Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 305

108
GAŅITASĀRASANGRAHA.
optionally chosen (maximum available amount of an instalment) by (whatever happens to be) the outstanding (fractional part of the number of terms in the series), to the amount of the (first) instalment as multiplied by the sum of that series in arithmetioal progression, which has (one for the first term, one for the common difference, and has for the number of terms the integral value of) the quotient obtained by dividing (the above optionally chosen maximum) amount of debt (discharged at an instalment) hy the (above amount of the first) instalment. The interest thereon is that which accrues for the period of an instalment. The time (of an instalment) divided by the amount of the (first) instalment and multiplied by the (optionally chosen maximum) amount of debt (discharged at an instalment) gives rise to the time (which is the time of the discharge of the whole debt).
Examples in illustration thereof. 72 and 73). A certain man utilised, (for the discharge of a debt) bearing interest at 5 per cent (per month), 60 (as the available maximum amount) with 7 as the first instalment amount, increasing it by 7 in successive instalments due every of a month. He thus gave in discharge of the debt the sum of a scries in arithmetical progression consisting of be terms, and gave also the interest accruing on those multiples of 7. What is the debt anwunt corresponding to the sum of the series, what is that interest (which he paid), and (what is) the time of discharge of that debt ?
731 to 76. A certain inan utilised for the discharge of a debt, bearing interest at 5 per cent (per mensem), E0 (as the available maximum amount) with 8 as the first instalment amount, increasing it by 8 in successive instalments due every I of a month. IIe thus
8 represents the number of terms of the series in arithmetical progression, which has 1 for the first term and 1 for the common difference, and is the agra or the outstauding fractional part. The sum of the above-mentioned series, viz., 36, multiplied by 7, the amount of the first instalment, is added to the product of : und 60, which latter is the maximum available amount of an instalment. Thus, we get 36 X 7+ X 60 = 204*, which is the required capital amount in the due debt. The interest on 2004 for of a month at the rote of 5 per cent per mensem will be the interest paid on the whole. The time of discharge will be ( 7) X 20 = 4 months.