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

34 DETERMINATONS
took a house bearing a rent of 40 (rûpas) per month. Say,
learned man, after how much time is the debter relieved of
his debt, and what does the rich man get by the gain of bare
accommodation.¹
Rule for converting several bonds into one :
51. The sum (samâsa) of the interests (phala) (accru-
ing on the given bonds) for the elapsed months (gatakâla), being
divided by the sum (aikya) of the interests (on the same
bonds) for one month, gives the time (in months for the equi-
valent single bond); and 100 times the sum of the interests for
one month (on the bonds), being divided by the sum of the
capitals (dhanayoga) (of the bonds), gives the rate of interest
per cent (per month) (for the single bond).²
Let the capitals, rates of interest and the times elapsed for the given
n bonds be as follows :
Capitals : P₁, P₂, P₃,..., Pₙ.
Rates of interest : r₁, r₂, r₃, ... , rₙ per cent per month
Times elapsed : t₁, t₂, t₃, .. , tₙ months.
Then the time elapsed (t) and the rate of interest (r) for the equivalent
single bond are given by
P₁ t₁ r₁ / 100 + P₂ t₂ r₂ / 100 + ... + Pₙ tₙ rₙ / 100
t = —————————————————————————————————————— months,
P₁ r₁ / 100 + P₂ r₂ / 100 + P₃ r₃ / 100 +....+ Pₙ rₙ / 100
( P₁ r₁ / 100 + P₂ r₂ / 100 + P₃ r₃ / 100 +....+ Pₙ rₙ / 100 ) × 100
and r = ——————————————————————————————————————————————————————
P₁ + P₂ + P₃ + .... + Pₙ
per cent per month.
Âryabhaṭa II puts the above results in the following simplified forms : ³
P₁ t₁ r₁ + P₂ t₂ r₂ + ... + Pₙ tₙ rₙ
t = ——————————————————————————— months,
P₁ r₁ + P₂ r₂ + ... + Pₙ rₙ
P₁ r₁ + P₂ r₂ + ... + Pₙ rₙ
and r = ——————————————————————— per cent per month.
P₁ + P₂ + ... + Pₙ

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¹ A similar example occurs in GK, I, p. 73, lines 8-10.
² Cf. GT, p. 86, lines 12-15. Also see GSS, vi. 77-77½.
³ See MSi, xv. 33. The reading as emended by S. Dvivedi is
incorrect.
Indological Truths