# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३१२

एतत् पृष्ठम् परिष्कृतम् अस्ति
116
GAŅITASĀRASAŃGRAHA.

(in the end. What is the buying price, what is the selling price, and what the equal sale-amount?)

The rule for arriving at (the solution of a problem wherein) optionally chosen quantities (are) bestowed in optionally chosen multiples for an optionally chosen number of times :-

111. Let the penultimate quantity be added to the ultimate quantity as divided by its own corresponding multiple number, and let the result of this operation be divided by that (multiple number which is associated with this) penultimate quantity (given in the problem). What results (from carrying out this operation throughout in relation to all the various quantities bestowed) happens to be the (required) original quantity.

Examples in illustration thereof.

112${\displaystyle {\tfrac {1}{2}}}$ and 118${\displaystyle {\tfrac {1}{2}}}$. A certain lay follower of Jainism went to a Jina temple with four gate-ways, and having taken (with him) fragrant flowers offered them (thus) in worship with devotion:- At the four gate-ways, they became doubled, then trebled, then quadrupled and then quintupled (respectively in order.) The number of flowers offered by him was five at every (gate-way). How many were the lotuses (originally taken by him)?

114${\displaystyle {\tfrac {1}{2}}}$. Flowers were obtained and offered in worship by devotees with devotion, the flowers (so offered) being (successively) 3, 5. 7 and 8; (their corresponding) multiple quantities being ${\displaystyle {\tfrac {1}{2}},{\tfrac {1}{3}},{\tfrac {1}{4}}}$ and ${\displaystyle {\tfrac {5}{2}}}$ (in order. Find out tho original number of flowers).

Thus ends proportionate division in this chapter on mixed problems.