पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३०७

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CHAPTER VI--MIXED PROBLEMS.

as prakṣēpaka, give out the proportionate distribution of the flowers.

86${\tfrac {1}{2}}$.(A sum of) 480 was divided among five men in the proportion of 2, 3, 4, 5 and 6; O friend, give out (the share of each).

The rule for arriving at (certain) results in required proportions:-

87${\tfrac {1}{2}}$.^[*] The (number representing the) rate-price is divided by (the number representing) the thing purchasable therewith; (it) is (then) multiplied by the (given) proportional number; by means of this, (we get at) the sum of the proportionate parts, (through) the process of addition. Then the given amount multiplied by the (respective) proportionate parts and then divided by (this sum of) the proportionate parts gives rise to the value (of the various things in the required proportion).

Another rule for this (same) purpose:-

88${\tfrac {1}{2}}$.^[*] Multiply the numbers representing the rate-prices (respectively) by the numbers representing the (given) proportions of the (various) things (to be purchased); then divide (the result) by the (respective) numbers measuring the things purchasable for the rate-price; the resulting quantities happen to be the (requisite) multipliers in the operation of prakṣēpaka. The intelligent man may (then) give out the required answer by adopting the rule-of-three.

Again a rule for this (same) purpose:-

89${\tfrac {1}{2}}$.^[*] The (numbers representing the various) rate-prices are respectively divided by their own related (numbers representing the) things purchasable therefor and are (then) multiplied by their related proportional numbers. With the help of these, the remainder (of the operation should be carried out) as before.

 

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87${\tfrac {1}{2}}$ to 89${\tfrac {1}{2}}$.^  In working the example in stanza 90${\tfrac {1}{2}}$ and 91${\tfrac {1}{2}}$ according to these rules 2, 3 and 5 are divided by 3,5 and 7 respectively and are similarly multiplied by 6,3 and 1. Thus we have ${\tfrac {2}{3}}\times 6,{\tfrac {3}{5}}\times 3,{\tfrac {5}{7}}\times 1=4,{\tfrac {9}{5}},{\tfrac {5}{7}}$. These are the proportional parts. The rules in stanzas 88${\tfrac {1}{3}}$ and 89${\tfrac {1}{2}}$ require thereafter the operation of prakṣēpaka to be applied in relation to these proportional parts; but the rule in stanza 87${\tfrac {1}{3}}$ expressly describes this operation.