________________
CHAPTER VI-XIXID PROBLEMI.
187
eminent merchant (among them), deducting his own investment, said that that (value) was in fact 22. Then another said that it was 23; then another said 24; and tho fourth said that it was 27; (in saying so) each of them deduotoil bis own investod amount (from the total value of the commoility for sale, O friend, tell mo separately the value of the (share in the commodity owned by each!
The rule for arriving at qual amounts of wealth, (ng owned in precions gems, after mutnally exchanging any desired number of gome:
163. The number of gems to be given away is multipliod by tho totul mumber of men (taking part in the exchange). This product is (neparately) subtracted from the umber (of the gems) for sale (owned by each); the continued product of the romainders (no obtained) gives riso to the value of the gein (in each onko), provided the remainder relating to it is given up Tin obtaining such a procluct).
Eramples in illustration thereuf.
104. The first man hal 6 azuro.blue gom (of equal value), tho second man had 7 (similar) omoralds, and the other--tbe third man--had 8 (similar) (diamonds. Each (of thom), on giving to oach of the others) the value of a single gem (owned by himself), became oyunl (in wealth-value to the others. What is the value of a gem of ench variety ?)
165 and 166. The first man has 16 azure-blue yems, the Bocond has 10 emeralds, and the third man has 8 diamonds. Each among them gives to each of the others 2 goins of the kind owned by hiinself; and then all three inen come to be possessed of equal
163. Let m, n, p, be rispectively the numbers of the three kinds of soms owned by three different persons, and a the number of goms inutanlly erohangod and let z, y, , be the value in oriler of mingle gain in tho three varieties concerned. Then it may be ensily found out as required that < < (n - 8a) (p - lei;
im-8a) (p - Bay,
18
