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148
GANITABĀRASAKURAHA.
optionally choson quantity, (it) gives rise to the weights of each of the two small) balls of gold. The varna (of each of these (little balls of gold) as also that of the gold gifted by the other person in the transaction) has to be arrived at as before with the aid of tho (given) final average varna in each caso). If in this manner both sets of answers (arrived at) happen to tally (with the requirements of the problem), the two varnas arrived at in accordance with the previously adopted optiou become the verified varnas montioned in relation to the two (given) little halls of gold. If, (howevor, those answers do) not (tally), the carnas belonging to the first set (of answers) have to be made (as the case may be) a little less or a littlo moro; (then the averago varna corresponding to these modified component varnas has to be further obtained). Thereafter, the difference between this (average) varna and the previously obtained (untallying average) varna is written down; (and the requirod proportionate quantities) are (therefrom) derived by means of the operation of the Rule of Three: and the varnas (arrived at according to the option chogen before, when respectively diminished by one of these two quantities and increased by the other, turu out to be evidently tho reyuired varnas (here).
An example in illustration thereof.
213--215. Two morchants will versed in cstimating tho value of gold asked cach other (for an exchange of gold). Then the first (of them) said to the other-"If you give me half (of your gold), I shall combine that small pellet of gold with my own gold and make (tho whole become gold ot) 10 rurnas." Then this other Baid--"If I only obtain your rold by ouc-third (thereof), I shall likowiso make the whole (gold in my possession become
Thus, in the second exobungo, we see an increase of 40-35 or 5 in the som of the products of weight and varna, while tho (leoreude and the inoronse in relation to the originally choson rarnas are 9-8 or 1 and 18-13 or 3.
But the required increase in the sum of the products of weight and varra in the second exchange is 36-35 or 1. Applying the Rule of Three, we get the corresponding deorease and increase in the varpas to be and
Therefore, the varras are 9- or 8 and 18+ or 187.
