पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२५८

62

GAŅIITASĀRASAŃGRAHA

Examples in compund fractions.

100 to 102. To offer in worship at the fact of Jina, lotuses, jasamines, kēlakīs and lilies were purchased in return for the payment of ${\tfrac {1}{2}}{\text{ of }}1$ , ${\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {1}{5}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}$, ${\tfrac {1}{3}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{5}}$, ${\tfrac {1}{7}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {1}{7}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}$, ${\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{3}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {1}{5}}{\text{ of }}{\tfrac {1}{3}}{\text{ of }}{\tfrac {1}{3}}{\text{ of }}{\tfrac {1}{2}}$, and ${\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{5}}$, of a paņa. Sum of these (paid quantities) and give out the result.

103 and 104. A certain person gave (to a vendor) ${\tfrac {1}{2}}{\text{ of }}1$, ${\tfrac {1}{2}}{\text{ of }}{\tfrac {1}{3}}{\text{of}}{\tfrac {1}{2}}$, ${\tfrac {1}{4}}{\text{ of }}{\tfrac {7}{9}}$, ${\tfrac {2}{3}}{\text{ of }}{\tfrac {2}{7}}$, and , ${\tfrac {2}{7}}{\text{ of }}{\tfrac {1}{9}}$, (of a paņa) out of the 2 paņas (in his possession), and brought fresh ghee for (lighting) the lamps in a Jina temple. O friend, give out what he remaining balance is.

105 and 106. If you have taken pains in connection with compound fractions, give out (the resulting sum) after adding these (following fractions):- ${\tfrac {2}{5}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {13}{6}}{\text{ of }}{\tfrac {1}{3}}$, ${\tfrac {1}{13}}{\text{ of }}{\tfrac {5}{18}}$, ${\tfrac {1}{9}}{\text{ of }}{\tfrac {1}{8}}$, ${\tfrac {4}{13}}{\text{ of }}{\tfrac {1}{9}}$ and ${\tfrac {1}{2}}{\text{ of }}{\tfrac {3}{4}}{\text{ of }}{\tfrac {1}{5}}$

The rule for finding out the one unknown (element common to each of a set of compound fractions whose sum is given):--

107. The given sum, when divided by whatever happens to be the sum arrived at in accordance with the rule (mentioned) before by putting down one in the place of the unknown (element in the compound fractions), gives rise to the (required) unknown (element) in (the summing up of) compound fractions.

An example in illustration thereof.

108. The sum of ${\tfrac {1}{8}}$, ${\tfrac {1}{4}}{\text{ of }}{\tfrac {1}{2}}$, ${\tfrac {1}{5}}{\text{ of }}{\tfrac {1}{2}}$, ${\tfrac {1}{5}}{\text{ of }}{\tfrac {3}{4}}{\text{ of }}{\tfrac {1}{6}}$, of a certain quantity is ${\tfrac {1}{2}}$. What is this unknown (quantity) ?

The rule for finding out more than one unknown (element, one such occurring in each of a set of compound fractions whose sum is given):--

109. Make the unknown (values of the various partially known compound fractions) to be (equivalent to) such optionally chosen

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109. This rule will be clear from the following working of the problem given in stanza No. 110:--

Splitting up ${\tfrac {1}{2}}$, the sum of the intended fractions, into 3 fractions according to rule No. 78, we get ${\tfrac {1}{6}},{\tfrac {1}{?}}{\text{ and }}{\tfrac {1}{4}}$. Making these the values of the three