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 337

140
GANITASARASANGRAHA.
the products obtained by multiplying the several component) quantities of gold by (their respective varņas) is to be subtraoted. 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 varna (of an unknown component quantity of gold) gives rise to the (required weight of that) gold.
Another rule in relation to the unknown varna :
1764. The sum of the products of the (various component quantities of) gold as multiplied by their respective varnas is to be subtracted from the product of the total quantity of gold as multiplied by the resulting varņa. 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.
1774 and 178. With gold of 6, 4 and 3 (in weight),characterised respectively by 13, 8 and 6 as their varņas, 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. Subtraot the sum, obtained by adding together the products of the various component quantities of) gold as multiplied by their respective varmas, 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.