GANITASĀRASANGRAHA. The rule for arriving separately at the rate-interest of the rate- capital from the quantity fepresenting the mixed sum obtained by adding together the capital amount lent out, which is itself equal to the rate-interest, and the interest on such capital lent out :- 44. The rate-capital as multiplied by the rate-time is divided by the other time (for which interest has accrued); the square root of this (resulting quotient) as multiplied by the (given) mixed sum once, and (then) 'as combined with the square of half of that (above-mentioned) quotient, when diminished by the half of this (same) quotient, becomes the (required) rate-interest (which is also equal to the capital lent out). 102 Examples an illustration thereof. 45. The rate-interest per 100 per 4 months is unknown. That (unknown quantity) is the capital lent out; this, when combined with its own interest, happens to be 12; and 25 months is the time for (which) this (interest has accrued. Find out the rate-interest equal to the capital lent out). 46. The rate-interest per 80 per 3 months is unknown; 74 is the mixed sum of that (unknown quantity taken as the) capital lent out and of the interest thereon for 1 year. What is the capital here and what the interest ? The rule for separating the capital, which is of the same value in all cases, and the interest (thereon for varying periods of time), from their mixed sum :-- 47. Know that, when the difference between (any two of) the (given) mixed sums as multiplied by each other's period* (of 44. Symbolically, N CT ·xm + t C 2¹ 2 2 t CT 2 t =C. I which is equal to c. 47. Symbolically, my to me ti ti to
- By "the period of interest "here is meant the time for which interest has
accrued in connection with any of the given mixed sums of capital and interest.
