Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 334

CHAPTER VI --MIXED PROBLEMS.
137
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 27; (in saying so) each of them deducted his own invested amount (from the total value of the commodity for sale). O friend, tell me separately the valae 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 totul 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 (80 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. The first man had 6 azure-blue gems (of equal value), tho second man had 7 (similar) emeralds, and 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 gecond has 10 emeralds, and the third man 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 gem iu the three varieties concerned. Then it may be easily found out as required that = (n --- 3a) (p - 3a);
y = m-3a) (p -- Sa); = (m - 3a) (n - 3a);
18