Lilavati (Bhaskaracharya)

The Rule for Barter

original: "bhāṇḍapratibhāṇḍaka"

The mathematical procedure for the exchange of commodities is the same as the previous rules, but the denominators and numerators of the prices and quantities are swapped. 42.

Example:
If three mangoes are obtained for one drammaA standard silver coin. in the market, and twenty fine pomegranates are also obtained for one dramma, then tell me, friend, if ten mangoes are exchanged, how many pomegranates should be received? 43.

Statement original: "nyāsaḥ": 3 20 1 10
The Pomegranates obtained: 66 and 2/3.
Calculation: (10 × 20) / 3 = 66.66

Thus ends the Miscellaneous Chapter in the Lilavati of the illustrious Bhaskara.

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Calculations on Mixtures

original: "Miśravyavahāra"

The Rule:
Multiply the principal original: "pramāṇa" by its time, and multiply the interest original: "phala" by the time of the loan. Divide each of these by the sum of these two products. When these results are multiplied by the total mixture the sum of principal and interest, they yield the principal and interest respectively. 1.

Or, the Rule of Supposition:
original: "iṣṭakarmavidhi"
Assume a value for the principal. Subtract that assumed principal from the total mixture to find the interest. 2.

Example:
If the interest rate is five per hundred per month, and the total sum of the principal and its interest after one year is one thousand, tell me, what are the principal and the interest separately? 3.

Statement: 5 100 12 1
Principal wealth original: "mūladhana": 625.
Interest original: "kalāntara": 375.

By the Rule of Supposition:
As an example, let the assumed principal be 1.
5 100 12 1
The rules of five, seven, and nine quantities...