optionally chosen quantity, (it) gives rise to (the weights of each of the two small) balls of gold. The varņa (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 the (given) final average varņa (in each case). It in this manner both sets of answers (arrived at) happen to tally (with the requirements of the problem, the two varņa arrived at in accordance with the previously adopted option become the verified varņas mentioned in relation to the two (given) little balls of gold. If, (however, these answers do) not (tally), the varņas 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 varņa corresponding to these modified component varņa has to be further obtained). Thereafter, the difference between this (average) varņa and the previously obtained (untallying average) varņa is written down; (and the required proportionate quantities) are (therefrom) derived by means of the operation of the Rule of Three: and the varņas (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 varņas (here).
An example is illustration thereof.
213-215. Two merchants well versed in estimating the value of gold asked each 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 varņas” 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 tho products of weight and varņa, while the decrease and the increase in relation to the originally chosen varņas are 9-8 or 1 and 16-13 or 3.
But the required increase in sum of the products of weight and varņa in the second exchange is 36–35 or 1. Applying the Rule of Three, we get the corresponding decrease and increase in the varņas to be and .
Therefore, the varņa are 9-- or and or
