in the third year it increased by 10%. At the end of the third year, its strength was nearly 10842. What was the strength at the beginning of the first year?
Option 1: 8000
Option 2: 10000
Option 3: 6500
Option 4: 12000
Correct Answer: 10000
Solution :
Percentage increase in strength of school in first year = 12%
Percentage decrease in strength of school in second year = 12%
Percentage increase in strength of school in third year = 12%
Strength of school at the end of third year = 10842
Let the strength of the school in the beginning be $x$.
Strength of school at the end of first year = $x+\frac{12}{100}x$ = $1.12x$
Strength of school at the end of second year = $1.12x-\frac{12}{100}\times1.12x$ = $0.9856x$
Strength of school at the end of third year = $0.9856x+\frac{10}{100}\times0.9856x$ = $1.0842x$
So, $1.08416x$ = 10842
$\therefore x$ = 10000
Hence, the correct answer is 10000.
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