पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३४६

GANITASĀRASANGRAH.. optionally chosen 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 the (given) final average varna (in each case). If in this manner both sets of apswers (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 varmas 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 vana corresponding to these modified component varnas has to be further obtained). Thereafter, the difference between this (average) varna and the previously obtained (untallying average) vurma is written down; (and the required proportionate quantities) are (therefrom) derived by means of the operation of the Rule of Three: and "the vurnas (arrived at according to the option chosen before, when respect- ively) diminished by one of these two quantities and increased by the other. turn out to be evidently the required varnas (here). 148 An example in 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 vurnas." 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 m the sum 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 16-13 or 3. But the required increase in the sum of the products of weight and varga in the second exchange is 36-35 or 1. Applying the Rule of Thiec, we get the corresponding decrease and increase in the varnas to be and , Therefore, the varnas are 9- or 8 and 13+ or 13%.