पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

52 DETERMINATIONS
Ex. 80. (The rates of sale) of pomegranates, mangoes,
and wood-apples are respectively 1 for 2 (rûpas), 5 for 3 (rûpas),
and 2 fruits for 1 (rûpa). Bring 100 (fruits) for 80 (rûpas).¹
(v) MEETING OF TWO TRAVELLERS
Rule for finding the time in which the fast traveller, who starts
travelling on the same track after the slow traveller has
already covered a specified distance, would overtake the slow
traveller :
65. By the difference between the speeds per day of the
fast and slow travellers divide the distance already travelled
by the slow traveller. This gives the time (in days in which
the fast traveller would overtake the slow one).²
Ex. 81-82. When a person, travelling ( at the speed of )
8 yojanas per 5 minus ½ days, has already travelled for 6 minus
¼ days, another person, who travels ( at the speed of) 3 yojanas
a day, starts travelling (from the same place) along the same
track. Say, after calculating, when the latter traveller would
overtake the former.³
Rule for finding the time when two travellers, one fast and
the other slow, who, starting simultaneously from the
same place, are destined to go to a specified distance
and then to come back by the same track, will meet each other
on the way, one going ahead and the other coming back :
66(i). The (length of the) track divided by half the
sum of the speeds per day (of the two travellers) gives the
time (in days) at meeting.⁴
The time at meeting is evidently measured since the start of travel.
Ex. 83. One man travels ( at the speed of) 8 yojanas
(a day) and another (at the speed of) 2 yojanas (a day).
(They start simultaneously from the same place, and after
reaching the destination come back by the same track).
¹ Cf. GSS, vi. 147½-149, 150.
² Cf. BM, III, A 13, 3 recto; GSS, vi. 326½.
³ Cf. BM, III, B4, 4 recto; E 2, 53 recto; E 2, 53 verso; GSS, vi. 327½.
⁴ Cf. GSS, vi. 319 (ii).