# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९०

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94
GAŅIITASĀRASAŃGRAHA.

Double Rule-of-three.

The rule for arriving at (the value of) the interest which (operation) is of the nature of double rule-of-three :--

4. The number representing the Icchē, i.e., the amount the interest whereon is desired to be found out, is multiplied by the time connected with itself and is then multiplied by (the number representing ) the (given ) rate of interest for the given capital ; (then the resulting product) is divided by the time and the capital quantity (connected with the rate of interest); this (quotient) is, in arithmetic, the interest of the desired amount.

Examples in illustration thereof.

5.Purānas, 50, 60, and 70 (in amount) were lent out on interest at the rate of 3, 5 and 6 per cent (per mensem respectively); what is the interest for 6 months ?

6.(A sum of) 30 kārșāpaṇas and 8 paṇas were lent out on interest at the rate of ${\displaystyle 7{\tfrac {1}{2}}}$ per cent (per month) ; what is the interest produced in exactly ${\displaystyle 7{\tfrac {1}{2}}}$ months ?

7.The interest on 60 for 2 months is seen to be 5 purāṇas with 3 paṇas; what would be the interest on 100 for 1 year?

8.The interest for 1 months and a half on leading out 150 is 15. What would be the interest obtained at this rate on 300 for 10 months ?

9.A merchant lent out 63 kārșāpaṇas at the rate of 8 for 108 (per month). What (is the interest) for ${\displaystyle 7{\tfrac {1}{5}}}$ months ?

The rule for finding out the capital lent out:--

10.The capital quantity (involved in the rate of interest) is multiplied by the time connected with itself and is then divided

4. Symbolically ${\displaystyle {\tfrac {c\times t\times I}{T\times C}}}$, where T, C and I are respectively the time, capital and interest of the pramāṇa or the rate, and t, c and i are respectively the time, capital and interest of the iccha. For an explanation of pramāṇa, iccha, &c,see note under Ch. V. 2.

5. Unless otherwise mentioned, the rate of interest is for 1 month.

10. Symbolically ${\displaystyle {\tfrac {C\times T\times i}{I\times t}}}$