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CHAPTER VI-MIXED PRORLEUR
151
The rule to arrivo at (the unknown) capital with the aid of certain known and unknown profits (in a given transaction):
222. By means of the operation of proportionate distribution, the (unknown) profiis are to be determined from the mixed sum (of all the profits) minus the (known) profit. Then the capital of the person whose investment is unknown results from dividing his profit hs that (samo common factor which has been lisod in the process of proportionate distribution above).
An exemple in it/ustration thereof. 223-22:). According to agreement some three merchants carried out (the operation of) buying and selling. The capital of tric first of them) consisted of six purinas, that of the second of cight purrins, but that of the third was not known. The profit obtained by all those (three) men was 96 puramus. lu fnet the profit obtained by him (this third person) on the imknown capital happened to be 10 purinas. What is the amount thrown by him (into the transaction), and what is the prolit (of each) of the other two merchants? O friond, if you know the operation of proportionate distribution, tell me this) after making the (110centary) calouiation.
The rule for arriving at the wagos (due ini kinl for having carried certain given things over a part of the stipulated distance according to a given rate):--
226. 1'rom the square of the product (of the numerical valun) of the weight to be carried and hail of the stipuuted distalloe
220. Algebraically, the formulas given in the rule in
-N OW ) - abd (D-R) were worn to found out,
D-d a= the total weight to be carrive, D = the total dimance, the distance KON over, and the total Waris promined. It may be noted here that the rate of the wagen for the two waves of the journey in the name, althongh the amount paid for each mage of the jonrney is not in accordance with the promised rate for the whole journey.
The formula is rasily derived from the following equation containing the duta in the problem :
adla --) (D-d).
