पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२८३

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CHAPTER V--RULE-OF-THREE

7.^[7]A good piece kṛṣṇāgaru^[1], 12 hastas in length and 3 hastas in diameter, is consumed (at the rate of) 1 cubic angula a day. What is the time required for the (complete) consumption of this cylinder ?

8. (If) a vāha of very superior black gram, along with 1 drōņa,1 āḍhaka and 1 kuḍava (thereof), has been purchased by means of $10{\tfrac {1}{2}}$ svarņas, what measure (may we purchase of it) by means of $100{\tfrac {1}{2}}$ svarņas?

9. Where 1${\tfrac {1}{8}}$ pala of kuńkuṃa is obtainable by means of $3{\tfrac {1}{2}}$ purāņas, what measure (of it) may (we obtain) there by means of 100 purāņas ?

10. By means of $7{\tfrac {1}{2}}$ palas of ginger, $13{\tfrac {1}{2}}$ paņas were obtained; say, O friend, what (may be obtained) in return for $32{\tfrac {1}{2}}$ palas of ginger?

11. By means of $4{\tfrac {1}{2}}$ kārṣāpaṇas, a man obtains $16{\tfrac {1}{2}}$ palas of silver; what (weight does he obtain thereof) by means of 10,000 karṣas

12. By means of $7{\tfrac {2}{3}}$ palas of camphor, a man obtains 5 dīnāras along with 1 bhāga, 1 aṃśa and 1 kalā'. What (does he obtain) here by means of 1,000 palas (thereof) ?

13. The man who purchases here $5{\tfrac {1}{2}}$ palas of ghee by means of $3{\tfrac {1}{2}}$ paṇas-what (measure of it does the purchase) by means of $100{\tfrac {1}{8}}$ karṣas?

14. By means of $5{\tfrac {1}{3}}$ purāṇas, $16{\tfrac {1}{2}}$ pains of cloths were obtained. O friend, say what (number of them may be obtained) by means of 61 karṣas?

15-16.^[15-16]There is a square well without water, (cubically) measuring 512 hastas. A hill rises on its bank; from the top

 

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7.^ Here the process of finding out, from the given diameter, the area of the cross-section of a cylinder is supposed to be known. This is given in the sixth Vyavahāra, in the 19th stanza, where the area of a circle is said to be approximately equal to the diameter squared and then divided by 4 and multiplied by 3.

^ Kṛṣṇāgaru is a kind of fragrant wood burnt in fire as intense.

15-16.^  In this problem, the stream of water is as long as the mountain is high, so that as soon as it reaches the bottom of the mountain, it is supposed to cease to flow at the summit. For finding out the quantity of water in Vāhas, etc., the relation between cubical measure and liquid measure should have been given. The Sanskrit commentary in P and the Kanarese ṭīkā in B state that 1 cubic aṅgula of water is equal to 1 kaṛṣā thereof in liquid measure.