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 = ?

Solution (By Examveda Team)

$$\eqalign{ & \,\,\,\,\,\,1|\overline 1 \,\,\overline {10} \,\,\overline {25} \,(105 \cr & \,\,\,\,\,\,\,\,\,|\,\,1 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - \cr & \,\,20|\,\,\,\,\,\,10 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,0 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - \cr & 205|\,\,\,\,\,\,\,10\,25 \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,10\,25 \cr & \,\,\,\,\,\,\,\,\,| - - - - - - - \cr & \,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{X}} \cr & {\text{Number of rows}} \cr & {\text{ = }}\sqrt {10914 + 111} \cr & = \sqrt {11025} \cr & = 105 \cr} $$