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

38 DETERMINATIONS
Ex. 64. (Three pieces of gold of weights) 10, 7, and 5
mâṣas are seen to be of 9, 8, and 6 varṇas (respectively). On
being mixed up and refined, they become of 11 varṇa. Say the
weight of the refined gold.
Rule for finding the unknown varṇa of one of the pieces of
gold, when the varṇa of the alloy of those pieces of gold is
known :
54. The sum of the weights of (all) the pieces of gold
being multiplied by the varṇa of the alloy (of those pieces
of gold), (then) diminished by the products of weight and
varṇa (of the pieces of gold of known weight and varṇa), and
(then) divided by the weight of the piece of gold of unknown
varṇa, gives the (unknown) varṇa.¹
That is, if n pieces of gold of weights w₁, w₂, ..., wₙ and varṇas
v₁, v₂, ..., vₙ respectively are mixed up with another piece of gold of
weight w and of unknown varṇa, and the varṇa of the alloy is found to
be v', then the unknown varṇa v will be given by
v = ((w₁ + w₂ + .... + wₙ + w) v' - (w₁ v₁ + w₂ v₂ + ... + wₙ vₙ)) / w .
Ex. 65. 1, 2, and 6 suvarṇas of 5, 3, and 4 kṣayas
(respectively) being mixed up with a pala of gold of unknown
varṇa become of 12 varṇa. (Find the unknown varṇa).²
Just as the varṇa of gold indicates the fineness of gold, so the kṣaya
of gold indicates the impurity of gold. Gold of 1 kṣaya contains 1 part of
impurities and 15 parts of pure gold; gold of 2 kṣayas contains 2 parts of
impurities and 14 parts of pure gold; and so on. Thus the varṇa and kṣaya
are related by the formula
varṇa + kṣaya = 16.
Rule for finding the unknown weight of one of the pieces of
gold, when the varṇa of the alloy of those pieces of gold is
known :
55. The sum of the weights of the pieces of gold multi-
plied by the varṇa of the alloy (of those pieces of gold), (then)
¹ Cf. MSi, xv. 39 (i); GK, 1, p. 76, vs. 18.
² Similar examples occur in BM, III, H3, 18 recto; GSS, vi. 178; 179;
L (ASS), p. 102, vs. 107; GK, I, p. 77, lines 4-7.
Indological Truths