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

MIXTURES. THE CISTERN PROBLEM 55
Adding the preceding numbers to the succeeding ones, we get
6 14 26 50
Multiplying by the number of spectators who go away at the end of
the respective parts of the day, we get
6 14 26 50
Hence the spectator who saw the dance for ¼ of the day will have
to pay 6 rûpas ; the spectator who saw the dance for ²⁄₄ of the day will have
to pay 14 rûpas ; the spectator who saw the dance for ¾ of the day will
have to pay 26 rûpas ; and the spectator who saw the dance for the whole
day who will have to pay 50 rûpas.
Ex. 88. A palanquin is to be carried to a distance of
3 krośas by 10 men for 100 (rûpas as wages). Of those (men),
2, 3, and 5 stop away after going over 1, 2, and 3 krośas respec-
tively. (Calculate the wages of each of them separately).¹
Ex. 89-90. Five Brâhmaṇas, enchanters of stotras
(“hymns in praise of gods”), were invited by a certain person
to take part in the worship of the five faces of the five-faced
god Śiva on (a remuneration of) 300 rûpas. And they, on the
completion of worship of one, two, three, four, and five faces
respectively, went away (from the place of worship) one by
one.² Say what are their remunerations (separately).
(vii) THE CISTERN PROBLEM
Rule for finding the time in which a cistern would be filled
up by a number of drains flowing into it simultaneously, when
the times in which the cistern is filled up by each drain
separately are given :
69. Having divided unity severally by the (given)
fractions (of time), take the sum of the quotients and by that
sum divide unity (again) : this will give the time in which
the cistern is filled up (when all the drains are simultaneously
opened to flow into it).³
¹ Cf. GSS, vi. 231-232.
² What is meant is this : when the worship of the first face was com-
pleted by all the five Brâhmaṇas, one Brâhmaṇa left the place of worship ;
when the worship of the second face was completed by the remaining four
Brâhmaṇas, one more Brâhmaṇa left the place of worship ; when the
worship of the third face was completed by the remaining three Brâhmaṇas,
one more Brâhmaṇa left the place of worship ; and so on.
³ Cf. MSi, xv. 43; L (ASS), p. 91, vs. 96 ; GK, I, p. 94, line 2-3.