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

RULE OF THREE 23
been done) that (middle quantity) multiplied by the last
quantity should be divided by the first quantity.¹
Ex. 25. If 1 pala and 1 karṣa of sandal wood are ob-
tained for ten and a half paṇas, then for how much will
9 palas and 1 karṣa (of sandal wood of the same quality) be
obtained ?
Here
argument = 1 pala and 1 karṣa
= 1¼ or 5/4 palas ;
fruit = 10½ or 21/2 paṇas ;
and requisition = 9 palas and 1 karṣa
= 9¼ or 37/4 palas
Writing these quantities as directed in the rule, we have
┌───┬────┬────┐
│ 5 │ 21 │ 37 │
│ 4 │ 2 │ 4 │
└───┴────┴────┘
Then applying the rule, the required result
= [(21/2) × (37/4)] / [5/4] = (21×37) / (2×5) paṇas
or 4 purāṇas, 13 paṇas, 2 kākiṇīs and 16 varāṭakas.
Ex. 26. If 1⅓ palas of black pepper are obtained for
1¼ paṇas, then how much of that (black pepper) will be
obtained for (10 - ⅓) paṇas? Say quickly.
Ex. 27. If one and a half droṇas and three kuḍavas of
grain is obtained for 8, say, if you know, for how much will
one khārī and one droṇa (of that grain) be obtained.
Ex. 28. If 60+½ khārīs of grain is obtained for 100+⅓
rūpas, how much of that (grain) will be obtained for a quarter
of a rūpa ? ²
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¹ Cf. Ā, ii. 26; BrSpSi, xii. 10 ; GSS, v. 2(i) ; MSi, xv. 24-25(i) ; GT,
p. 68, vs. 86 ; SiŚe, xiii. 14 ; L (ASS), p. 71, vs. 73 ; GK, I, p. 47, vs. 60.
² Examples similar to Exs. 25-28 occur in GSS, iii. 3-6 ; v. 8, 9, 13,
14 ; GT, p. 68, vs. 87, p. 69, vs. 88 ; p. 70, vs. 90 ; p. 71, vv. 91, 92;
L (ASS), pp. 72-73, vv. 74, 76 ; GK, I, p. 47, lines 13-14, 17-18, p. 48,
lines 8-11 ; and also in Bhāskara I's comm. (629 A.D.) on Ā, ii. 26-27.