पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

54 DETERMINATIONS
(phala); then having divided them severally by the respec-
tive numbers of spectators, add the preceding results to
the succeeding ones. The results thus obtained being multi-
plied by the numbers of spectators who go away (at the end
of the respective parts of the day), give the amounts to be paid
(to the dancing party by the spectators who go away at the
end of the respective parts of the day).¹
By the word ‘fruit’ (phala) is meant here the amount to be paid to
the dancing party for the whole day.
The above rule is based on the assumption that the spectators
have to pay the dancing party in proportion to the time of seeing the
dance. That is, if the spectators who see the dance for the whole day
pay 96 rūpas in all, then the spectators who see the dance for ¼ of a day
will have to pay 96/4, i.e., 24 rūpas in all.
For the illustration of the rule see under the next example.
Ex. 86-87. One man saw a dance for one quarter of the
day, another for two quarters of the day, another for
three quarters of the day, and (yet) another till the end of the
day. The dancing party has to be paid by them a sum of
ninety six rūpas in all. If payment is to be made in propor-
tion to the time of seeing the dance, how much of that (sum)
should be paid by each of them separately?
Solution. Writing down the parts of the day during which the
various spectators saw the dance, we have
1/4 2/4 3/4 4/4
Diminishing the succeeding part by the preceding one, we get
1/4 1/4 1/4 1/4
Multiplying each of these by the fruit (i.e., by 96), we get
24 24 24 24
Dividing these numbers by the number of spectators who saw the
dance during the respective parts of the day, we get
6 8 12 24
¹ See GSS, vi. 230.