पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३३३

एतत् पृष्ठम् परिष्कृतम् अस्ति
137
CHAPTER VI--MIXED PROBLEMS.

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 the fourth said that it was 7 (in saying so) each of them deducted his own invested amount (from the total value of the commodity for sale). 0 friend, tell me separately the value of the (share in the) commodity owned by each.

The rule for arriving at equal amounts of wealth, (as owned in precious gems,) after mutually exchanging any desired number of gems:--

163.[*] The number of gems to be given away is multiplied by the total number of men (taking part in the exchange). This product is (separately) subtracted from the number (of the gems) for sale (owned by each); the continued product of the remainders (so obtained) gives rise to the value of the gem (in each case), provided the remainder relating to it is given up (in obtaining such a product).

Examples in illustration thereof.

164. Tho first man had 6 azurE-blue gEms (of equal value), the second man had 7 (similar) emeralds, the other the third man--had 8(similar) diamonds. Each (of them), on giving to each (of the others) the value of a single gem (owned by himself), became equal (in wealth-value to the others . What is the value of a gem of each variety ?)

165 and 166. The first man has 16 azure-blue gems, the second has 10 emeralds, and the third mam has 8 diamonds. Each among them gives to each of the others 2 gems of the kind owned by himself; and then all three men come to be possessed of equal

163.^  Let m,n,p, be respectively the numbers of the three kinds of gems owned by three different persons, and a the number of gems mutually exchanged; and let x,y,z be the value in order of a single gen in the three varieties concrened.

{\displaystyle {\begin{aligned}{\text{ Then it may be easily found out as required that }}x&=(n-3a)(p-3a);\\y&=(m-3a)(p-3a);\\z&=(m-3a)(n-3a);\end{aligned}}}