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

MIXTURES. SIMPLE INTEREST 33
(mûla), one after another (pṛthak pṛthak). [This will give
the number of complete months elapsed (gata-mâsa) and a
residue of the capital (mûla-śeṣa), if any]. Now calculate
interest for a month on the residue (śeṣasya-mâsika-phalaṁ),
and subtract that from the amount of monthly instalment
(mâsikopanayât) : by the remainder divide the interest for
a month on the residue (mâsikaphala) as multiplied by the
number of complete months elapsed (mâsa) and increased by
the residue of the capital (mûlaśeṣa).¹ The quotient added
to the number of complete months elapsed (gatamâsa) gives
the time (in months) of recovery of the capital (together
with interest).²
Let C be the capital lent out, i the rate of interest per cent per
month, I the amount of monthly instalment of payment, and T + 1/t,
t > 1, the time in months in which the money is recovered with interest.
Now suppose that the P.W.s of the 1st, 2nd,....... Tth instalments
having been subtracted one after another from C, the residue left is R.
Then evidently, R is the P.W. of I/t for (T + 1/t) months, so that
100 × (I / t)
R = ------------------------ ,
100 + (T + 1/t) i
(Ri / 100) · T + R
whence 1/t = ------------------- ·
I - (Ri / 100)
Hence the required time T + 1/t
(Ri / 100) · T + R
= T + ---------------------- months.
I - (Ri / 100)
Ex. 55-56. A rich man lent to somebody a sum of 100
rûpas at 5 per cent (per month simple interest) and from him
¹ The reading mâsaśeṣayug occurring in the Sanskrit text should be
mûlaśeṣayug.
² Cf. GK, I, p. 72, lines 14-15 ; and p. 73, lines 1-6.