पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३०४

106 GANITASĀRASANGRAHA. that interest ou one for the time of discharge to which one is added; the capital lent out is (thus arrived at) Examples in illustration thereof. 64 In accordance with the rate of 5 per cent (per mensem), 2 months is the time for each instalment; and paying the instalment of 8 (ou each occasion), a man here became free (from debt) in 60 months What is the capital (borrowed by him)? 65 A certain person gives once in 12 days an instalment of 23, the rate of interest being per cent (per mensem) What is the capital amount of the debt discharged in 10 months The rule for arriving separately at the varions capital-amounts which, when combined with or diminished by their respective interests, are equal to one another, from their mixed sum, (the interests being either added to the capital amounts in all the given cases or subtracted from them similarly in all the given cases) :- 66 One is to be either combined with or dimmished by the mterest (accruing) thereon for the (given) period of time (in cach case in accordance with the respectively given rate of interest; then again in each case, one is divided respectively by these (combined or diminished quantities arrived at as before) There- after the (given) mixed sun (of the various capital amounts lent out) is divided by the sum of these (resulting quotients), and in relation to the mixed sum (so treated) the process of multipli- cation is to be conducted (separately in each case by multiplying it) by (the corresponding) proportionate part (of the above- mentioned sum of the quotients). This gives rise to the capital 66. Symbolcally, 1+ Similarly, 1 1 T₁ x C₁ tx I₁ do And so on for cs, ca, &c. + m 1 + 1 1x tx I Ty C₂ do. + &c. 1 1+ 1 1 x t x I, Tix C₁ 1 x 1 T₂ x C₂ ==C. = C₂₂