# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३५५

एतत् पृष्ठम् परिष्कृतम् अस्ति
159
CHAPTER VI--MIXED PROBLEMS.

Examples in illustration thereof.

253${\displaystyle {\tfrac {1}{2}}}$-255${\displaystyle {\tfrac {1}{2}}}$. Three merchants begged money from the hands of each other. The first begged 4 from the second and 5 from the third man, and became possessed of twice the money (then on hand with both the others). The second (merchant) begged 4 from the first and 6 from the third, and (thus) got three times the money (held on hand at the time by both the others together. The third man begged 5 from the first and 6 from the second, and (thus) became 5 times (as rich as the other two). O mathematician, if you know the mathematical process known as citra-kuṭṭīkāra-miśra, tell me quickly what may be the moneys they respectively had on hand.

256${\displaystyle {\tfrac {1}{2}}}$-258${\displaystyle {\tfrac {1}{2}}}$. There were three very clever persons. They begged money of each other. The first of them begged 12 from the second and 13 from the third, and became thus 3 times as rich as these two were then. The second of them begged 10 from the first and 13 from the third, and thus became 5 times as rich (as the other two at the time). The third man begged 12 from the second and 10 from the first, and became (similarly) 7 times as rich. Their intentions were fulfilled. Tell me, O friend, after calculating, what might be the moneys on hand with them.

The rule for arriving at equal capital amounts, on the last man giving (from his own money) to the penultimate man an amount equal to his own, (and again on this man doing the same in relation to the man who comes behind him, and so on) :-

259${\displaystyle {\tfrac {1}{2}}}$.[*] One divided by the optionally chosen multiple quantity (in respect of the amount of money to be given by the one to the other) becomes the multiple in relation to the penultimate man's amount. This (multiplier) increased by one becomes the multiplier of the amounts (in the hands) of the others. The

259${\displaystyle {\tfrac {1}{2}}}$. ^ The rule will be clear from the following working of the problem given in st. 263${\displaystyle {\tfrac {1}{2}}}$.

${\displaystyle 1\div {\tfrac {1}{2}}}$ or 2 is the multiple with regard to the penaltimate man's amount; this 2 combined with 1, i.e., 3 becomes the multiple in relation to the amounts of the others.