Lilavati (Bhaskaracharya)

The Problem of the Cistern

Example Verse 8:
If three pipes original: "yais tribhir"; though the text mentions three, it lists four rates: 1, 1/2, 1/3, and 1/6. fill a well in one day, half a day, one-third of a day, and one-sixth of a day respectively, then oh friend, tell me quickly: in what fraction of a day will that well be filled if all the pipes are opened at the same time?

Statement of the Calculation:
nyāsaḥThe formal layout or "statement" of the mathematical data.
The rates are: 1, 1/2, 1/3, and 1/6.
To solve this, one should divide these units into the whole This refers to the rule of using reciprocals to find the combined rate of work: 1/1 + 1/(1/2) + 1/(1/3) + 1/(1/6) = 1 + 2 + 3 + 6..
Through the sum of these, we get 12.
Then divide 1 (the "whole") by this sum.
nyāsaḥThe layout of the result.
The result is 1/12.
original: "kalālavyāḥ" — The time taken is 1/12th of a day.

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The Rule for Purchase and Sale

karaṇa-sūtramA formulaic rule for computation.
Divide the individual amounts by their own price parts, then multiply by the specific portions desired. Having then multiplied these by the total mixed wealth, divide by the sum of those results. This yields the individual costs of the commodities in order.

Example Verse 9:
If three measures of rice are obtained for one dramma A standard silver coin., and eight measures of mung beans are obtained for thirteen kākiṇīs A smaller copper coin; usually 64 kākiṇīs equal 1 dramma., and a priest has requested a mixture consisting of two parts rice and one part mung beans, costing a total of two and a half drammas—tell me, what are the quantities?

Statement of the Data:

The table shows the working out of the "Rule of Proportional Purchase." The mathematician calculates the relative cost of 2 parts rice and 1 part mung beans based on their differing price points to find how much of the 2.5 drammas is spent on each.