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Shri Mahavir Jain Aradhana Kendra
www.kobatirth.org
Acharya Shri Kailassagarsuri Gyanmandir
CHAPTER VI-MIXED PROBLEMS.
127
numbers immediately above it, (till the topmost figure in the chain becomes included in the operation), is to be arrived at. Thereafter) this resulting sum and the divisor in the problem (give rise), in the shape of two remainders, (to the two values of) the unknown quantity (which is to be multiplied by the given dividend-coefficient in the problern), which (values are related either to the known given quantity that is to be added or to the known given quantity that is to be subtracted, according as the nuraber of figure-links in the above-mentioned chain of quotients is even or odd. (Where, however, the given groups, increased or decreased in more than one way, are to be divided or distributed in more than one proportion), the divisor related to the larger group-value, (arrived at as explained above in relation to either of two specified distributions), is to be divided over and over (as above by the divisor
Carry out the required process of continued division :07)59(0
59
59)67(1
After discarding the first quotient, the others are written
down in a chain thus:-- 8)5907
Below this are next written down 1 and 1, 56
the last equal divisor and remainder. Here
also, as in Vallika-kutsikára, it is worthy 3)8(2
of note that in the last division there can be 1
really no remainder, as 2 is fully divisible
by 1. But since the last remainder is 2)3(1 1+13 = 14 wanted for the chain, it is allowed to occur
by making the last quotient smaller than
possible. And to the last number 1 here, ada 1)2(1
13, which is the remainder obtained by dividing 80 by 67; the 14 so obtained in also written down at the bottom of the chain,
which now becomes complete. Now, by the continned process of multiplying and adding the figures in this
chain, ay already explained in the note under stanza No. 115), 1-392
we arrive at 592. This is then divided by 67; and the remain7-345
der 57 is one of the values of a, when 80 is taken as negative 2-47 1--16
owing to the number of figures in the chain being odd. When 1-15
80 is taken as positive, the value of x is 67 - 57 or 10. If the number of figures in the chain happen to be even, then the value of tiret arrived at is in relation to the positive agra ; if this value be sa tracted from the divisor, the value of x in relation to a negative agra is arrived at..
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