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 sent to do so. What (amount) does he give for each (of the various kinds of birds that he buys)? The rule for arriving at the measure of two given commodities whose prices are interchanged:- 154. Let (the numerical value of) the sum of the (total selling and buying) money-prices (of the two given commodities) be divided by (the numerical measure of) the sum (of the commodities put together); then let the difference (between the above-mentioned buying and selling prices) be divided by the (numerical measure of any such) difference as may be obtained by subtracting any optionally chosen commodity-quantity from the given measure of the sum of the given commodities. If the operation 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 be obtained in the second operation), the rates at which those commodities are purchased is obtained. Then if the same operation of sankramana as 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). The alter- nation (of these above-mentioned purchase-rates) gives rise to the sale-rates. This is the solution of (this kind of) problems as propounded by the learned; and the rule (itself) has been declared by the great Jina. I 154. The algebraical representation of the method described in the rule may be given thus in relation to the problem proposed in stanzas 155 and 156- Let ax + by 104 aybe 116. a+b=20 Adding I and II, we have (a + b) (x + y) = 220 II II[ ... .. 1V ..+y=11 V .... .... .... .... .. ..... .. ... ... ... Agam subtracting I from II, we get (a-b) (y-x) = 12 Now 26 is optionally chosen to be equal to 6. a+b-2b or a-b-20-6 or 14 .... ..
- y-x=13
Carry out the operation of sankramana with reference to VI and III, and the values of x, y, a and b are all made out.
VI VII VII and V, and
