Lilavati (Bhaskaracharya) (1800) - Page 16

The individual values are 238, 66, and 2. When these are multiplied by their respective portions and divided by the sum of the portions, the resulting quantities obtained are 4, 6, and 32. These figures conclude the previous problem regarding the weights of camphor, sandalwood, and aloe wood purchased for a fixed sum.

The Rule of Gem Exchange

Verse 11:
In the category of gem-trading, the rule of procedure is as follows:
Subtract the number of merchants from the quantity of gems held by each. The OCR text uses 'nagaiḥ' (mountains/seven), but the mathematical logic here uses the number of merchants, which is four. With these remainders, divide a chosen number; the results will be the prices of the gems. Alternatively, the prices may be found by taking the product of the remainders and dividing it by each individual remainder.

Verse 12 (Problem):
Here is an illustration: Eight rubies, ten sapphires, one hundred pearls, and five topazes are held by four gem merchants. Out of mutual affection, each merchant gives one of his own gems to each of the other three. As a result, they all become equal in wealth. O friend, tell me the individual prices of those gems!

Statement of the Problem:
Quantities: 8 | 10 | 100 | 5
These represent Māṇikya (Ruby), Indranīla (Sapphire), Muktāphala (Pearl), and Padmarāga (Topaz).

The gift to be given is determined as 4 This likely refers to the subtraction factor based on the four merchants.. The remainders of the gems after subtraction are, in order:
4 | 6 | 96 | 1
Calculated as 8-4=4; 10-4=6; 100-4=96; 5-4=1.

When an assumed number IṣṭaAn arbitrary number chosen to facilitate the calculation, often the Least Common Multiple. of 96 is divided by these remainders, the resulting prices for the gems are:
24 | 16 | 1 | 96

The resulting equal wealth for each merchant is 232 Using these prices, the total value of the gems held by each merchant after the exchange becomes 233 in standard editions; the OCR 232 suggests a minor variant or calculation difference.. First, the calculation for the five...