पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३४२

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एतत् पृष्ठम् परिष्कृतम् अस्ति
146
GANITASARASANGRAHA.

multiplying the (given proportional quantities of the various kinds of the exchanged) gold by (their respective specified) varņas. (The resulting quotient) is to be multiplied by the original varņa (of the gold to be exchanged). If by this product as diminished by one, tho increase (in the weight of gold due to exchange) is divided, and the quotient (so obtained) is subtracted from the original wealth of gold, the remaining (weight of unexchanged) gold is arrived at. This (weight of the unexchanged gold) is then to be subtracted from the sum (of the weight) of the original gold and the increase (in weight due to exchange). Then if the resulting remainder (here) is divided by the sum of the proportional multiple numbers connected with the exchange, and is then multiplied by (each of those) proportional numbers (separately), the (various weights of) gold obtained in exchange and characterised by the specified varņas and the specified proportions are arrived at.

An example in illustration thereof.

204-205. There is a certain merchant desires of obtaining profit; and the gold (in his possession) is of 16 varņas and 200 in weight. A portion of it is exchanged in return for (four different kinds of gold characterised respectively by 12, 8, 9 and 10 varņas, (so that those varieties of gold are by weight) in proportions which begin with 1 and are then (regularly) multiplied by 2. The gain (in the weight of gold resulting out of this exchange transaction) is 102. What is the remaining (weight of the unexchanged) gold? Tell me also the weights of gold obtained in exchange corresponding to those (above-mentioned varņas ).

The rule for arriving at (the weight of the original (quantity of) gold with the aid of the gold exchanged (in part), and with the aid (of the weight) of gold seen to be in excess (in consequence of the exchange )

206. Each specified part of (the original) gold (to be exchanged) is divided by the varņa corresponding to its exchange (The resulting quotient is in each case to be) multiplied by the