Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 345

148
GANITASĀRASANGRAHA.
optionally chosen quantity, (itgives 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 option become the verified varnas mentioned in relation to the two (given) little balls of gold. If, (however, these answers do) not (tally), the varnas belonging to the first set (of answers have to be made (as the case may be) a little less or a little more; (then the average 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 required proportionate quantities) are (therefrom) derived by means of the operation of the Rule of Three : and the varnas (arrived at according to the option chosen before, when respectively) diminished by one of these two quantities and increased by the other, turn out to be evidently the required varnas (here).
An example in illustration thereof. 213--215. Two merchants well versed in estimating the 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 the whole become gold of) 10 varnas.” Then this other said-"If I only obtain your gold by one-third (thereof), I shall likewise make the whole (gold in my possession become
Thus, in the second exchange, we see an increase of 40-35 or 5 in the sun of the products of weight and varna, while the decrease and the increase in relation to the originally chosen varnas are 9-8 or 1 and 10-13 or 3.
But the required increase in the sum of the products of weight and varna in the second exchange is 36-35 or 1. Applying the Rule of Three, we get the corresponding decrease and increase in the varnas to be and
Therefore, the varnas are 9- or 88 and 13 + { or 13%.