157 CHAPTER VI-MIXED PROBLEMS. to the several cases) are diminished by the product of the particular specified fractional part as multiplied by the number of cases less by two. The difference is divided by the particular specified multiple quantity as increased by one. The result is the money on hand (in the particular case). Examples in illustration thereof. 242-243. Two travellers saw a purse contaming money (dropped) on the way. One of them said (to the other), "By secur- ing half of this money (in the purse), I shall become twice as rich (as you)." The other said, "By securing two-thirds (of the money in the purse), I shall, with the money I have on hand, have three times as much money as what you have on hand." What are the moneys on hand, and what the money in the purse? 241-244. Two travellers saw on the way a purse containing money; and the first of them took it up and (said, that) that money along with the money that he had on hand became twice the money of the other (traveller This) other (said that that money in the purse with the aid of what he had on hand would be) three times (the money in the hand of the first traveller). What is the money on hand (in the case of each of them), and what the money in the purse ? 245-247. Four men saw on the way a purse containing money. The first among then said, "If I secure this purse, I shall with the money already on hand with me become (possessed of money which will be) eight times (the money on hand with the remaining travellers)" Another (said, that the money in the- purse with what he had on hand) would be nine times the money on hand with the rest (among them). Another (said that similarly he) would be possessed of ten times the mouey, and another (that he) would be possessed of eleven times the money. Tell me quickly, O mathematician, what the money in the purse was and how much the money in the hand of each of them was. 248. Four men saw on the way a purse containing money. (Then), with what each of them had on hand, the , , , and parts (respectively) of this (money in the purse) became twice,
