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

MIXTURES. ALLIGATION 39
diminished by the products of weight and varṇa (of the pieces
of gold of known weights and varṇas), and (then) divided by
the varṇa of the piece of gold of unknown weight minus the
varṇa of the alloy, gives the (unknown weight of) gold.¹
That is, if n pieces of gold of weights w₁, w₂, ..., wₙ and varṇas
v₁, v₂, ..., vₙ respectively are mixed up with a piece of gold of varṇa v but
of unknown weight, and the varṇa of the alloy is found to be vʹ, then
the unknown weight w will by given by
w = [(w₁ + w₂ + ... + wₙ) vʹ − (w₁v₁ + w₂v₂ + ... + wₙvₙ)] / (v − vʹ)
Ex. 66. 2, 3, and 4 mâṣas of gold of kṣayas 7, 4, and 5
(respectively) being mixed up with some gold of kṣaya 2, the
alloy is found to be of kṣaya 4. Quickly say with how much
of that gold (of kṣaya 2 have they been mixed up).²
Rule for finding how much of inferior gold (and how much
of pure gold) will have to be taken in constructing a number
of test sticks of progressively decreasing varṇas :
56. The weight in terms of mâṣas (mâṣâtmaka mâna) of
one (test) stick being divided by the difference in terms of
yavas between the varṇas (of pure and inferior gold) and multi-
plied one time, 2 times, etc., of the progressive decrease of
varṇa in terms of yavas, gives the respective amounts of inferior
gold.³
That is, if n test sticks of weight w and varṇas 16 − k, 16 − 2k,...,
16 − nk are to be made out of pure gold and inferior gold of varṇa 16 − K,
then for the construction of those test sticks we will have to take the
following amounts of inferior gold in the respective order :
(w / K) × k, (w / K) × 2k, ......, (w / K) × nk.
¹ Cf. BM, III, H3, 18 verso; GSS, vi. 175½, 180; MSi, xv. 41; L
(ASS), p. 103, vs. 108; GK, I, p. 77, vs. 20.
² Cf. BM, III, H3, 18 verso; GSS, vi. 181; L (ASS), p. 103, vs. 109;
GK, I, p 77, lines 16-19.
³ Cf. GK, I, p. 78, lines 18-21, and p. 79, lines 1-2. Also see GSS,
vi. 192.