पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३३८

140 GANITASĀRASANGRAHA. the products obtained by multiplying the (several component) quantities of gold by (their respective varnas) is to be subtracted. The remainder, when divided by the known component quantity of gold, (the varna of which is to be found out), gives rise to the required rarna; and when divided by the difference between the resulting varna and the known vurna (of an unknown component quantity of gold) gives rise to the (required weight of that) gold. Another rule in relation to the unknown varna :- 176. The sum of the products of the (various component quantities of) gold as multiplied by their respective zarnas is to be subtracted from the product of the total quantity of gold as multi- plied by the resulting varna. Wise people say that this remainder when divided by the weight of the gold of the unknown varna gives rise to the required varna. Examples in illustration thereof 177 and 178. With gold of 6, 4 and 3 (in weight), characterised respectively by 13, 8 and 6 as their zarnas, 5 in weight of gold of an unknown varna is mixed. The resulting varna of the mixed gold is 11. O you, friend, who know the secrets of calculation, tell me the numerical value of this unknown varna. -179. Seven in weight (of a given specimen) of gold has exactly 14 as the measure of its varna; then 4 in weight (of another specimen of gold) is added to it. The resulting varna is 10. Give out the unknown varna (of this second specimen of gold). The rule for arriving at the unknown weight of gold :- 180. Subtract the sum, obtained by adding together the products of the (various component quantities of) gold as multiplied by their respective varnas, from the product of the sum (of the known weights) of gold as multiplied by the now durable resulting varna; the remainder divided by the difference between the (known) varna of the unknown quantity of gold and the resulting durable varna (of the mixed gold) gives rise to the (weight of) gold.