________________
110
GANITASÁRASANGRAHA.
Proportionate Division.
Hereafter we shall expound in this chapter on mixed problems the working of proportionate division :
79. The operatiou of proportionate division is that wherein the (giveu) collective quantity to be divided) is first divided by the sum of the numerators of the cominon-denominator-fractions (representing the various proportionate parts), the denominators of which fractions are struck off out of consideration; and (then it) has to be multiplied (respectively in cach case) by (these) proportional numerators. This is called kuttiköra by the Icarned.
Examples in illustration thereof.
80%. Here, (in this problem, 120 gold pieces are divided anong 4 servants in the respective) proportional parts of , and . O arithmetician, tell me quickly what they obtained.
813. (The sum of) 363 dināras was divided among live, the first ono (among them) getting 3 parts, and 3 being the common ratio successively in relation to the shares of the others). What was the share of cach
82; to 85). A certain faithful xrävaka took a number of lotus Aowers, and going into thc Jina temple conducted (theroin) with devotion the worship of the chief Jinas that were worthy of worship. He offered part to Vrsabha, , to worthy Päráva, and th to Jinapati, and to sage Suvrata ; he dovotedly gave to Ariştanémi who destroyed all the eight kinds of karmas and who was beloved by the world, and I of 1 to Jinasånti: 480 lotuscs were brought (for this purpose.) By adopting the operation known
794. In working the example in stanos 804 according to this rule we get:
t =a.1. After removing the denominators here, we have 6, 4, 3 and 3. These are also called praksepas or proportional numerators. The sum of these io 15, by which the amount to be distributed, vis., 120, is divided ; and the resulting quotient 8 in separately multiplied by the proportional namerators 6, 4, 3 und 3. Then the mounts thus obtained are 6 x 8 or 48, + x 8 or 32, 3 x 8 or 94,X 8 or 16. It is worthy of note that praksapre moans both the operation of proportionate division and proportional numerator.
