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

MIXTURES. ALLIGATION 37
Ex. 62. Of what varṇa do (the three pieces of gold of)
5 plus ⅓, 4 plus ⅙, and 7 plus ½ māṣas and 11 plus ½, 10, 8
minus ½ varṇas (respectively) become when mixed in one ?¹
Rule for finding the varṇa of the refined gold (obtained by
mixing up and refining a number of pieces of gold of given
weights and varṇas), when the weight of the refined gold is
known :
53(i). The sum of the products of varṇa and weight
of the several pieces of gold, being divided by (the weight of)
the refined gold, gives the varṇa (of the refined gold).²
That is, if n pieces of gold of weights w₁, w₂, ..., wₙ and varṇas
v₁, v₂, ... , vₙ respectively are mixed up and refined, then the varṇa v
of the refined gold is given by
w₁v₁ + w₂v₂ + ... + wₙvₙ,
v = -------------------------
w
where w is the weight of the refined gold.
The rationale is similar to that of rule 52(ii).
Ex. 63. 5, 8, and 6 suvarṇas of varṇas 12, 9, and 15 minus
½ respectively, being mixed up and refined, are seen to be
reduced to 16 suvarṇas in all. Quickly say the varṇa of that
(refined gold).
Rule for finding the weight of the refined gold, when the
varṇa of the refined gold is known :
53(ii). The same (sum of the products of varṇa and
weight of the several pieces of gold), being divided by the
varṇa (of the refined gold), gives the weight of the refined gold.³
That is, if n pieces of gold of weights w₁, w₂, ... , wₙ and of
varṇas v₁, v₂, .. , vₙ respectively are mixed up and refined, then the weight
w of the refined gold is given by
w₁v₁ + w₂v₂ + ... + wₙvₙ
w = --------------------------- ,
v
where v is the varṇa of the refined gold.
¹ Similar examples occur in BM, III, H 1, 16 verso; H 2, 17 recto
and 17 verso; GSS, vi. 170-171½.
² Cf. MSi, xv. 39 (ii); GK, I, p. 76, vs. 18.
³ Cf. BM, III, H3, 18 recto; GSS, vi. 175½, 176½, MSi, xv. 40;
L (ASS), p. 102, vs. 106; GK, I, pp. 76-77, vs. 19.