Question
The number of trees in each row of a garden is equal to the total number of rows in the garden. After 111 trees have been uprooted in a storm, there remain 10914 trees in the garden. The number of rows of trees in the garden is = ?
Answer: Option B
$$\eqalign{
& \,\,\,\,\,\,1|\overline 1 \,\,\overline {10} \,\,\overline {25} \,(105 \cr
& \,\,\,\,\,\,\,\,\,|\,\,1 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,20|\,\,\,\,\,\,10 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,0 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& 205|\,\,\,\,\,\,\,10\,25 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,10\,25 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{X}} \cr
& {\text{Number of rows}} \cr
& {\text{ = }}\sqrt {10914 + 111} \cr
& = \sqrt {11025} \cr
& = 105 \cr} $$
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$$\eqalign{
& \,\,\,\,\,\,1|\overline 1 \,\,\overline {10} \,\,\overline {25} \,(105 \cr
& \,\,\,\,\,\,\,\,\,|\,\,1 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& \,\,20|\,\,\,\,\,\,10 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,0 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - \cr
& 205|\,\,\,\,\,\,\,10\,25 \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,10\,25 \cr
& \,\,\,\,\,\,\,\,\,| - - - - - - - \cr
& \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{X}} \cr
& {\text{Number of rows}} \cr
& {\text{ = }}\sqrt {10914 + 111} \cr
& = \sqrt {11025} \cr
& = 105 \cr} $$
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