Lilavati (Bhaskaracharya)

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Having obtained the fractions 4/9 and 5/9, the sum of these 9/9 Which equals 1. acts as the divisor. These fractions, 4/9 and 5/9, are then multiplied by the mixed capital The total amount spent on both goods combined.. When the resulting values 52/448 and 112/512 are divided by that sum, the individual prices for the rice and mung beans are found to be 8/9 and 1/9. In this same way, each portion multiplied by the mixed capital—26/64 and 15/64—and then divided by the sum, yields the specific quantities of rice and mung beans: 4/24 and 5/24.

In this calculation, the price of the rice is 10 kākiṇīsA copper coin equal to 1/4 of a pana or 1/64 of a dramma., 13 varāṭakasCowrie shells, the smallest unit of currency; usually 20 varāṭakas equal one kākiṇī., and 9 fractional parts. The price of the mung beans is 2 kākiṇīs, 6 varāṭakas, and 2 fractional parts.

The Problem of Camphor and Sandalwood

Problem Statement:
O delighter of the merchant class! If one palaA unit of weight, roughly 35-50 grams depending on the region. of camphor is obtained for two niṣkasA high-value gold coin or weight; in this system, 1 niṣka equals 16 drammas., and if one pala of sandalwood is obtained for one-eighth of a dramma original: "drammāṣṭabhāgena", and half a pala of aloe is obtained for ... The text is abbreviated here, referring to the rates in the next section. If someone desires a mixture of these in portions of one, sixteen, and eight respectively, and spends exactly one niṣka, tell me the amounts!

Statement of the Calculation:
nyāsaḥThe formal layout of the numerical data for the calculation.

Total mixed wealth: 1 niṣka. This is multiplied by sixteen, becoming 16 drammas.
The individual prices are multiplied by their own parts and divided by the quantity units, resulting in 3, 2, 2, and 1. The sum of these is 36. These, when multiplied by the mixed total, become 512, 32, and 128. When divided by the sum, the individual costs of the camphor and the other ingredients are produced...

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