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

42 DETERMINATIONS
thus obtained) being divided by the (same) fractions, each
increased by 1, then multiplied by the (respective) varṇas,
and then divided by the (respective) weights of the gold
balls, give the varṇas (of the two gold balls).¹
That is, if _w_₁ and _w_₂ be the weights of two gold balls whose
varṇas are _V_₁ and _V_₂ respectively, _v_₁ the varṇa of the alloy formed by mixing
the first gold ball with a/b part of the second, and _v_₂ the varṇa of the
alloy formed by mixing the second gold ball with c/d part of the first, then
_V_₁ = [_w_₁ + (a/b) _w_₂] / [(1 + a/b) _w_₁] · _v_₁,
_V_₂ = [_w_₂ + (c/d) _w_₁] / [(1 + c/d) _w_₂] · _v_₂.
Of these results, the first follows from equations (4) and (6) of the
previous rule, and the second from equations (5) and (6).
Ex. 69. There are two small balls of gold of equal
worth (i.e., having equal quantities of pure gold), whose com-
bined weight is 5 māṣas. When they are respectively combined
with ⅔ part and ½ part of the other, they become of 10 and 9
varṇas respectively. (Find their weights and varṇas separa-
tely).
Ex. 70. O learned one, there are two small balls of
gold of equal value. When taken together, their weight is 12
māṣas ; and when they are respectively combined with ⁵/₇ part
and ⅕ part of the other, they become of 12 and 10½ varṇas
respectively. (Find their weights and varṇas separately).
(iii) PARTNERSHIP
Rule for finding the shares of the partners in the produce :
59(i). To obtain the individual shares (of the partners)
in the produce (phalâvâptyai), the seeds (contributed by the
partners) (prakṣepa), as divided by their sum, should be severally
multiplied by the produce (phala).²

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¹ See also GSS, vi 209-212; and GK, I, p. 81, lines 9-18.
² Cf. BrSpSi, xii. 16 (i); SiŚe, xiii. 19 (i); L (ASS), p. 90, vs. 94; GK,
I, p. 54, lines 11-12. Also see GSS, vi, 79½ ; MSi, xv. 36.