पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३१२

GANITASARASANGRAHA. purchasing rate. By reversing the processes, one may arrive at the valuation of the highest capital (invested in the transaction). 114 Examples in illustration thereof. 103 The capital amonuts invested by (three) men are (re- apectively) 2, 8 and 36; 6 is the price at which the remnants of the commodity are to be sold. Having purchased and sold at the same rates, they became possessors of equal wealth (Find out the buying and selling prices) 104 Those three persons took up 13, and 2 (as their re- spective capital amounts) and conducted the operations of buying sad selling (in relation to the same commodity at the same rates of price); by selling the remnant (in the cud) at a price represented by 6, they became possessors of equal wealth (Find out their buying and selling prices.) 105. The quantity measuring the equal wealth is 41, and the price at which the remnants of the commodity are sold is 6. O arithmetician, tell me quickly what the highest capital (mvested) is, and what the (various) capitals are. 106 In the case where 35 dinaras give the numerical measure of the equal wealth, and is the price at which the remnant is to be sold, you tell me, O arithmetician, what the highest capital (invested) is. spoken of as the remnant, and the price at which this remnant is sold is the remnant-price Symbolically, let a, a + b and a + b + c be the capitals, where the last 1s the ज्येष्ठधन or the largest capital, snd let p be the चरमार्घ or the remnant- price, then, according to the rule, a + b + c + 1 = the vending rute, and (a + b + c + 1) p - 1 = the purchasing rate From these, it can be easily shown that the sum of the amounts realised by selling the commodity at the vending rate and the remnant at the remnant- price turns out to be the same in each case. It may be noted that the purchasing rate happens in problems beaning on this rule to be the same in value as the or the equal sale-proceeds. 105 It may be noted here that, according to the rule, it is only the largest sapital that is found ont, while the other apitals iequired in the problem are optionally chosen, so as to be less than the largest capital.