the mixed gold gives rise to the (resulting) varņa. (The original varņa of any component part thereof), when divided by the latter resulting varņa (of the mixed up whole), and multiplied by the (given) quantity of gold (in that component part), gives rise to (that) corresponding quantity of (the mixed) gold (which is equal in value to that same component part thereof).
An example in illustration thereof.
170 to 171. There are 1 part (of gold) of 1 varņa, 1 part of 2 varņas, 1 part of 3 varņas, 2 parts of 4 varņas, 4 parts of 6 varņas,7 parts of 14 varņas, and 8 parts of 15 varņas. Throwing these into the fire; make them all into one (mass), and then (say) what the varņa of the mixed gold is. This mixed gold is distributed among the owners of the foregoing parts. What does each of them get ?
The rule for arriving at the required weight of gold (of any desired varņa equivalent in value to given quantities of gold) of given varņas:-
172. The given quantities of gold are all (separately) multiplied by their respective varņas, and the products are added. The resulting sum is divided by the total weight of the mixed gold; the quotient is to be understood as the resulting average varņa. This (above-mentioned sum of the products) is separately divided by the desired varņas (to arrive at the required equivalent weight of this gold).
Examples in illustration thereof.
173. Twenty paņas (in weight of gold) of 16 varņas have been exchanged for (gold of) 10 varņas in quality; you give out how many purāņas (in weight) they become now.
174. One hundred and eight (in weight of) gold of varņas is exchanged for (gold of) 14 varņas. What is the (equivalent quantity of this new) gold ?
The rule for finding out the unknown varņa :-
175. From the product obtained by multiplying the total quantity of gold by the resulting varņa of the mixture, the sum of
