146 GANITASĀRASANGRAHA. multiplying the (given proportional quantities of the various kinds of the exchanged) gold by (their respective specified) vurnas. (The resulting quotient) is to be multiplied by the original vurna (of the gold to be exchanged). If by this prodnet as dimmished by one, the increase (in the weight of gold due to exchange) is divided, and the quotient (so obtained) is subtracted from the ori- ginal 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 result- ing remainder (here) is divided 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 charac- terised by the specified vurnas and the specified proportions are arrived at. An example in illustration thereof. 204--205. There is a certain merchant desirous of obtaining profit; and the gold (in his possession) is of 16 varnas 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 varnus, (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 varnas). 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) :-
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206. Each specified part of (the original) gold (to be ex- changed) is divided by the varna corresponding to its exchange. (The resulting quotient is in each case to be multiplied by the
