# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९४

एतत् पृष्ठम् परिष्कृतम् अस्ति
98
GAŅIITASĀRASAŃGRAHA.

The time (for which the interest has accrued) combined with the interest therefor is 20. What is the time here ?

27. The capital put to interest at the rate of ${\displaystyle 1{\tfrac {1}{2}}}$ per ${\displaystyle 70{\tfrac {1}{2}}}$(per mensem) is 705. The mixed sum of its time and interest is 80. (What is the value of the time and of the interest ?)

28. The capital put to interest at the rate of ${\displaystyle 3{\tfrac {1}{2}}}$ per 80 for ${\displaystyle 2{\tfrac {1}{2}}}$ months is 400, and the mixed sum of time and interest is 36. (What is the time and what the interest ?)

The rule for arriving at the separation of the capital and the time of interest from their mixed sum:--

[29]. From the square of the given mixed sum (of the capital and the time), the rate-capital divided by its rate-interest and multiplied by the rate-time and by four times the given interest is to be subtracted. The square root of this (resulting remainder) is then used in relation to the given mixed sum so as to carry out the process of saṅkramaṇa.

Examples in illustration thereof.

30. This, viz., 4 Purāṇas is the interest on 70 (per month). The interest (obtained on the whole) is 25. The mixed sum (of the capital used and the time of interest) is ${\displaystyle 45{\tfrac {1}{4}}}$. What is the capital lent out ?

31. By landing out what capital for what time at the rate of 3 per 60 (per mensem) would a man obtain 18 as interest, 66 being the mixed sum of that time and that capital ?

32. It has been ascertained that the interest for ${\displaystyle 1{\tfrac {1}{2}}}$ months on 60 is only ${\displaystyle 2{\tfrac {1}{2}}}$. The interest here (in the given instance) is 24, and

29.^ Symbolically, ${\displaystyle {\tfrac {{\sqrt {m^{2}-{\tfrac {C\times t}{I}}\times 4i}}\pm m}{2}}=c}$ or tas the case may be, where m=c+t.

The value of the quantity under the rōt, as given in the rule, in (c-t)2; and the square rōt of this and the miśra hae the operation of saṅkramaṇa performed in relation to them.

For explanation of the saṅkramaṇa see Ch. VI.2