124 GANITASARASANGRAHA. the specified known quantity which is to be taken away (from the previous remainder) is added; and this resulting sum) is multiplied by that (same kind of) remaining fractional proportion (of the remainder as has been mentioned above). This is to be done as many times as there are distributions to be made Then these quantities so obtained should be deprived of their denomina- tors; and these denominator-less quantities (and the successive products of the above-mentioned remaining fractional proportions of the remainder) are (to be used as) the known quantity and the (other elements, viz., the cocfficient) mraltiple (of the unknown quantity and the divisor, required in relation to a problem on Vallikä-huttihära). Examples in illustration thereof. 131. On a certain man bringing mango fiuits (home, his) elder son took one fruit first and then half of what remained. (On the elder son going away after doing this), the younger (son) did similarly (with what was left there. He further took half The inle will be clear from the following working of the problem in 132- 133- Hele 1 is the first agra, and is the first agramsa, therefore 1-1 01 is the sesamsa. Now, obtain the product of agra and sesan sa or 1x3 01 3. White it down in 2 places. [ 1 {1} , add the second aga 1 (to one of the quantities) Then we have {}, multiply both by the next sēsīmsa 1-3 os ;, so that you get Repeat the quantities. 11 Take these figmes and add the thind agra as before, and you have ं [] multiply by the next sẽşamsa 1-3 or 4 and by the last ansa or, and you have {} III The denominators of the first hactions in these thice sets of fractions naked I, II, III, are dropped, and the numerators represent negative ayras in a problem on allhá-kuttikara, wherein the numerator and the denommator of each of the second fractions in those sets represent respectively the dividend coefficients and the divisor. Thus we have 2x - 2 is an integer, is an integer, and. 3 The value of a satisfying these three conditions gives the number of flowers. 4x10 9 is an integer. 8x38 81
