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

50 DETERMINATIONS
Rule for finding out how a specified number of creatures of
given rates can be bought for a specified price :
63-64. By the price of one creature of any variety
multiply the rate-creatures (of other varieties) in the order in
which they have been stated (in the problem) (and also the
number of creatures to be bought). From the products (corres-
ponding to the rate-creatures) severally subtract the respec-
tive rate-prices of the creatures (and from the product
corresponding to the number of creatures to be bought sub-
tract the specified price). Now multiply the various remain-
ders, excepting that obtained by subtracting the specified
price, by optional numbers (multipliers) which are to be
chosen in such a way that (i) the resulting products when
added together may yield (the remainder obtained by sub-
tracting) the specified price as sum, and (ii) on taking the
products of those multipliers and the respective rate-prices,
a negative number or zero may not be obtained for the multi-
plier of the creature which is without a multiplier. (The multi-
pliers for the various creatures, obtained in this way, when
multiplied by the respective rate-creatures, will give the
number of creatures of the different varieties that will be
bought for the specified price ; and the same multipliers
when multiplied by the rate-prices of the respective creatures
will give the prices that will be paid for the creatures of the
respective varieties).¹
For the explanation of this rule see under Ex. 78-79.
Ex. 78-79. Pigeons are sold at the rate of 5 for 3 (rûpas),
cranes at the rate of 7 for 5 (rûpas), swans at the rate of 9 for
7 (rûpas), and peacocks at the rate of 3 for 9 (rûpas). Knowing
the rates as stated above, bring 100 birds for 100 rûpas
for the amusement of the prince.²
¹ Cf. GK, I, p. 92, vv. 34(ii)-35. For other rules see GSS, vi. 146½, 151.
² The same example occurs in GSS, vi. 152-153; BBi (ASS), p. 163,
vs. 138; GK, I, p. 93, lines 2-5. A similar problem occurs in BM, III, E 3,
58 verso, which may be stated as : ‘A man earns 3 maṇḍas in a day, a
woman 1½ maṇḍas in a day, and a sûḍha ½ maṇḍa in a day. If 20 of
them earn 20 maṇḍas in a day, how many of each category are there?’