________________
CHAPTER VI-MIXED PROBLEMS.
135
was told to bring at these rates 100 birds for 100 panas for the amusement of the king's son, and was sont to do so. What (amount) does ho give for each (of the various kinds of birds that he buys)?
The rule for arriving at the incastro of two given commoditios whose prices are interchanged:
154. Let (tho numerical value of) the sum of the (total selling and buying) nonoy-prices of the two givon commodities) bo divided by the numerical measure of) the sum of the commodities put togother); then lot the differonce between thonbove-mentioned buying and selling prices) bo divided by the (numerical measuro of any such) difference as may bo obtained by subtracting any optionally chosen commodity-quantity from the given moasure of the sum of the given coinmodlities. If the oporation of sankramana is conducted in relation to these, (viz., the quotient obtained in the first operation above and any one of the many quotients that may bo oltained in the second operation), the rates at wbich those commodities are purchased is obtained. Then if tho samo operation of sankramana is relating to the sum of the commodities and to their difference is carried out, it of course gives rise to the numerical measure of) the commodities (in question). Tho alternation (of these above-mentional purchago-ratos) gives rise to the yale-rates. This is the solution of (this kind of) problems an propounded by the learned ; and the rulo (itself) has bocu doclared by the great Jina.
154. The algebraical representation of the method describwd in the rulo may he given thus in relation to the problem proposed in stunzi 155 and 160.
Let az + by == 101... ... ... ... ... ... 1
ay + lz=116 .. ...
dding I and II, we have (a + b) (x + y) = 220
1, 2 + y=11 ... ..... .... ) Again subtracting from 11, we get (a-6) (-) = 12 Now 2b in optionally chosen to be equal to 6. a+b - 20 or a-b=20 -or 14 ... ... ...
.. VI ..y-I=11 ... ... ... ... ... ... VII Carry out the operation of sankramana with reference to VII and V, aud Vi sod Ill; and thu values of z, y, a and bare all made out.
