पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३३१

133 birds for 5 panas, purchase, O friend, for 56 punas 72 birds and bring them (to me) So saying a man gave over the purchase- monev (to his friend) Calculato quickly and find out how many birds (of each variety he bought) for how many panas 150 For 3 punas, 5 palas of ginger are obtained; for 4 panas, 11 pulus of long pepper; and for 8 panes, 1 pala of pepper is obtained By means of the purchase-money of 60 panas, quickly obtain 68 palas (of these drugs) The rule for arriving at the desired numerical value of certain specified objects purchased at dosired rates for desired sunis of money as their total price.- 151. The rate-values (of the various things purchased are each separately) multiplied by the total value (of the purchase-n oncy), and the various values of the rate-money are (alike separately) 151 The following working of the problem given in 152-153 will illustrate the rule - 5 3 0 2 0 500 700 900 300 300 500 700 900 6 0 0 0 600 200 200 200 0 G 4 6 6 18 30 7 5 3 01 01:00 0 6 9 3 7 9 6 0 2 CHAPTER VI-MIXED PROBLEMS. 0 10 G 6 20 15 28 4.5 35 Write down the rate-things and the rate-piices in two rows, one below the other. Multaply by the total puce and by the total number of thugs iespectively Then subtract. Remove the common factor 100. Multi- ply by the chosen numbers 3, 4, 5, 6. Add the numbers. in each holizontal row and remove the common factor 6. 6 Change the position of these figuies, and write down in Otwo rows each figure as many times as there are compo- nent elements in the coresponding sum changed in position. Multiply the two rows by the late-prices and the rate- things respectively. Then remove the common factor 6 Multiply by the already chosen numbers 3, 4, 5, 6 numbers in the two rows represent the proportions according to which the total price and the total number of things become distributed. The 30 42 36 42 54 12 5 . 36 0 5 7 7 9 2 1 4 This iule relates to a problem in determinate equations, and as such, there may be many sets of answers, these auswers obviously depending upon the quantities chosen optionally as multipliers. It can be easily seen that, only when certain sets of numbers are chosen as optional multipliers, integral answers are obtained, other cases, fractional answers are obtained, which are of course not wanted. For an 36 explanation of the rationale of the proces, see the note 12 givon at the end of the chapter.