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162
GANITASĀRASANGRAHA.
2677. There were four merchants. Each of them obtained from the others half of what he had on hand at the time of the respective transfers of money). Then they all became possessed of equal amounts of money. What is the measure of the money (they respectively had) on hand (to start with) ?
The rule for arriving at the gain derived (equally) from Auccess and failure (in a gambling operation) :--
2684-2694. The two sums of the numerators and denominators of the two fractional multiple) quantities (given in the problem) have to be written down one below the other in the regular order, and (then) in the inverse order. Tho (summed up) quantities (in the first of these sets of two sums) are to be multiplied according to the vajrāpavartana process by the denominator, and (those in the second sct) by the numerator, (of the fractional quantity) corresponding to the other (summed up quantity). The results (arrived at in relation to the first set) are written down in the form of denominators, and thoso arrived at in relation to the second set are written down) in the form of numerators: (and the difference between tho denominator and numerator in cach set is noted down). Then by means of these differenoes the products obtained by multiplying (the sum of) the numerator and the denominator (of each of the given multiple fractions in the problem) with the denominator of the other are respectively) divided. These resulting quantities, multiplied by the value of the desired gain, give in the inverso order the measure of the moneys on hand (with the gamblers to stake).
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An example in illustration thereof. 270-2721. A great man possessing powers of magical charm and medicine saw a cock-fight going on, and spoko separately in
(a + b) a
2681-2695. Algebraioally,
(c + d) b (c + d) 6 - (a + b) * * * *
T. * p, and y = and y are the moneys on hand with the gamblers
G + b) d - (+ d)
* P, where
fractional parts
taken from them, and y the gain. This follows from
