# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९८

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102
GAŅIITASĀRASAŃGRAHA.

The rule for arriving separately at the rate-interest of the rate-capital from the quantity representing 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).

Examples in 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 ; ${\displaystyle 7{\tfrac {4}{5}}}$ 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, ${\displaystyle {\sqrt {{\tfrac {CT}{t}}\times m+\left({\tfrac {CT}{2t}}\right)^{2}}}-{\tfrac {CT}{2t}}=I}$ which is equal to c

47.^ Symbolically, ${\displaystyle {\tfrac {m_{1}t_{2}\backsim m_{2}t_{2}}{t_{1}\backsim t_{2}}}=c}$.

[*]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.