पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३२८

132

GAŅITASĀRASAṄGRAHA.

An example illustration thereof.

 

144${\tfrac {1}{2}}$ and 145${\tfrac {1}{2}}$. There are here fragrant citrons, plantains, wood-apples and pomegranates mixed up (in three heaps). The number of fruits in the first (heap) is 21, in the second 22, and in the third 23. The combined price of each of these (leaps) is 73. What is the number of tho (various) fruits (in each of the heaps), and what the price (of the different varieties of fruits) ?

The rule for arriving at the numerical value of the prices of dearer and cheaper things (respectively) from the given mixed value (of their total price):-

146${\tfrac {1}{2}}$.^[*] Divide (the rate-quantities of the given things) by their rate-prices. Diminish (these resulting quantities separately) by the least among them. Then multiply by the least (of the above mentioned quotient-quantities) the given mixed price of all the things and subtract (this product) from the given (total number of the various) things. Then split up (this remainder optionally) into as many (bits as there are remainders of the above quotient quantities left after subtraction); and then divide (these bits by those remainders of the quotient-quantities. Thus the prices of the various cheaper things are arrived at). These, separated from the total price, give rise to the price of the dearest article of purchase.

Examples in illustration thereof.

147${\tfrac {1}{2}}$ to 149. "In accordance with the rates of 3 peacocks for 2 paņas 4 pigeons for 3 paņas,5 swans for 4 paņas, and 6 sārasa

 

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146${\tfrac {1}{2}}$.^  The rule will be clear from the following working of the problem given in 147${\tfrac {1}{2}}$-149:-

Divide the ratio-quantities 3, 4, 5, 6 by the respective rate-prices 2, 3, 4, 5; thus we have ${\tfrac {3}{2}},{\tfrac {4}{3}},{\tfrac {5}{4}},{\tfrac {6}{5}}$. Subtract the least of these ${\tfrac {6}{5}}$ from each of the other three. we get ${\tfrac {3}{10}},{\tfrac {2}{15}},{\tfrac {1}{20}}$. By multiplying the given mixed price, 56 by the above mentioned least quantity ${\tfrac {6}{5}}$, we have $56\times {\tfrac {6}{5}}$. Subtract this from the total number of birds, 72. Split up the remainder ${\tfrac {24}{5}}$ into any three parts, say ${\tfrac {7}{5}},{\tfrac {6}{5}},{\tfrac {9}{5}}$. Dividing these respectively by ${\tfrac {3}{10}},{\tfrac {2}{15}},{\tfrac {1}{20}}$ we get the prices of the first three kinds of birds,${\tfrac {14}{3}},12,36$. The price of the fourth variety of birds can be found out by subtracting all these three prices from the total 56.