Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 314

CHAPTBR VI-MIXED PROBLEMS.
117
Vallika-kuttikära.
Hereafter we shall explain the process of calculation known as Vallika-kuttikära*:--
The rule underlying the process of calculation known as Vallikä in relation to Kuttīkāra (which is a special kind of division or distribution):
1151. Divide the (given) group-liumber by the (given) divisor; discard the first quotient; then put down one below the other the (various) quotients obtained by the successive division (of the various resulting divisors by the various resulting remainders ; again), put down below this the optionally choson number,
* It is so called because the method of kuttikara explained in the rule is banod upon a creeper.like chain of figures.
115$. The rule will become olear from the following working of the problem in stanza No. 1174.
Here it is stated that 63 heaps of plantains together with 7 separate fruits are exactly divisible among 23 persons ; it is required to find out the number of fruits in a heap. Here the 63 is called the group-number, and the numerical value of the fruits contained in each heap is called the 'group-value'; and it is this latter which has to be found out.
Now, according to the rule, we divide first the rise, or group-number 63, by the cheda or the divisor 23; and then we continue the process of division as in finding out H.C.F. of two numbers :23) 632 46
Here, the first quotient 2 is discarded; the other 17)23 (1
quotients are written down in a line one below the
other as in the wargin; then we have to choose such a number as, when multiplied by the last
remainder 1, and then combined with 7, (the 12
number of separate fruits given in the problem, 5)61
will be divisible by the last divisor 1. We accordingly choose 1, which is written down
below the last figure in the chain; and below 1)5(4
this chosen number, again, is written down the quotient obtained in the above division with
the help of the chosen number. Here we stop the division with the fifth remainder as it is the least remainder in the odd position of order in the series of divisions carried out here,
17
6)17(2