पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३७५

CHAPTER VI-MIXED PROBLEMS. 319. The un hanging velocity is dimunished by the first termi (of the velocities in series in arithmetical progression), and is (then) divided by the half of the common difference. On adding one (to the resulting quantity), the (required) time (of meeting) is arrived at (Where two persons travel in opposite directions, cach with a definite velocity), twice (the average distance to be covered by either of them) is the (whole) way (to he travelled). This when divided by the sum of their velocitics gives rise to the time of (thein) meeting. An example in allustration thereof. 320 Acertam person goes with a velocity of 3 in the beginning increased (regularly) by 8 as the (successive) common difference. The steady unchanging velocity (of another person) is 21 What may be the time of their meeting (again, if they start from the sauc place, at the same time, and move in the same direction)? 177 An example in illustration of the latter half (or the rule given in the stanza above). 321-321 One man travels at the rate of 6 yojanas and another at the rate of 3 yöjunas The (average) distance to be covered by either of them moving in opposite directions Is 108 yojanas. O arithmetician, tell me quickly what the time of their meeting together is. The ule for arriving at the time and distance of meeting to- gether, (when two persons start from the same place at the same time and travel) with (varying) velocities in arithmetical progression. 322 The difference between the two first terms divided by the difference between the two common differences, when multiplied by two and mercased by one. gives rise to the time of coming together on the way by the two persons travelling simultaneously (with two series of velocities varying in arithmetical progression). 319 Algebraically. (-u)- alt the time. 322). Algebraically n= b + 1 t, where is the unchanging velocity, 2 ( a x 2 + 1 b~ bi 2.3