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123
CHAPTER VI--MIXED PROBLEMS.

ascetics and left 3(fruits) as remainder. Again 3 (heaps) were (similarly) divided among 11 persons, and the remainder was 5 fruits; then again 5 of those heaps were similarly divided among 7, and there were 4 more fruits (left out) of them. O you arithmetician who know tho meaning of the kuṭṭīkāra process of distribution, tell me after thinking out well the numerical measure of a heap (here).

128. In the interior of the forest, 3 heaps (equal in value) of pomegranates were divided (equally) among 7 travellers, leaving 1 (fruit) as remainder; 7 (of such helps) were divided (similarly) among 9, leaving a remainder of 3(fruits; again) 5 (of such heaps) were (similarly) divided among 8, leaving 2 fruits as remainder, O arithmetician, what is the numerical value of a heap here).

129. There were 5 (heaps of fruits equal in numerical value), which after being combined with 2 (fruits of the same kind) were (equally) divided among 9 travellers (and left no remainder); 6 (heaps) combined with 4 (fruits) were (similarly) divided among 8 of them; and 4 (heaps) combined with 1 (fruit) were (also similarity) divided among 7 of them. Give out the numerical measure (of a heap here).

The rule for arriving at the original quantity distributed (as desired), after obtaining the remainder due to (the removal of certain specified) known quantities:-

130[*]. (Obtain) the product of the (given) known quantity (to be removed), as multiplied by the fractional proportion of what is 1eft (after a specified fractional part of what remains on the removal of the given known quantity has been given away). The next quantity is (obtained by means of) this (product), to whicn

 

 

130.^  Here the known quantity to be removed is called the agra. What remains after the removal of the agra is the remainder. That fraction of this remainder which is given or taken away is the agrāṅsa, and what is left of the remainder after the agrāṁśa is given or taken away is the śēsāṁśa or the remaining fractional proportion of the remainder. For example, where x is the quantity to be found out, and a is the agra in relation to the first distribution with as the fractional proportion distributed, happens to be the agrāṁsa, and to be the śēșāṁśa.