When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?

Solution(By Examveda Team)

$$\eqalign{ & x = 13p + 11\,{\text{and}}\,x = 17q + 9 \cr & \therefore 13p + 11 = 17q + 9 \cr & \Rightarrow 17q - 13p = 2 \cr & \Rightarrow q = \frac{{2 + 13p}}{{17}} \cr & {\text{Thr}}\,{\text{least}}\,{\text{value}}\,{\text{of}}\,p\,{\text{for}}\,{\text{which}} \cr & q = \frac{{2 + 13p}}{{17}}\,{\text{is}}\,{\text{a}}\,{\text{whole}}\,{\text{number}}\,{\text{is}}\,p = 26 \cr & \therefore x = \left( {13 \times 26 + 11} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = \left( {338 + 11} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = 349 \cr} $$