पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३५८

GANITASĀRASANGRAHA. amount of the last person (so arrived at) is to have one added to it. This is the process to be adopted. 160 Examples in illustration thereof. 260-261. Three sons of a merchant, the eldest, the middle, and the youngest, were going out along a road. The eldest son gave out of his capital amount to the middle son exactly as much as the capital amount of (that same) middle son. This middle son gave (out of his amount) to the last sor just as much as he had. (In the end), they all became possessed of equal amounts of money. O mathematician, think out and say what amounts they (respect- ively) had (with them) on hand (to start with). 262. There were five sons of a merchant. From the eldest (of them) the one next to him obtained as much money as he himself had on hand. All others also did accordingly (each one giving to the brother next to him as much as he had on hand. In the end) they all became possessed of equal amounts of money. What were the amounts of money they (respectively) had on hand (to start with)? 263. Five merchants became possessed of equal amounts of money after each of them gave out of his own property to the one who went before him half of what he possessed. Think out and 17 Now Multiplying the penultimate 1 by 2 and the other by 3, we get Adding 1 to the last Write down Multiply the penultimate 4 by 2, and the others by 3, and add 1 to the last .. Again Repeating the same operations as above we get ..... ... .. .. 1, 1. 2, 3. 2, 4 2, 4, 4. 6, 8, 13. 6, 8, 13, 13 18, 24, 26, 40. 54, 72, 78, 80, 121. The figures in the last row represent the amounts in the hands of the 5 merchants. Algebraically- a-bb-c =tc-da-f =f; where, a, b, c, d, f are the amounts on hand with the 5 merchants.