**Proportionate Division.**

Hereafter we shall expound in (this) chapter on mixed problems the working of proportionate division:-

^{[*]}. The operation of proportionate division is that wherein the (given) collective quantity (to be divided) is first divided by the sum of the numerators of the common-denominator-fractions (representing the various proportionate parts), donominators of which fractions are struck off out of consideration; and (then it) has to be multiplied (respectively in each case) by (these) proportional numerators. This is called *kuṭṭīkāra* by the learned.

*Examples in illustration thereof.*

. Here, (in this problem,) 120 gold pieces are divided among 4 servants in the (respective) proportional parts of and . O arithmetician, tell me quickly what they obtained.

. (The sum of) 363 *dīmāras* was divided among five, the first one(among them) getting 3 parts, and 3 being the common
ratio successively (in relation to the shares of the others). What was the state of each ?

to . A certain faithful *śrāvaka* took a number of lotus flowers, and going into the Jina temple conducted (therein) with devotion the worship of the chief Jinas that were worthy of worship. He offered part to Vṛṣabha, to worthy Pārśva, and to Jinapati, and to sage Suvrata.; he devotedly gave to Aristanémi who dostroyed all the eight kinds of *karmas' and to Jinaśānti. 480 lotuos were brought (for this purpose. ) By adopting the operation known*

.**^** In working the example in stanza according to this rule we get . After removing the denominators here, we have 6, 4, 3 and 2. These are also called *prakṣēpas* or proportional numerators. The sum of these is 15, by which the amount to be distributed, *viz.*, 120 is divided; and the resulting quotient 8 is separately multiplied by the proportional numerators,6,4,3 and 2. Then the amounts thus obtained are 6 x 8 or 48, 4 x 8 or 32, 3 x 8 or 24, 2 x 8 or 16. It is worthy of note that *prakṣēpas* means both the operation of proportionate division and a proportional numerator .