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

56 DETERMINATIONS
That is, if n drains severally fill up a cistern in
a₁/b₁, a₂/b₂, ... , aₙ/bₙ of a day,
then all the drains working together will fill up the cistern in
1 / (b₁/a₁ + b₂/a₂ + ... + bₙ/aₙ) of a day.
Ex. 91. In what time will the (four) drains, which
severally fill up a cistern in ½, ¼, ⅕, and ⅙ of a day, fill up
that cistern if they are opened simultaneously (to flow into
it) ? 1
(viii) WAGES PAID FROM THE COMMODITY
Rule for finding the wages of a porter who carries a commo-
dity over a part of the stipulated distance, when the wages
are to be paid out of the commodity itself :
70. (To obtain the wages for a part of the stipulated
distance) divide half the product of the commodity and the
stipulated distance as diminished by the square root extracted
from the square of half the product of the commodity and the
stipulated distance as diminished by the (continued) product
of the distance (already) gone over, the distance to be gone
over, the commodity, and the stipulated wages, by the
distance which is still to be gone over.²
Assuming that the (stipulated) wages for carrying a articles over the
(stipulated) distance d are w articles (out of those a articles), let the
wages for carrying those a articles over a distance d₁, where d₁ < d, be
x articles (out of those a articles). Then calculating at the same rate, the
wages for carrying the remaining a - x articles over the remaining distance
d - d₁ are equal to
(a - x) (d - d₁)x / (ad₁) articles.
But the remaining wages being w - x articles, we have
(a - x) (d - d₁)x / (ad₁) = w - x ,
1 Similar examples occur in Pṛthûdaka Svâmî's (860 A.D.) comm.
on BrSpSi, xii. 9; L (ASS), p. 91, vs. 97 ; GK, I, p. 94, lines 5-6.

• Cf. GSS, vi. 226. For another rule, see GK, I, p. 103, lines 10-15.