purchasing rate. By revorsing the processes, one may arrive at the valuation of the highest capital (invested in the transaction).
Examples in illustration thereof.
103. The capital amounts invested by (three) men are (respectively) 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 1, and 2 (as their respective capital amounts) and conducted the operations of buying and selling (in relation to the same commmodity at the same rates of price); by selling the remnant (in the end) at a price presented by 6, they become 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 bold is 6. O arithmetician, tell me quickly what the highest capital (invested) is, and what the (various) capitals are.
106. In the case where 35 dīnāras give the numerical measure of the equal wealth, and 4 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 is the ज्येष्ठधन or the largest capital, and let 2 be the चरमार्घ or the remnant price; then, according to the rule, a + b + c + 1 = the vending rate ; 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 remaining price turns out to be the same in each case.
It may be noted that the purchasing rate happens in problems bearing on this rule to be the same in value as the समधन 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 out ; while the other capitals required in the problem are optionally chosen, so as to be less than the largest capital.
