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

PROBLEMS ON ARITHMETIC SERIES 79
Rule for finding the number of days elapsed when two
travellers, starting at a specified interval of time, meet each
other for the second time after their first meeting :
97-98. In relation to the first traveller, assume an
arbitrary number, greater than the caya (i.e., acceleration)
for the second traveller, for the caya (i.e., acceleration) ; and
another arbitrary number (iṣṭa) for the mukha (i.e., initial
speed). In relation to the second traveller, assume another
arbitrary number to denote the pada (i.e., the number of days
elapsed at the first meeting) ; and from the corresponding
pada (i.e., the number of days elapsed at the first meeting) for
the first traveller, calculate the âdi (i.e., the initial speed) for
the second traveller.
Now divide the phala (i.e., the distance travelled by each
traveller at their first meeting) severally by the padas (for the
two travellers) and take the difference of the two; diminish
that (difference) by half the difference of caya × pada for
the two travellers ; and then divide that by half the diffe-
rence between the cayas (for the two travellers) : the quotient·
gives the days elapsed at the second meeting (of the two
travellers) (since the first meeting).¹
That is to say, the number of days (D) elapsed at the second meeting
of the two travellers since their first meeting is given by
( s / (n - d) - s / n ) - ½ {n f₁ - (n - d) f₂}
D = ---------------------------------------------------- ,
½ (f₁ - f₂)
where f₁ and f₂ are the accelerations of the two travellers, n is the number
of days elapsed at the first meeting since the start of the first traveller,
(n - d) is the number of days elapsed at the first meeting since the start of
the second traveller, and s is the distance travelled by the two travellers at
their first meeting.

---

¹ Cf. GK, I, p 110, lines 9-14, and p. 111, lines 1-2