पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३०६

108 GANITASARASANGRAHA. optionally chosen (maximum available amount of an instalmcut) by (whatever happens to he) 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 arithmetical 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 deht (discharged at an instalment) by the (ahove amount of the first) instalment. The interest thereon is that which accrucs 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 ntilised, (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 duc every of a month. He thus gave in discharge of the debt the sum of a scries in arithmetical progression consisting of terms, and gave also the interest accruing on those multiples of 7 What is the debt amount corresponding to the sum of the series, what is that interest (which he paid), and (what is) the time of discharge of that debt? 73 to 76. A certain man utilised for the discharge of a debt, bearing interest at 5 per cent (per mensem), 80 (as the available maximum amount) with 8 as the first instalment amount, increasing it by 8 in successive instalments due every of a month. IIc thus S 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 outstanding fractional part. The sum of the above-mentioned series, viz, 30, multiplied by 7, the amount of the first instalment, is added to the product of and 60, which latter is the maximum available amount of an instalment. Thus, we get 36 X 7+ x 60=0, which is the required capital amount in the due deht. The interest on 2 for of a month at the rate 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.