पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३३६

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एतत् पृष्ठम् परिष्कृतम् अस्ति
140
GAŅITASĀRASAṄGRAHA.

the products obtained by multiplying the (several component) quantities of gold by (their respective varņas) is to be subtracted. The remainder, when divided by the known component quantity of gold, (the varņa of which is to be found out), gives rise to the required varņa; and when divided by the difference between the resulting varņa and the known varņa (of an unknown component quantity of gold) gives rise to the (required weight of that) gold.

Another rule in relation to the unknown varņa :-

176. The sum of the products of the (various component quantities of) gold as multiplied by their respective varņa 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 varņa gives rise to the required varņa.

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 varņas in weight of gold of an unknown varņa is mixed. The resulting varņa of the mixed gold is 11. O you, friend, who know the secrets of calculation, tell me the numerical value of this unknown varņa,

179. Seven in weight (of a given specimen) of gold has exactly 14 as the measure of its varņa; then 4 in weight (of another specimen of gold) is added to it. The resulting varņa is 10. Give out the unknown varņa (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 varņas, from the product of the sum (of the known weights) of gold as multiplied by the now durable resulting varņa; the renmainder divided by the difference between the (known) varņa of the unknown quantity of gold and the resulting durable varņa (of the mixed gold) gives rise to the (weight of) gold.