Lilavati (Bhaskaracharya)

...[the result is] 30. Here, the Statement original: "nyāsaḥ" of the two substances, which have been brought to a commonality of their Standard original: "pramāṇa", is: 32 | 8 over 5 | 70. The result obtained is 2 Khādis a large unit of measure for grain, 2? Droṇas a measure of volume, 1/16th of a Khādi, 7 Āḍhakas, and 1 Prastha and 2 [parts].
Calculation involving rule of three and specific measurements like Khādi.

The Inverse Rule of Three

The rule for the Inverse Rule of Three original: "vyasta trairāśika" is as follows: The Requirement and the others are placed as before, with the Result in the middle. However, it should be known by those skilled in mathematics that the calculation of the result is reversed in the Inverse Rule of Three. 21.
The rule for the inverse rule of three (Vyasta Trairāśika).

Mathematicians know that the Inverse Rule of Three is applied in cases involving the age and value of living beings, the weight and purity of gold, and in the division of quantities. 22.
Verse 21: Contexts where the inverse rule of three is applied, such as age/value of living beings, purity of gold, and mathematical divisions.

Example:
If a sixteen-year-old female slave original: "dāsī" costs one hundred [coins], what is the value of a twenty-year-old? In ancient markets, the value of a laborer was often inversely proportional to age after a certain point, as younger workers offered more years of future service.
Verse 22: Example: If a sixteen-year-old female slave costs one hundred coins...

Statement:
| 16 | 100 | 20 |
Verse 23: ...what is the price of a twenty-year-old? Mathematical setup: 16 | 100 | 20.

The result original: "phala" obtained is 80.

Statement for the second example:
| 2 | 8 | 6 |
The result obtained is 8/3?.
original: "tabdhaṃ," likely a scribal variant for "labdhaṃ" (obtained).

Example:
If gold of ten Purities original: "varṇa," a measurement of gold fineness; higher "varṇa" indicates higher purity is obtained at the rate of one Pana a copper coin for one Nishka a gold coin, then tell me, how much is obtained if the purity is fifteen original: "tithi," a word-symbol for 15 based on the days of the lunar fortnight? 24.
Verse 24: Example involving gold purity: If ten-purity gold yields a Pana for a Niska, what does fifteen-purity yield?

Statement:
| 10 | 1 | 15 |

The gold obtained is 2 over 3.

Example:
If a heap of grain yields a measure of one hundred when measured with a seven-Āḍhaka measure per month, then if the measure is five...